Common Core Math

Table of 9 shows the results of adding 9 repetitively. Learning the 9 Times Table is quite necessary as without this primary knowledge you might feel the concepts of math more challenging to understand. One interesting fact about the Multiplication Table of 9 is that you get the next multiples of 9 by increasing the tens digit and decreasing the first digit at every step.

Math Tables makes it easy for you to perform quick calculations in mathematics. Go through the entire article to learn about the Tips & Tricks to Memorize the Multiplication Table of Nine, How to Read and Write the Table of 9. Download the Printable Multiplication Chart of 9 for free from here and take your preparation to next level.

9 Times Multiplication Chart

We have provided Table of 9 in image format here. You can use this Multiplication Table of 9 Chart as a quick reference and download the image for free and resolve your queries. Students can recite it regularly and try to memorize it so as to apply these fundamentals in learning higher concepts in the mere future. You can stick this Multiplication Chart of 9 on your walls so that you can read them before you go to bed daily.

How to Read 9 Times Table?

Know how to read the Table of Nine orally by having a glance at the below modules. They are in the following fashion

One time nine is 9

Two times nine is 18

Three times nine is 27

Four times nine is 36

Five times nine is 45

Six times nine is 54

Seven times nine is 63

Eight times nine is 72

Nine times nine is 81

Ten times nine is 90

Eleven times nine is 99

Twelve times nine is 108

Nine Times Multiplication Table up to 20 | How to write a Multiplication Table of Nine?

Referring to Table of 9 you can learn multiplication facts about the table easily. Here, we have provided the Nine Times Table up to 20 numbers. You can use Table of 9 to perform mental math calculations right in your head. Enhance your problem-solving skills and speed of solving problems in your competitive exams by applying this knowledge. Also, learn how to write the Nine Times Multiplication Table by checking the table provided in tabular format.

9	X	1	=	9
9	X	2	=	18
9	X	3	=	27
9	X	4	=	36
9	X	5	=	45
9	X	6	=	54
9	X	7	=	63
9	X	8	=	72
9	X	9	=	81
9	X	10	=	90
9	X	11	=	99
9	X	12	=	108
9	X	13	=	117
9	X	14	=	126
9	X	15	=	135
9	X	16	=	144
9	X	17	=	153
9	X	18	=	162
9	X	19	=	171
9	X	20	=	180

Importance of Multiplication Table of Nine?

In general, Multiplication Table is obtained by multiplying the number 9 with all natural numbers. Refer to the following modules to know the importance of it. They are in the following fashion

• You can Identify the Patterns of Multiples easily.
• Furthermore, learning the Nine Times Multiplication Table helps you to solve problems on long division, multiplication, HCF, LCM problems easily.
• Memorizing the Nine Table you can enhance your speed of solving mathematical problems.

Tips for Learning 9 Times Table

In the below image you can notice the digits in one’s place reduce by 1 and while going from top to bottom. On the other hand, the digits in the tens place increase by 1 from top to bottom. If you keep these points in mind the Multiplication Table of 9 is quite simple to remember.

Get More Math Tables:

0 Times Table	1 Times Table	2 Times Table
3 Times Table	4 Times Table	5 Times Table
6 Times Table	7 Times Table	8 Times Table
10 Times Table	11 Times Table	12 Times Table
13 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

Solved Examples involving Table of Nine

1. Using the table of 9, evaluate 9 times 5 minus 3?

Solution:

Let us write 9 times 5 minus 3 mathematically

= 9*5-3

= 45-3

= 42

Thus, 9 times 5 minus 3 is 42

2. Mihir buys 9 packets of 14 pencils each. Using 9 times table find how many pencils has he bought in total?

Solution:

No. of Packets Mihir Bought = 9

No. of Pencils in each packet = 14

Number of Pencils Mihir bough in total = 9*14

= 126

Therefore, Mihir bought 126 pencils in total.

3. Using the table of 9, check whether 9 times 4 minus 9 is 27?

Solution:

Let us put the given statement in the form of a mathematical expression

= 9*4-9

= 36-9

= 27

Multiplication Table of 4 includes the multiples of 4 and is similar to the table of 2. Learning the 4 Times Multiplication Table helps you keep a track of even numbers. Keeping the Math Tables at your fingertips helps you solve the math questions in mind in no time. By going through the entire article you will learn how to read and write the Four Times Table, Tips & Tricks to Memorize the Multiplication Table of Four.

4 Times Multiplication Chart

Table of 4 is provided in image format for the sake of students. Learning 4 Table is quite essential to solve the mathematical problems fastly. Use the 4 Times Table over here to do calculations in mind and save a lot of time in competitive exams. You can download the Multiplication Table of Four for free of cost and try to memorize it regularly.

How to Read Four Times Table?

