Common Core Math

Dividing Decimals is much similar to dividing Whole Numbers, except the way we handle the decimal point. Refer to the Dividing Decimal by a Whole Number Step by Step, Solved Examples, etc. Get a good hold of the concept and know How to Divide a Decimal by a Whole Number. Learn the entire procedure used to Divide Decimals by a Whole Number and solve related problems with ease.

Also, Read: Multiplying Decimal by a Decimal Number 

Dividing Decimals – Definition

The process of Dividing Decimals is much similar to the normal division. All you need to keep in mind is to place the decimal point correctly in the quotient. To divide a decimal by a whole number, the division is performed in the same way as in whole numbers ignoring the decimal point. Place the decimal point in the quotient in the same position as in the dividend.

How to Divide a Decimal by a Whole Number?

Follow the simple steps provided below to get acquainted with the Division of a Decimal with a Whole Number. They are along the lines

• Write the division in standard form and divide the whole number part of the decimal number with the divisor.
• Here dividend is the decimal number and the divisor is the whole number.
• Place the decimal point in the quotient above the decimal point of the dividend. Get the tenths digit down.
• Divide the dividend with the divisor.
• Try adding Zeros in the dividend till you get a Zero Remainder.

Solved Examples on Division of a Decimal by Whole Number

1. Solve 112.340 ÷ 5?

Solution:

Decimal Number 112.340 is the dividend and 5 is the whole number. Place the decimal point in the quotient above the decimal point of the dividend 112.340.

Now, we are going to bring down the 3. But, because it follows the decimal point, we have to place a decimal point in the quotient. Later we can bring down the next number.

Therefore, 112.340 ÷ 5 = 22.468

2. Solve 215.8 ÷ 3?

Solution:

Decimal Number 215.8 is the dividend and 3 is the whole number. Place the decimal point in the quotient above the decimal point of the dividend 215.8

Now, we are going to bring down the 8. But, because it follows the decimal point, we have to place a decimal point in the quotient. Later we can bring down the next number.

Therefore, 215.8 ÷ 3 = 71.93

3. Find 142.82 ÷ 4?

Solution:

Decimal Number 142.82 is the dividend and 4 is the whole number. Place the decimal point in the quotient above the decimal point of the dividend 142.82

Now, we are going to bring down the 8. But, because it follows the decimal point, we have to place a decimal point in the quotient. Later we can bring down the next number.

Therefore, 142.82÷ 4 = 35.705

In Multiplication of Decimals, you will learn how to multiply a decimal by decimal. While Multiplying Decimals firstly ignore the decimal points and place the decimal point in the product in a way that decimal places in the product are equal to the sum of decimal places in the given numbers. Refer to the complete article to be well versed with details like Procedure for Multiplying Decimals, Solved Examples on Decimal Multiplication explained step by step.

Also, Read: Multiplying Decimal by a Whole Number

How to Multiply a Decimal by Decimal?

Follow the below-listed guidelines on how or multiply a decimal by decimal. They are along the lines

• Multiply both the numbers as if they are whole numbers and don’t consider the decimal points.
• Place the decimal point after leaving digits equal to the total number of decimal places in both the numbers.
• Remember to count the decimal places from the unit’s place of the product.

Solved Examples on Multiplying Decimal by a Decimal

1. Find the product of 1.3 × 1.3

Solution:

First while performing the multiplication of decimals ignore the decimal points and perform the multiplication as if they are whole numbers

13

x 13

——–––

39

130

(+)

——–––

169

——–––

Count the total number of decimal places i.e. both in the multiplicant and multiplier together. Now, place the decimal point with as many decimal places are in the given numbers.

Since 2 decimal places are there place the decimal point counting from the unit’s place of the product.

Thus the product becomes 1.69

Therefore, the Product of 1.3 by 1.3 gives 1.69

2. Find the product of 3.5 × 0.06?

Solution:

First while performing the multiplication of decimals ignore the decimal points and perform the multiplication as if they are whole numbers

35

x 6

——–––

210

——–––

Count the total number of decimal points both in multiplicand and multiplier together. Place a decimal point as many decimal places are there in the given numbers.

Since there are 3 decimal places all together in given numbers place a decimal point counting from the unit’s place of the product.

Thus, the product becomes 0.210

Therefore, the product of 3.5 by 0.006 gives 0.210

3. Multiply 118.12 by 3.5?

Solution:

Before performing the decimal multiplication multiply as if they are whole numbers and ignore the decimal points.

11812

x     35

——–––––––

59060

35436

(+)

——–––––––

413420

——–––––––

Count the total number of decimal points both in multiplicand and multiplier together. Place a decimal point as many decimal places are there in the given numbers.

Since there are 3 decimal places all together in given numbers place a decimal point counting from the unit’s place of the product.

Thus, the product becomes 413.420

Therefore, the product of118.12 by 3.5 gives 413.420

Do you wish to learn Multiplication of Decimal with a Whole Number? Then this is the right place where you will get complete knowledge on Step by Step Procedure for Multiplication of Decimal with a Whole Number. Check out the Definition, Solved Examples listed here to get a grip on the concept. Learn the approach used here so that it becomes easy for you during your math calculations.

Also, See:

• Adding Decimals
• Subtracting Decimals

How to Multiply a Decimal by a Whole Number?

To Multiply a Decimal with a Whole Number follow the simple procedure listed below. They are along the lines

• Multiply the decimal as you would do with the whole number.
• Count the number of decimal places in the factors.
• Now, mark the decimal point in the result obtained from right to left as per the number of decimal places in the given decimal number.

Worked Out Problems on Multiplication of Decimals with a Whole Number

1. Find the Product

6.36 × 7

Solution:

Firstly, ignore the decimal places and multiply as if it is they are whole numbers.

Count the number of decimal places in the given decimal number and place the decimal point in the result obtained after multiplication. Rewrite the product with 2 decimal places as the decimal 6.36 has 2 decimal places.

Thus, the product of 6.36 × 7 gives 44.52

2. The length and breadth of a rectangle are 16.82 m and 6 m. Find the area of the rectangle?

Solution:

Length of a Rectangle = 16.82 m

Breadth of a Rectangle = 6m

Area of Rectangle = l*b

= 16.82*6

Ignore the decimal places and multiply as if it is they are whole numbers.

=

Count the number of decimal places in the given decimal number and place the decimal point in the result obtained after multiplication. Rewrite the product with 2 decimal places as the decimal 16.82 has 2 decimal places.

Thus, the product of 16.82*6 results in 100.92

3. Find the Product 8.54×3?

Solution:

Firstly, ignore the decimal places and multiply as if it is they are whole numbers.

Count the number of decimal places in the given decimal number and place the decimal point in the result obtained after multiplication. Rewrite the product with 2 decimal places as the decimal 8.54 has 2 decimal places.

Place the decimal point in the product with 2 decimal places i.e. 25.62

4.  The length and breadth of a rectangle are 11.82 m and 3 m. Find the area of the rectangle?

Solution:

Length of the Rectangle = 11.82m

Breadth of Rectangle = 3m

Area of Rectangle = l*b

= 11.82*3

Count the number of decimal places in the given decimal number and place the decimal point in the result obtained after multiplication. Rewrite the product with 2 decimal places as the decimal 11.82 has 2 decimal places.

Place the decimal point in the product with 2 decimal places i.e. 35.46

A multiple is the product of one number with another number. Also, we can define a multiple as the result that is obtained by multiplying a number by an integer. But it is not a function. The multiples of the whole numbers are found by doing the product of the counting numbers and that of whole numbers. For example, multiples of 5 can be obtained when we multiply 5 by 1, 5 by 2, 5 by 3, and so on.

Example 1: Find the multiples of whole number 4?
Firstly, do the multiplication of 4 with other numbers to get multiples of 4.
Multiplication: 4 x 1, 4 x 2, 4 x 3, 4 x 4, 4 x 5, 4 x 6, 4 x 7, 4 x 8
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32
Solution: The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32,……

Example 2: Find the multiples of whole number 6?
Firstly, do the multiplication of 6 with other numbers to get multiples of 6.
Multiplication: 6 x 1, 6 x 2, 6 x 3, 6 x 4, 6 x 5, 6 x 6, 6 x 7, 6 x 8
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48.
Solution: The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48,……

Also, Check: Common Multiples

Properties of Multiples

Here we have given some important Properties of Multiples. Check out the properties and get a grip on them to make your learning easy.
(i) Every number is a multiple of itself.
For example, the first multiple of 5 is 5 because 5 × 1 = 5.
(ii) The multiples of a number are infinite.
We know that numbers are infinite. Therefore, the multiples of a number also infinite. If you take the example of multiples of 2, we begin with 2, 4, 6, 8, 10, 12, 14,…. and so on.
(iii) The multiple of a number is greater than or equal to the number itself.
For example, if we take the multiples of 3: 3, 6, 9, 12, 15, .… and so on. We can see that: The 1st multiple of 3 is equal to 3: 3 × 1 = 3. The 2nd multiple, the 3rd multiple, and the following multiples of 3 are all greater than 3 (6 > 3, 9 > 3, ….)
(iv) 0 is a multiple of every number.

Common Multiples

Multiples that are common to any given two numbers are known as common multiples of those numbers. Check out the example for better understanding.
Consider two numbers– 2 and 3. Multiples of 2 and 3 are –
Multiples of 2 = 2, 4, 6, 8, 10, 12, ….
Multiples of 3 = 3, 6, 9, 12, 15, 18,……….
We observe that 6 and 12 are the first two common multiples of 2 and 3. But what can be the real-life use of common multiples?
Suppose Arun and Anil are cycling on a circular track. They start from the same point but Arun takes 30 seconds to cover a lap while Anil takes 45 seconds to cover the lap. So when will be the first time they meet again at the starting point?
This can be deduced from the list of common multiples. Arun and Anil will meet again after 90 minutes.

First Ten Multiples of the Numbers

Find out the first ten multiples of the numbers from the below figure.

Multiples of Different Numbers

When two numbers are multiplied the result is called the product of the multiple of given numbers. If the number 6 is multiplied with other numbers, then you get different multiples. Also, if the number 7 is multiplied with other numbers, then you get different multiples.

Solved Examples on Multiples

1. Find the first three multiples of 7.

Solution:
The given number is 7.
To find the first three multiples of 7, you need to multiply 7 with 1, 2, 3.
7 × 1 = 7
7 × 2 = 14
7 × 3 = 21

So, 7, 14, 21 are the first 3 multiples of 7.

2. Four friends Alex, Ram, Vijay, and Venu decided to pluck flowers from the garden in the order of the first four multiples of 5. Can you list the number of flowers that each of them plucked as a series of the first four multiples of 5?

Solution:
Given that four friends Alex, Ram, Vijay, and Venu decided to pluck flowers from the garden in the order of the first four multiples of 5.
To find the first four multiples of 5, you need to multiply 5 with 1, 2, 3, and 4.
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
The first four multiples of 5 are (5 × 1) = 5, (5 × 2) =10, (5 × 3) = 15, and (5 × 4) = 20.

Hence, Alex plucked 5 flowers, Ram plucked 10 flowers, Vijay plucked 15 flowers and Venu plucked 20 flowers.

3. Sam loves watering plants. Her mom asked her to water the pots which were marked in the order of the multiples of 8. However, she missed a few pots. Can you help her identify the pots that she missed in the following list: 8, 16, __, 32, __, 48, 56, 64, __?

Solution:
Given that Sam’s mom asked her to water the pots which were marked in the order of the multiples of 8.
Let us start counting the multiplication table of 8: 8 × 1 = 8, 8 × 2 = 16, 8 × 3 = 24, 8 × 4 = 32, 8 × 5 = 40, 8 × 6 = 48, 8 × 7 = 56, 8 × 8 = 64, 8 × 9 = 72.

The missed pots are 24, 40, and 72.

Divisible by 3 is possible when the sum of the given digits is divisible by 3. Check out how a number is divisible by 3 in this article. We have given different examples along with a clear explanation here. Also, we have included some of the tricks to find out the process to find a number that is divisible by 3. Improve your math solving skills by learning the different tricks in math operations. Verify all the articles on our website and make your real-life happy with the best math learning process.

Also, See:

• Divisibility Rules
• Divisible by 6

How to Test if a Number is Divisible by 3 or Not?

Follow the below procedure to find out the numbers either are divisible by 3 or not.

1. Note down the given number.
2. Add all the digits of a given number.
3. Check out the output of addition is divisible by 3 or not.
4. If the output is divisible is 3, the given number is divided by 3. If not the given number is not divisible by 3.

Divisible by 3 Examples

(i) 60

The given number is 60.
Add the digits of the given number.
Add 6 and 0.
6 + 0 = 6.
The number 6 is divisible by 3.

Hence, 60 is divisible by 3.

(ii) 74

The given number is 74.
Add the digits of the given number.
Add 7 and 4.
7 + 4 = 11.
The number 11 is not divisible by 3.

Hence, 74 is not divisible by 3.

(iii) 139

The given number is 139.
Add the digits of the given number.
Add 1, 3, and 9.
1 + 3 + 9 = 13.
The number 13 is not divisible by 3.

Hence, 139 is not divisible by 3.

(iv) 234

The given number is 234.
Add the digits of the given number.
Add 2, 3, and 4.
2 + 3 + 4 = 9.
The number 9 is divisible by 3.

Hence, 234 is divisible by 3.

(v) 196

The given number is 196.
Add the digits of the given number.
Add 1, 9, and 6.
1 + 9 + 6 = 16.
The number 16 is not divisible by 3.

Hence, 196 is not divisible by 3.

(vi) 156

The given number is 156.
Add the digits of the given number.
Add 1, 5, and 6.
1 + 5 + 6 = 12.
The number 12 is divisible by 3.

Hence, 156 is divisible by 3.