Learn how to read 4 Times Table by referring to the below modules. They are as such

One time four is 4

Two times four is 8

Three times four is 12

Four times four is 16

Five times four is 20

Six times four is 24

Seven times four is 28

Eight times four is 32

Nine times four is 36

Ten times four is 40

Eleven times four is 44

Twelve times four is 48

How to Write Multiplication Table of 4? | Table of 4 upto 20

Check out the 4 Times Table given below in tabular format and learn how to write Four Table. We have listed the first 20 multiples of four here for your comfort. Utilize the handy 4 Times Table Chart over here to perform quick calculations in math. Have a deeper insight into the multiplication process by availing the Table of Four present here.

4	x	1	=	4
4	x	2	=	8
4	x	3	=	12
4	x	4	=	16
4	x	5	=	20
4	x	6	=	24
4	x	7	=	28
4	x	8	=	32
4	x	9	=	36
4	x	10	=	40
4	x	11	=	44
4	x	12	=	48
4	x	13	=	52
4	x	14	=	56
4	x	15	=	60
4	x	16	=	64
4	x	17	=	68
4	x	18	=	72
4	x	19	=	76
4	x	20	=	80

Benefits of referring to Multiplication Table of Four

Students are advised to go through the below-listed points to know about the importance of the 4 Table. They are as follows

• You can solve mathematical problems involving multiplication and division easily by learning the Four Times Table.
• Learning the Multiplication Table of 4 you can perform quick calculations.
• 4 Times Multiplication Chart helps you to understand the patterns easily.
• Can be a great savior to do your mental math calculations right in your head.

Tips to remember Table of 4

Follow the below-listed tips so that you can remember the Four Times Table easily. They are along the lines

• There is a pattern for every 10 multiples of four i.e. 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
• The last digits of the multiples always repeat so that you can remember them easily.

Get More Math Tables:

0 Times Table	1 Times Table	2 Times Table
3 Times Table	5 Times Table	6 Times Table
7 Times Table	8 Times Table	9 Times Table
10 Times Table	11 Times Table	12 Times Table
13 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

Examples involving Four Times Table

1. Using the table of 4, evaluate 4 times 3 minus 3?

Solution:

First, let us write the given statement mathematically

= 4*3-3

= 12-3

= 9

Hence, 4 times 3 minus 3 is 9.

2. Applying 4 times table, check whether 4 times 6 plus 10 is 34?

Solution:

Let us write the given statement mathematically

= 4*6+10

= 24+10

= 34

Hence, Prooved.

3. If x times 4 = 40, then, find the value of ‘x’ using the Multiplication Table of 4?

Solution:

Given x*4 = 40

x = \(\frac { 40 }{ 4 } \)

= 10

Therefore, the value of x is 10.

4. Johny keeps all of his books on 6 shelves with 4 books on each shelf. Using the table of 4, find how many books does he have in his collection?

Solution:

Johny arranged 4 books on each shelf

No. of Books Johny keeps on 6 Shelves = 6*4

= 24

Therefore, Johny has 24 Books in his collection.

Math Tables are very important for primary school students and aspirants who are appearing for the competitive exams for quick mental math calculations. On this page, we have come up with the 11 Times Table. Eleven Times Table is the multiplication table of 11 where we get the product of multiplying 11 with whole numbers. Learning & memorizing Table of 11 is relatively easier.

The first 9 multiples of 11 table are always a repetition of the same digit like, 11 × 1 = 11, 11 × 2 = 22, 11 × 5 = 55, 11 × 79 = 99, etc. Go ahead and learn how to read and write the eleven times multiplication table, tips to remember the table of eleven, and download a free printable multiplication chart of 11.

Multiplication Chart of Eleven | 11 Times Table Chart

Table of 11 Chart is given here in an image form for better understanding and quick reference. Students can easily download the eleven times multiplication chart from here and try to memorize it regularly for doing quick multiplication of different quantities in day-to-day calculations and in competitive exams like GMAT and CAT. However, you can also have a quick revision of the 11 times table by downloading the chart and pasting it to your room walls.

Learn How to Write the Multiplication Table of 11 up to 20

Multiplication Table of Eleven up to 20 whole numbers are given in the below table for better learnings and fast calculations. 11 Table is very important to solve the maths problems based on division and multiplication operations. 11 Times Table can be helpful to do long mathematical calculations faster and improve your problem-solving skills. So, go through the below-provided Eleven Times Table and learn how to write mathematically.

11	x	1	=	11
11	x	2	=	22
11	x	3	=	33
11	x	4	=	44
11	x	5	=	55
11	x	6	=	66
11	x	7	=	77
11	x	8	=	88
11	x	9	=	99
11	x	10	=	110
11	x	11	=	121
11	x	12	=	132
11	x	13	=	143
11	x	14	=	154
11	x	15	=	165
11	x	16	=	176
11	x	17	=	187
11	x	18	=	198
11	x	19	=	209
11	x	20	=	220

Read First 10 Multiples of Eleven Times Table

One time eleven is 11

Two times eleven are 22

Three times eleven are 33

Four times eleven are 44

Five times eleven are 55

Six times eleven are 66

Seven times eleven are 77

Eight times eleven are 88

Nine times eleven are 99

Ten times eleven are 110

Tips to Remember the Table of Eleven

Students who are trying to memorize the 11th table can go with these tips to learn easily and remember the table of 11 for a long run.