(vii) 174

The given number is 174.
Add the digits of the given number.
Add 1, 7, and 4.
1 + 7 + 4 = 12.
The number 12 is divisible by 3.

Hence, 174 is divisible by 3.

(viii) 278

The given number is 278.
Add the digits of the given number.
Add 2, 7, and 8.
2 + 7 + 8 = 17.
The number 17 is not divisible by 3.

Hence, 278 is not divisible by 3.

(ix) 279

The given number is 279.
Add the digits of the given number.
Add 2, 7, and 9.
2 + 7 + 9 = 18.
The number 18 is divisible by 3.

Hence, 279 is divisible by 3.

(x) 181

The given number is 181.
Add the digits of the given number.
Add 1, 8, and 1.
1 + 8 + 1 = 10.
The number 10 is not divisible by 3.

Hence, 181 is not divisible by 3.

Solved Problems on Rules of Divisibility by 3

Fill the correct lowest possible digit in the blank space to make the number divisible by 3.

(i) 15335_

The given number is 15335_.
Add the digits of the given number.
Add 1, 5, 3, 3, and 5.
1 + 5 + 3 + 3 + 5 = 17.
By adding 1 to the number 17, it becomes 18. The number 18 is divisible by 3.
The lowest possible digit in the blank space to make the number divisible by 3 is 1.

Hence, 153351 is the required digit of a given number.

(ii) 20_987

The given number is 20_987.
Add the digits of the given number.
Add 2, 0, 9, 8, and 7.
2 + 0 + 9 + 8 + 7 = 26.
By adding 1 to the number 26, it becomes 27. The number 27 is divisible by 3.
The lowest possible digit in the blank space to make the number divisible by 3 is 1.

Hence, 201987 is the required digit of a given number.

(iii) 8420_1

The given number is 8420_1.
Add the digits of the given number.
Add 8, 4, 2, 0, and 1.
8 + 4 + 2 + 0 + 1 = 15.
By adding 0 to the number 15, it becomes 15. The number 15 is divisible by 3.
The lowest possible digit in the blank space to make the number divisible by 3 is 0.

Hence, 842001 is the required digit of a given number.

(iv) 749_262

The given number is 749_262.
Add the digits of the given number.
Add 7, 4, 9, 2, 6, and 2.
7 + 4 + 9 + 2 + 6 + 2 = 30.
By adding 0 to the number 30, it becomes 30. The number 30is divisible by 3.
The lowest possible digit in the blank space to make the number divisible by 3 is 0.

Hence, 7490262 is the required digit of a given number.

(v) 998_32

The given number is 998_32.
Add the digits of the given number.
Add 9, 9, 8, 3, and 2.
9 + 9 + 8 + 3 + 2 = 31.
By adding 2 to the number 31, it becomes 33. The number 33 is divisible by 3.
The lowest possible digit in the blank space to make the number divisible by 3 is 2.

Hence, 998232 is the required digit of a given number.

(vi) 1_7072

The given number is 1_7072.
Add the digits of the given number.
Add 1, 7, 0, 7, and 2.
1 + 7 + 0 + 7 + 2 = 17.
By adding 1 to the number 17, it becomes 18. The number 18 is divisible by 3.
The lowest possible digit in the blank space to make the number divisible by 3 is 1.

Hence, 117072 is the required digit of a given number.

Rounding off the numbers means shortening the length of the number from long digits by replacing it with the nearest value. Round of to the nearest 1000 means minimizing the given decimal number to its nearest 1000 value. Check out the complete concept to learn the process to Round off the Numbers to Nearest 1000. We have also given Solved examples for your best practice.

Also, See:

• Round off to Nearest 10
• Round off to Nearest 100

How to Round off the Numbers to Nearest 1000?

Based on the below steps, we can easily round the numbers to the nearest 1000.
1. First, Find out the thousand’s digit in the number.
2. Next, choose the next smallest number (that is the hundredths digit of the number).
3. Now, check the hundred’s digit is either <5 (That means 0, 1, 2, 3, 4) or > = 5 (That is 5, 6, 7, 8, 9).
(i) If the digit is < 5, then the hundreds place is replaced with the digit ‘0’.
(ii) If the digit is > = 5, then the hundred’s digit is replaced with the digit ‘0’, and the thousand’s place digit is increased by 1 digit.

For example, Number 3350 Round to the Nearest 1000.
Step 1: Thousand’s digit of the number is 3.
Step 2: Hundreds digit of the number is 3.
Step 3: The hundred’s digit ‘3’ is < 5. So, we have to apply 3(i) conditions. That is, the hundred’s placed is replaced with the digit ‘0’.
3350 Rounding of the nearest 1000 is equal to 3000.

Rounding to Nearest 1000 Examples

1. Round of the number 2850 to nearest 1000.

Solution:
The given decimal number is 2850.
Step 1: Thousand’s digit of the number 2850 is ‘2’.
Step 2: Hundred’s digit of the number 2850 is ‘8’.
Step 3: The hundred’s digit of the number ‘8’ is > 5. So, the hundred’s digit is replaced by ‘0’ and the thousand’s digit is increased by ‘1’. That is
3000.

By rounding the number 2850 to its nearest 1000, it is equal to 3000.

2. Round of the number 5059 to nearest 1000.

Solution:
The given decimal number is 5059.
Step 1: Thousand’s digit of the number 5059 is ‘5’.
Step 2: Hundred’s digit of the number 5059 is ‘0’.
Step 3: The hundred’s digit of the number ‘0’ is < 5. So, the hundred’s digit is replaced by ‘0’. That is
5000.

By rounding the number 5059 to its nearest 1000, it is equal to 5000.

3. Round of the number 7985 to nearest 1000.

Solution:
The given decimal number is 7985.
Step 1: Thousand’s digit of the number 7985 is ‘7’.
Step 2: Hundred’s digit of the number 7985 is ‘9’.
Step 3: The hundred’s digit of the number ‘9’ is > 5. So, the hundred’s digit is replaced by ‘0’ and the thousand’s digit is increased by ‘1’. That is
8000.

By rounding the number 7985 to its nearest 1000, it is equal to 8000.

4. Round of the number 6500 to nearest 1000.

Solution:
The given decimal number is 6500.
Step 1: Thousand’s digit of the number 6500 is ‘6’.
Step 2: Hundred’s digit of the number 6500 is ‘5’.
Step 3: The hundred’s digit of the number ‘5’ is = 5. So, the hundred’s digit is replaced by ‘0’ and the thousand’s digit is increased by ‘1’. That is

By rounding the number 6500 to its nearest 1000, it is equal to 7000.

5. Round of the number 1287 to nearest 1000.

Solution:
The given decimal number is 1287.
Step 1: Thousand’s digit of the number 1287 is ‘1’.
Step 2: Hundred’s digit of the number 1287 is ‘2’.
Step 3: The hundred’s digit of the number ‘2’ is < 5. So, the hundred’s digit is replaced by ‘0’. That is
1000.

By rounding the number 1287 to its nearest 1000, it is equal to 1000.

6. Round off the below numbers to the nearest 1000.
(i) 50,105.
(ii) 25, 657
(iii) 3562
(iv) 9254
(v) 4895
(vi) 78962

Solution:
(i) The given decimal number is 50,105.
Step 1: Thousand’s digit of the number 50,105 is ‘0’.
Step 2: Hundred’s digit of the number 50,105 is ‘1’.
Step 3: The hundred’s digit of the number ‘1’ is < 5. So, the hundred’s digit is replaced by ‘0’. That is
50,000.
By rounding off the number50,105 to its nearest 1000, it is equal to 50,000.
(ii) The given decimal number is 25,657.
Step 1: Thousand’s digit of the number 25,657 is ‘5’.
Step 2: Hundred’s digit of the number 25,657 is ‘6’.
Step 3: The hundred’s digit of the number ‘6’ is > 5. So, the hundred’s digit is replaced by ‘0’, and the thousand’s digit of the number is increased by ‘1’. That is
26,000.
By rounding the number 25,657 to its nearest 1000, it is equal to 26,000.
(iii) The given decimal number is 3562.
Step 1: Thousand’s digit of the number 3562 is ‘3’.
Step 2: Hundred’s digit of the number 3562 is ‘5’.
Step 3: The hundred’s digit of the number ‘5’ is = 5. So, the hundred’s digit is replaced by ‘0’, and the thousand’s digit of the number is increased by ‘1’. That is
4000.
By rounding the number 3562 to its nearest 1000, it is equal to 4000.
(iv) The given decimal number is 9254.
Step 1: Thousand’s digit of the number 9254 is ‘9’.
Step 2: Hundred’s digit of the number 9254 is ‘2’.
Step 3: The hundred’s digit of the number ‘2’ is < 5. So, the hundred’s digit is replaced by ‘0’. That is
9000.
By rounding of the number 9254 to its nearest 1000, it is equal to 9000.
(v) The given decimal number is 4895.
Step 1: Thousand’s digit of the number 4895 is ‘4’.
Step 2: Hundred’s digit of the number 4895 is ‘8’.
Step 3: The hundred’s digit of the number ‘8’ is > 5. So, the hundred’s digit is replaced by ‘0’, and the thousand’s digit of the number is increased by ‘1’. That is
5000.
By rounding the number 4895 to its nearest 1000, it is equal to 5000.
(vi) The given decimal number is 78,962.
Step 1: Thousand’s digit of the number 78,962 is ‘8’.
Step 2: Hundred’s digit of the number 78,962 is ‘9’.
Step 3: The hundred’s digit of the number ‘9’ is > 5. So, the hundred’s digit is replaced by ‘0’, and the thousand’s digit of the number is increased by ‘1’. That is
79,000.
By rounding the number 78,962 to its nearest 1000, it is equal to 79,000.

18 Times Table is one of the difficult tables below 20. To make you learn 18-time table easily, we have given 18 Times Table Multiplication Chart. 18 times table values are double the values of 9 times table. This is a very important table for children to quickly solve the solutions and for mental ability. There are various ways to learn the 18 Multiplication Table. We have provided the different Math Tables along with the explanation below. Check out all the ways and make your learning simple.

How to Read Table of 18?

One time eighteen is 18

Two times eighteen are 36

Three times eighteen are 54

Four times eighteen are 72

Five times eighteen are 90

Six times eighteen are 108

Seven times eighteen are 126

Eight times eighteen are 144

Nine times eighteen are 162

Ten times eighteen are 180

Eleven times eighteen are 198

Twelve times eighteen are 216

Multiplication Table of 18 up to 20

Check out the multiplication table of 18 and remember the output to make your math-solving problems easy.

Tricks to Remember 18 Times Table

(i) If you know the 9 times table, then you can easily remember the 18 times table. Yes, add the resultant values of the 9 times table to the 9 times table. That is,
9 X 1 = 9 + 9 = 18 = 18 X 1 = 18.
9 X 2 = 18 + 18 = 36 = 18 X 2 = 36.
9 X 3 = 27 + 27 = 54 = 18 X 3 = 54.
9 X 4 = 36 + 36 = 72 = 18 X 4 = 72.
9 X 5 = 45 + 45 = 90 = 18 X 5 = 90.

(ii) If you know the 17 times table, then it is very easy to remember 18 times table. Yes,
17 X 1 = 17 + 1 = 18 = 18 X 1 = 18.
17 X 2 = 34 + 2 = 36 = 18 X 2 = 36.
17 X 3 = 51 + 3 = 54 = 18 X 3 = 54.
17 X 4 = 68 + 4 = 72 = 18 X 4 = 72.
17 X 5 = 85 + 5 = 90 = 18 X 5 = 90.
……17 X 10 = 170 + 10 = 180 = 18 X 10 = 180.

(iii) One more tip to remember 18 times table is
19 X 1 = 19 – 1 = 18 = 18 X 1 = 18.
19 X 2 = 38 – 2 = 36 = 18 X 2 = 36.
19 X 3 = 57 – 3 = 54 = 18 X 3 = 54.
19 X 4 = 76 – 4 = 72 = 18 X 4 = 72.
19 X 5 = 95 -5 = 90 = 18 X 5 = 90.
…..19 X 10 = 190 – 10 = 180 = 18 X 10 = 180.

Get More Tables:

Solved Example on Eighteen Times Table

1. By using the 18 Times Table find the (i) 18 times 4 (ii) 18 times 6 minus 4 (iii) 18 times 2 plus 6 (iv) 18 times 3 multiple of 2?

Solution:
(i) 18 Times 4.
By using the 18 times table,
18 Times 4 in mathematical is equal to 18X 4 = 72.
So, 18 Times 4 is equal to 72.
(ii) 18 times 6 minus 4.
By using the 18 Times table,
18 Times 6 minus 4 can be written as 18 X 6 – 4 in mathematical.
18 X 6 – 4 = 108 – 4 = 104.
So, 18 times 6 minus 4 is equal to 104.
(iii) 18 times 2 plus 6
By using the 18 times table,
We can write the 18 times 2 plus 6 as 18 X 2 + 6.
18 X 2 + 6 = 36 + 6 = 42.
Therefore, 18 Times 2 plus 6 is equal to 42.
(iv) 18 times 3 multiple of 2
By using the 18 times table,
We can write the 18 times 3 multiple of 2 as 18 X 3 X 2.
18 X 3 X 2 = 54 X 2 = 108.
Therefore, 18 Times 3 multiple of 2 is equal to 108.

A cumulative frequency is the sum of frequency values of class or basic value. The frequency values are equal to the number of times the score or basic value or class is repeated. For Example, Class : 1 ,2, 1, 1, 1, 3,3, 3, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8. The cumulative frequency of a value of a variable is the collection of data of a number of values less than or equal to the value of the variable. The cumulative frequency of a class interval that is overlapping or nonoverlapping is the sum of the frequencies of earlier class intervals and the concerned class interval.

Also, Read: Medians and Altitudes of a Triangle

Cumulative Frequency Examples

1. The Following Table gives the frequency distribution of marks obtained by the 30 students. Find the Cumulative frequency based on the below values?

Solution: Based on the student’s marks and the frequency of the marks, we can easily find out the cumulative frequency. Cumulative frequency is the sum of the frequency of marks of the students. That is,

So, the cumulative frequency is 5, 17 ( 5 + 12), 27 (17 + 10), and 30 (27 + 3).

2. The below table gives the mass of 30 objects with the frequency. Find out the cumulative frequency for the objects?

Solution: As per the given information We have mass objects and the frequency of the mass of objects. The cumulative frequency is the sum of the frequency of mass of objects. That is

Finally, the cumulative frequency of the mass of objects is 10, 16, 36, and 51.

3. The below-given details are the ages of the employees in a particular company and the frequency of the ages of employees. Find the cumulative frequency for the given data?

Solution: As per the given details,
Ages of the employees in a company and the frequency of ages of the employees are noted. The cumulative frequency of the ages of employees is

4. A cloth store contains different colors of clothes. The color details, the cumulative frequency of some colors, and the frequency of the colors are given below, find the final cumulative frequency?

Solution: The given details are colors of cloths are white, brown, black, red, and pink.
The frequency of the colors is 10, 18, 20, 2, and 6.
The cumulative frequency of colors is the sum of the frequency of the colors. That is,
White – 10
Brown – 10 + 18 = 28
Black – 28+ 20 = 48
Red – 48 + 2 = 50
Pink – 50 + 6 = 56.
So, the final cumulative frequency of the colors is equal to 56.

5. For the collection of numbers 10, 12, 35, 10, 10, 12, 12, 35, 35, 35, 35, 10, 13, 11, 11, 13, 11, 13, and 10? What is the cumulative frequency of 13?

Solution: As per the given information
The given numbers are10, 12, 35, 10, 10, 12, 12, 35, 35, 35, 35, 10, 13, 11, 11, 13, 11, 13, and 10.
The frequency of the numbers is
Number – frequency
10 – 5
11 – 3
12 – 3
13 – 3
Cumulative frequency is equal to the sum of the frequency and the cumulative frequency of the 13 is equal to the sum of the frequency of less than or equal to 13. That is
5 + 3+ 3 + 3 = 14.
Therefore, the cumulative frequency of 13 is equal to 14.

6. The marks of 100 students are given below with the frequency. Find the cumulative frequency and answer the following questions.
(i) How many students obtain less than 41 % marks?
(ii) How many students obtain at least 51% marks?

Solution: The cumulative frequency is

(i) How many students obtain less than 40 marks?
The number of students obtaining less than 41% of marks is 31 – 40% cumulative frequency = 65.
(ii) How many students obtain at least 51% marks?
The number of students obtaining at least 51% of marks =total number of students – the number of students obtaining less than or equal to 41 – 50%.
= 100 – 75 = 25.

So, the number of students obtaining at least 51% of marks is equal to 25.

Want to learn how to simplify decimals involving addition and subtraction? If so, you have come to the right place where you can get a complete idea of the Simplification of Decimals. Learn the approach used for simplifying decimals involving addition and subtraction so that you can apply the same while solving related problems.  Refer to Worked Out Problems for Decimal Simplification explained in the further modules to clearly understand the concept.

Do Read:

• Adding Decimals
• Subtracting Decimals

How to Add or Subtract Decimals?

Go through the simple process available here to simplify decimals involving the addition and subtraction of decimals. They are as follows

• The first and foremost step is to convert the given decimals to like decimals.
• Write the decimals one below the other depending on the place value of digits.
• Later, solve using the order of operation accordingly.

Worked Out Problems on Simplification of Decimals involving Addition and Subtraction

1. Simplify the following 20.10 + 74.38 – 35.69?

Solution:

Converting into like decimals and solving using order of operation.

As the given decimals are all like decimals there is no need to annex zeros. And we can go with the order of operation and simply the expression further.

Step 1: Addition

20.10

74.38

(+)

——–

94.48

——–

Step 2: Subtraction

94.48 – 35.69

Check out the worked out procedure for subtracting 35.69 from 94.48 below

Therefore, the value of 20.10 + 74.38 – 35.69 is 58.79

2. Simplify the following 14.6078 – 0.37 + 0.6?

Solution:

Given decimals are 14.6078, 0.37, 0.6

First convert the given decimals to like decimals. We can do so by simply annexing with zeros i.e. the maximum number of decimal places among the given decimal numbers.

Since the maximum number of decimal places among the given decimal numbers is 4. We will annex with required zeros to make the given decimals to decimal places of 4

By Converting into like decimals we have the following

14.6078 ➙ 14.6078

0.37 ➙ 0.3700

0.6 ➙ 0.6000

Now, that you are done with annexing zeros simplify the given expression as per the order of operations.

Step 1: Subtraction

Check out how decimal 0.3700 is subtracted from the decimal value 14.6078

Step 2: Addition

Align the given decimals as per decimal points so that given decimals are arranged in Proper Decimal Value and then perform Addition of Decimals.

14.2378

0.6000

(+)

——–––

14.8378

——–––

Therefore, the value of 14.6078 – 0.37 + 0.6 is 14.8378

3. What must be added to 19.33 to obtain 47.87?

Solution:

19.33+x = 47.87

x = 47.87-19.33

= 28.54

Thus, 28.54 must be added to 19.33 is 47.87

4. What must be subtracted from 281.6 to obtain 18.88?

Solution:

28.16-x=18.88

Rearranging the given equation we have

28.16-18.88=x

x = 9.28

5. Simplify the following.

75.102 + 64.38 – 25.99

Solution:

First convert the given decimals to like decimals. We can do so by simply annexing with zeros i.e. the maximum number of decimal places among the given decimal numbers.

Amongst the given decimals 75.102 is having the maximum number of decimals i.e. 3

Change the rest of the decimals to like decimals by padding with required number of zeros to make them decimals having 3 decimal places

Converting Unlike Decimals to Like Decimals we have

75.102 ➙ 75.102

64.38 ➙ 64.380

25.99 ➙ 25.990

Step 1: Addition

Look out the decimal addition process for decimals 75.102 and 64.380

Step 2: Subtraction

139.482-25.990

Thus, the value of 75.102 + 64.38 – 25.99 is 113.492

Subtracting Decimals is a bit complex when compared to regular subtraction. Get to know about the definition of Decimals before learning how to subtract Decimal Numbers. Usually, Decimal Numbers are Numbers that have a decimal point in between them. It has two parts and the one to the left of the decimal point is the Whole Number and the one to the right of the decimal point is called the Decimal Part or the Fractional Part. Be aware of Step by Step Procedure on Subtracting Decimal Numbers, Worked Out Examples on Decimal Subtraction, etc.

Also, Read:

• Decimals
• Adding Decimals

How to Subtract Decimal Numbers?

Follow the simple steps listed below so that you can Subtract the Decimal Numbers easily. They are in the following fashion

• Note down the decimal numbers one under the other and line up the decimal points.
• Convert the unlike decimals to like decimals by padding with required zeros based on the maximum number of digits next to the decimal for any number of decimals.
• Write the smaller decimal number beneath the larger decimal number in the column.
• Arrange the decimals in a way that the decimals of the same place lie in the same column.
• Subtract the numbers in the columns from the right as in regular subtraction.
• Remember to place the decimal point in the result similar to the decimal places above it.

Worked out Problems on Subtracting Decimals

1. Subtract the Decimal 12.59 from 34.4?

Solution:

Given Decimals are 12.59, 34.4

Before Subtracting Decimals convert them to like decimals by padding with zeros.

The maximum number of decimal places among the given decimal numbers is 2. So, Annex with Zeros so as to obtain 2 places of decimals.

12.59➙12.59

34.4➙34.40

Subtract the Smaller Number from the Larger Number. Align the Decimal Numbers Lined up so that the decimals of the same place lie in the same column

Borrow as usual

34.40

12.59

(-)

——–—

21 .81

——–—

2. Subtract the Decimal 5.62 from 7.84?

Solution:

Given Decimals are 5.62, 7.84

Since both the decimals have an equal number of decimal places there is no need for Annexing of Zeros to convert them to like decimals.

Subtract the smaller number from the larger number. Place them one under the other number columnwise and perform regular subtraction and place a decimal point in the result similar to the decimal places above it.

7.84

5.62

(-)

——–—

2.22

——–—

3. Calculate the value of 8.005-0.35?

Solution:

Given Decimals are 8.005 and 0.35

The maximum number of decimal places among the given decimals is 3. So Pad with a required number of zeros to make them like decimals.

By converting them to like decimals we get

8.005 ➙ 8.005

0.35 ➙  0.350

Subtracting the smaller number from the larger number we have

8.005

0.350

(-)

——–—

7.655

——–—

FAQs on Subtracting Decimals

1. How do you subtract decimals step by step?

• Write down the decimal numbers, one under the other, with the decimal points lined up.
• Add zeros so that numbers have the same length and become like decimals.
• Then subtract normally, and remember to put the decimal point in the result.

2. Why do you need to align decimal points before subtracting?

In order to make sure all the numbers are in the Proper Place Value column and align the decimal points. Thus we place ones to one’s place, tenths to tenths, hundredths to hundredths, and so on.

3. What should be done first in subtracting decimals?

The first and foremost step to be done while subtracting decimals is to line up the decimal points so that similar place values are lined up.

The Addition of Decimals is a bit complex compared to regular natural numbers or whole numbers. Before, we learn how to add decimal numbers let us learn firstly about Decimals. Decimal Numbers are used for representing a number with greater precision in comparison to integers or whole numbers. A Dot is placed in a decimal number namely Decimal Point. Refer to the complete article to be well versed with the Procedure for Adding Decimals, Solved Examples on Decimal Addition, etc.

Also, Read: Decimals

How to Add Decimal Numbers?

Follow the below-listed steps to add decimal numbers easily and they are as such

• Arrange the given decimal numbers lined up vertically one under the other.
• Firstly, pad the numbers with zeros depending on the maximum number of digits present next to the decimal for any of the numbers and change them to like decimals.
• Arrange the Addends in a way that digits of the same place are in the same column.
• Add the numbers from right similar to the usual addition.
• Later, place the decimal point down in the result in the same place as the numbers above it.

Decimal Addition Examples

1. Add the Decimals 2.83, 10.103, 534.8?

Solution:

Given Decimals are 2.83, 10.103, 534.8

Before performing the Addition of Decimals you have to convert the given decimals to like decimals by padding with zeros.

The Maximum Number of Decimal Places in the given decimals is 3. So, Change the given decimals to like decimals having 3 places of decimals

2.83  ➙ 2.830

10.103  ➙10.103(Since it already has 3 places of decimal remains the same)

534.8  ➙ 534.800

Align the Like Decimals one under the other vertically and perform the addition operation as usual

Carry  1

002.830

010.103

534.800
(+)

——–—

547.733

——–—

2. Add 7.1, 5.26?

Solution:

Given Decimals are 7.1, 5.26

Before performing the Addition of Decimals you have to convert the given decimals to like decimals by padding with zeros.

The Maximum Number of Decimal Places in the given decimals is 2. So, Change the given decimals to like decimals having 2 places of decimals

7.1  ➙ 7.10

5.26 ➙ 5.26

Align the Like Decimals one under the other vertically and perform the addition operation as usual

7.10

5.26

(+)

——–

12.36

——–

3. Add Decimals 8.35, 53.002?

Solution:

Given Decimals are 8.35, 53.002

Before performing the Addition of Decimals you have to convert the given decimals to like decimals by padding with zeros.

The Maximum Number of Decimal Places in the given decimals is 3. So, Change the given decimals to like decimals having 3 places of decimals

8.35    ➙ 8.350

53.002 ➙ 53.002

Align the Like Decimals one under the other vertically and perform the addition operation as usual

08.350

53.002

(+)
——––

58.352

——––

FAQs on Adding Decimals

1. What is a Decimal Number?

A Decimal Number can be defined as a number whose whole number part and fractional part is separated by a decimal point.

2. What is meant by Adding Decimals?

Adding Decimals is much similar to adding whole numbers except for a few technical details. For Decimals, we line up the decimal points so that whole number parts line up and decimal parts line up.

3. How to add Decimals?

Write down the decimals one under the other with decimal points lined up. Put in Zeros so that numbers have the same length and add them as regular numbers and place a decimal point in the result.

Do you want to know how to form the greatest and smallest numbers using the digits? If yes, then stay tuned to this page. On this page, students can learn about the detailed steps to form the largest and smallest numbers with their definitions. We have also covered plenty of examples on the formation of the greatest and the smallest numbers in the below-mentioned sections.

What is Greatest and Smallest Number?

The greatest number is a number which is having the highest value when compared with other numbers. And we can also say that the largest number has all the digits arranged in descending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit from the given digits must be placed at the extreme left side of the number to raise its value.

The smallest number is a number that is having the lowest value compared with other numbers. In the lowest number, the digits are arranged in ascending order. If the given digits have 0, we never write 0 at the extreme left place, instead write at the second place from the left to get the smallest number.

Detailed Process on Formation of Greatest and the Smallest Number

Check out the step-by-step process of forming the greatest and smallest numbers from the given digits along the lines.

• To form the greatest numbers from the given digits, arrange the digits in descending order. And the extreme left digit has the highest value when compared with others.
• To form the lowest numbers from the given digits, arrange the digits in ascending order. And the extreme left digit has the lowest value compared with other digits.
• If there is a 0, then don’t write 0 at the extreme left position instead place it at the second place from the left to obtain the lowest number.

Example:

Form the greatest and smallest number using the digits 5, 4, 8, 6.

To form the greatest number, follow these steps.

• The smallest digit is placed at one’s place
• The next greater digit at ten’s place and so on
• The greatest digit is placed at the highest place of the number

To form the smallest number, follow the reverse procedure

• The greatest digit is placed at one’s position
• The next smaller digit is placed at ten’s position and so on.
• So, the smallest digit is placed at the highest place of the number.

The ascending order of the numbers 4, 5, 6, 8

So, the smallest number is 4568.

The descending order of the numbers 8, 6, 5, 4

So, the greatest number is 8654.

Also, Read

• Comparison of Integers

Worked Out Examples on the Formation of Greatest and the Smallest Number

Example 1:

Write the greatest and smallest 4 digit numbers using the digits 1, 0, 8, 4

Solution:

The given digits are 1, 0, 8, 4.

We know that the four-digit number has four places those are thousands, hundreds, tens, and ones. If the given digits are arranged in descending order (from greatest to lowest value), we get the greatest number. If digits are arranged in ascending order (from lowest to highest), we get the smallest number.

The descending order is 8 < 4 < 1 < 0.

The ascending order is 0 < 1 < 4 < 8.

                                     Th      H       T       O

Greatest number           8       4       1       0
Lowest Number            1       0       4       8

As the given digits have 0, place zero at the second-highest position i.e hundredth position.

So, the greatest number using the digits 1, 0, 8, 4 is 8410.

The smallest number using the digits 1, 0, 8, 4 is 1048.

Example 2:

Write the greatest and smallest 5 digit number using the digits 7, 5, 6, 8, 2.

Solution:

The given digits are 7, 5, 6, 8, 2.

                           Tth      Th     H       T       O 
Greatest number    8       7       6       5       2
Smallest number    2       5       6       7       8

Arrange the given digits in the descending order 2 < 5 < 6 < 7 < 8.

To get the greatest number, the greatest digit 8 is placed at the highest valued place, i.e., ten thousand place, next smaller digit 7 at thousands place, next smaller digit 6 at hundred’s place, still smaller digit 5 is placed at ten’s place and the smallest digit 2 at one’s or units place.

Therefore, the greatest 5 digit number using the digits 7, 5, 6, 8, 2 is 87652.

Arrange the given digits in the ascending order 8 > 7 > 6 > 5 > 2.

To get the smallest number, the greatest digit 8 is placed at the lowest valued place i.e one’s place, next highest digit 7 is placed at ten’s place, next highest digit 6 is placed at hundred’s place, still greatest digit 5 is placed at thousand’s place, remaining digit 2 is placed at ten thousand place.

Therefore, the smallest 5 digit number using the digits 7, 5, 6, 8, 2 is 25678.

Example 3:

Write the greatest and smallest 5 digit number using 1, 2, 5. The digit may be repeated.

Solution:

The given digits are 1, 2, 5.
 Tth      Th     H       T       O
Greatest number    5       5       5       2       1

Smallest number    1       1       1       2       5

Arrange the given digits in the descending order 1 < 2 < 5

Since we have to make the greatest 5 digit number using 3 digits, we will repeat the greatest digit required a number of times.

To get the greatest number, the greatest digit 5 is placed at the highest valued place, i.e., ten thousand place, next smaller digit 5 at thousands place, next smaller digit 5 at hundred’s place, still smaller digit 2 is placed at ten’s place and the smallest digit 1 at one’s or units place.

Therefore, the greatest 5 digit number using the digits 1, 2, 5 is 55521.

To get the smallest number, the smallest digit 1 is placed at ten thousands-place, next greater digit 1 at thousand’s place, still greater digit 1 at hundred’s place, next greatest digit 2 is placed at ten’s place,  and greatest digit 1 at one’s or units place.

Therefore, the smallest 5 digit number using the digits 1, 2, 5 is 11125.

Example 4:

Write the greatest and smallest 4 digit number using 8, 7, 1, 4.

Solution:

The given digits are 8, 7, 1, 4.

       Th     H       T       O 
Greatest number      8       7       4       1

Smallest number       1       4       7       8

Arrange the given digits in the descending order 1 < 4 < 7 < 8

The greatest number using the digits 8, 7, 1, 4 is 8741.

To get the smallest number, we arrange the digits in ascending order.

Ascending order of 8, 7, 1, 4 is 8 > 7 > 4 > 1.

The smallest number using the digits 8, 7, 1, 4 is 1478.

FAQs on Formation of Greatest and Smallest Numbers

1. How to obtain the greatest and the smallest among the group of numbers?

The greatest number among the number of numbers is obtained by arranging the group of digits in the descending order and writing the numbers as it is. The smallest number is obtained by arranging the group of digits in the ascending order and representing them as it is.

2. Which is the greatest and smallest 4 digit number?

The greatest 4 digit number is 9999 and the smallest 4 digit number is 1000.

3. What is the ascending order?

The process of arranging the group of numbers or items of the same category from the lowest to the highest in value is called the ascending order.

Multiplication is one of the important arithmetic operations which helps to solve math problems easily. Usually, math tables are used for solving multiplication problems. So, make use of the Multiplication Tables for 0 to 25 and get the solution for your multiplication word problems quickly and easily. Students can get different types of word problems in the below sections.

What is Meant by Multiplication?

Multiplication is one of the basic arithmetic operations which gives the result of combining groups of equal sizes. Multiplication is a process of repeated addition. It is represented by the cross “x”, asterisk “*”, dot “.” symbol. When we multiply two numbers the answer is called the product.

Solved Problems on Multiplication

Question 1:

Find the product of 125 and 78.

Solution:

Given numbers are 125, 78.

125 x 78 = 9750

Question 2:

The product of two numbers is 175 and the multiplier is 7. Find the multiplicand?

Solution:

Given that,

The product of two numbers = 175

Multiplier = 7

Multiplicand = ?

Multiplicand * multiplier = Product

Multiplicand * 7 = 175

Multiplicand = 175/7

So, multiplicand = 25

Question 3:

Solve 78 x 96?

Solution:

Multiplicand = 78

Multiplier = 96

78 x 96 = 7488.

Also, Read

• Multiplication of Integers

Worked out Word Problems on Multiplication

Question 1:

The weight of a rice bag is 50 kg. What will be the weight of 75 such bags?

Solution:

Given that,

Weight of a rice bag = 50 kg

Weight of 75 rice bags = 50 x 75

So, the total weight of 75 rice bags is 3750 kgs.

Question 2:

The price of a wooden box is $179 and a plastic box is $82. Find the cost of 40 wooden boxes and 150 plastic boxes in total?

Solution:

Given that,

The price of a wooden box = $179

The price of a plastic box = $82

The cost of 40 wooden boxes = 179 x 40 = 7160

The cost of 150 plastic boxes = 150 x 82 = 12300

The total cost of 40 wooden boxes and 150 plastic boxes = 7160 + 12300

= 19460

Therefore, the total cost of 40 wooden boxes and 150 plastic boxes is $19460.

Question 3:

A toy costs $216. How much will be paid for such 56 toys?

Solution:

Given that,

The cost of one toy = $216

The amount to be paid to buy 56 toy means add 216, 56 times

Otherwise, multiply 216 and 56 the obtained product is the amount paid.

So, the amount paid for 56 toys = 216 x 56

Therefore, $12096 must be paid to buy 56 toys.

Question 4:

The monthly salary of a man is $3156. What is his annual income by salary?

Solution:

Given that,

The monthly salary of a man = $3156

The annual income of the man by salary = Add man’s salary 12 times

Or, multiply the man’s monthly salary by 12 months to get the annual income in dollars.

So, the annual income of the man by salary = 3156 x 12

Therefore, the annual income of the man by salary is $37872.

Question 5:

Each student of class IV $75 for the flood victims. If there are 368 students in class IV, what is the total amount of money collected?

Solution:

Given that,

All the students of Class IV have given $75 for the flood victims

The total number of students in class IV = 368

The total amount of money collected from class IV students for flood victims = 75 should be added 368 times.

Otherwise, multiply the number of students by the amount each student is given.

So, the total amount of money collected from class IV students for flood victims = 75 x 368

Therefore, the total amount of money collected from class IV students for flood victims is $27600.

Question 6:

Prove that by adding multiplicand, multiplier times is equal to multiplicand into multiplier by solving the following question.

Ramu buys 7 pencils in a shop. The cost of each pencil is $2. Find the total amount paid to buy 7 pencils.

Solution:

Given that,

The cost of each pencil = $2

The number of pencils bought = 7

The amount paid to buy 7 pencils = cost of each pencil x total number of pencils bought

= 2 x 7

= $14

The amount paid to buy 7 pencils = Add the total number of pencils by the cost of each pencil times

= 2 + 2 + 2 + 2 + 2 + 2 + 2

= $14

Therefore, the cost of 7 pencils is $14

Hence proved.

Question 7:

A truck can carry 2,545 kg of coal per trip. How much coal will be carried if the truck makes 135 trips?

Solution:

Given that,

A truck can carry 2,545 kg of coal per trip

The amount of coal carried by 135 trips = 2545 x 135 = 343575

Therefore, 3,43,575 kgs of coal will be carried if the truck makes 135 trips.

Question 8:

There are 365 days in a year. How many days are there in 29 years?

Solution:

Given that,

The number of days in a year = 365

The number of days in 29 years = 365 x 29

Therefore, the number of days in 29 years is 10585.

Question 9:

A bookseller sells 875 books per day in the month of July. How many books will he be able to sell in 25 days of July?

Solution:

Given that,

A bookseller sells 875 books per day in the month of July

The number of books the bookseller will sell in 25 days of July = 875 x 25

Therefore, 21875 books will the bookseller be able to sell in 25 days of July.

Question 10:

There are 1125 students in a school. If a student pays $ 365 as fees and $ 150 as bus charge per month, how much money is collected after 8 months?

Solution:

Given that,

The number of students in a school = 1125

A student pays $ 365 as fees and $ 150 as bus charge per month

The amount of money collected from one student in a month = 365 + 150 = 515

The total amount of money collected from all students in a month = 515 x 1125 = $579375

The total amount of money collected from all students in 8 months = $579375 x 8

Therefore, the total amount of money collected from 1125 students of a school as fee and bus fee in 8 months is $4635000.

A net is a flattened out 3-dimensional solid. It is the basic skeleton outline in two dimensions, that can be folded and glued together to obtain the 3D structure. Nets are used for making 3D shapes. In the below sections, we have discussed the nets of different geometric shapes along with the examples.

Nets of Solids – Definition

A geometry net is a two-dimensional shape that can be folded to form a three-dimensional solid. When the surface of a three-dimensional figure is laid out flat showing each face of the solid, the pattern obtained is called the net. Nets are useful in finding the surface area of the solids. The following are some steps we must take to determine whether a net forms a solid:

• Ensure that the net and a solid have the same number of faces and that there is a match between the shapes of faces of the solid and the shapes of the corresponding faces in the net.
• Visualize how the net is to be folded to form the solid and all the sides fit together properly.

Nets of Cube

A cube is a 3-dimensional figure having 6 faces of equal length. The cube has 8 vertices, 12 edges. All the faces of a cube are in square shape. The plane angles of the cube are the right angle. The edges opposite to each other are parallel.

Cube Image

11 possible nets of a cube

Nets of Cylinder

A cylinder has two parallel bases joined by a curved surface at a fixed distance. The bases are in circular shape and the center of two bases are joined by a line segment, called the axis. The perpendicular distance between the bases is the height and the distance from the axis to the outer surface is the radius of the cylinder.

Cylinder Image

Nets of Cylinder

Nets of Rectangular Prism

A rectangular prism has six faces and each face is a rectangle. Both the bases of the prism are rectangles and other lateral faces are also rectangles. it is also called a cuboid.

Rectangular Prism Image

Nets of a Rectangular Prism

Nets of Triangular Prism

A triangular prism is a polyhedron having two triangular bases and three rectangular sides. Like other prisms, two bases are congruent and parallel. The prism has 5 faces, 9 sides and 6 vertices.

Triangular Prism Image

Nets of Triangular Prism

Nets of Cone

A cone is a shape formed by using a set of line segments which connects a common point, called vertex to all the points of a circular base. the distance between vertex to base of the cone is known as its height.

Cone Image

Nets of Cone

Also, Read

• Common Solid Figures
• Three-Dimensional Figures(3D Shapes)

Nets of Square Pyramid

A three-dimensional geometric shape with square base and four triangular faces all those faces meet at a single point is called the square pyramid. If all triangular faces have equal edges, then this pyramid is called an equilateral square pyramid.

Square Pyramid Image

Nets of Square Pyramid

Solved Examples on Nets of Solid

Example 1:

Sketch the net of the solid shape given below.

Solution:

If the pyramid is unfolded along its edges we get the following net.

The net of the pentagonal pyramid is as follows.

Example 2:

Sketch the net of the solid shape given below.

Solution:

If the prism is unfolded along its edges we get the following net.

The net of the hexagonal prism is as follows.

Example 3:

Sketch the net of the solid shape given below.

Solution:

If the prism is unfolded along its edges we get the following net.

The net of the hexagonal prism is as follows.

Frequently Asked Questions on Nets of Solid

1. How are nets useful in real life?

Nets are used in finding the surface area of the solids. The examples of nets are all three dimensional geometric shapes. Some of the 3 dimensional geometric shapes are square pyramid, cone, cylinder, triangular prism, rectangular pyramid, rectangular prism nad others.

2. Can a solid have different Nets?

Yes, a solid have different nets. Visualize how the net is folded to form a solid and make sure that all sides fit together properly. Make sure the solid and the net have same number of faces, shape of faces should match.

3. What is the net of a 3D shape?

The net of a 3D shape is what it looks like if it is opened out flat. A net can be folded up to ake a 3D shape. There can be several possible nets for one 3D shape. Draw a net on paper, then fold it into the shape.

4. How many nets are there for a cube?

There are exactly eleven nets that will form a cube.