1. The first tip to remember the table of eleven is simply multiple the single-digit whole number with 11 and get the multiple as the same number next to it. For example, take a single-digit number ie., 7 when you multiplied with 11 it gives 77. Like this, you can memorize the table of 11 up to 9 numbers.
2. The trick to memorize the multiplication table of 11 for 2 digit numbers is as follows:
   • When you take the 2 digit number multiplied by 11, the product should be in the pattern called the sum of the digits of the number and put the sum between the two digits of the original two-digit number.
   • For instance, when 11 is multiplied by 15, calculate the sum of 1 and 5, ie., 6, and take the number to place between 1 and 5. The final answer is 165. The product of 11 and 15 is 165, mathematically 11 × 15 = 165.

Get More Math Tables:

0 Times Table	1 Times Table	2 Times Table
3 Times Table	4 Times Table	5 Times Table
6 Times Table	7 Times Table	8 Times Table
9 Times Table	10 Times Table	12 Times Table
13 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

Solved Examples involving 11 Times Multiplication

1. Merra went to the government school and distributed 8 chocolates each to the kids in class 5. There were 11 kids in class 5. Use the 11 Times Table, find how many chocolates were distributed in total?

Solution:

Given that, there were 11 kids in class 5, and she distributed 8 chocolates each to the kids.

Hence, from the table of 11, 8 × 11= 88 chocolates

Thus, Merra distributed 88 chocolates in total.

2. Applying the multiplication table of 11, calculate the number which when multiplied to 11 gives 66?

Solution:

We know that when a number is multiplied by 1, it gives the same number.

So, we have to find the number that gives 66 when multiplied to 11.

By using the table of 11, 11 x 6 = 66

Therefore, the number is 6 which gives 66 when multiple to 11.

3. Use 11 times table, evaluate 11 times 5 minus 10  plus 20.

Solution:

First, write down 11 times 5 minus 10  plus 20 mathematically.

ie., 11 times 5 minus 10  plus 20 = 11 x 5 – 10 + 20

Now, apply the 11 times table, to get the result for 11 times 5 minus 10  plus 20

11 x 5 – 10 + 20 = 55 – 10 + 20 = 65

Thus, 11 times 5 minus 10  plus 20 is 65.

Multiplication Table of 6 provides the values we get when 6 is multiplied by all whole numbers. One Interesting Fact about Table of 6 is that it is the smallest positive integer that is neither a square number nor a prime number. Math Tables once mastered can be foundation blocks to learn higher-order concepts that you might come across in the later classes. Six Table can be interpreted as equal groups of 6 or repeated addition of 6.

6 Times Table Chart

Students who are facing difficulty learning the Six Table can always check the below image as a quick guide. Download the Multiplication Chart of Six from here and practice the table on a day-to-day basis. We don’t charge any amount from you and you can always seek help from the Multiplication Table for 6 to have a deeper knowledge on the process of multiplication.

How to Read Table of 6?

Refer to the following lines and learn how to read Six Times Table Orally. Try to Read out loud regularly and this way you can retain the Table of Six for a longer duration.

One time six is 6

Two times six is 12

Three times six is 18

Four times six is 24

Five times six is 30

Six times six is 36

Seven times six is 42

Eight times six is 48

Nine times six is 54

Ten times six is 60

Eleven times six is 66

Twelve times six is 72

How to Write a Multiplication Table of Six? | 6 Times Table up to 20

By checking out the Six Times Table present below in tabular format, you can learn how to write the Multiplication Table of 6. Use the table of 6 present here for speedy calculations and clear the competitive exams with much ease. You can always look up to us whenever you are stuck at some point while memorizing the 6 Times Multiplication Table.

6	x	1	=	6
6	x	2	=	12
6	x	3	=	18
6	x	4	=	24
6	x	5	=	30
6	x	6	=	36
6	x	7	=	42
6	x	8	=	48
6	x	9	=	54
6	x	10	=	60
6	x	11	=	66
6	x	12	=	72
6	x	13	=	78
6	x	14	=	84
6	x	15	=	90
6	x	16	=	96
6	x	17	=	102
6	x	18	=	108
6	x	19	=	114
6	x	20	=	120

Get More Math Tables:

0 Times Table	1 Times Table	2 Times Table
3 Times Table	4 Times Table	5 Times Table
7 Times Table	8 Times Table	9 Times Table
10 Times Table	11 Times Table	12 Times Table
13 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

Advantages of Learning Multiplication Table of 6

There are numerous benefits of referring to the 6 Times Table and they are listed in the below fashion

• Memorizing or Learning the Table of 6 is an essential skill to solve problems related to fractions, decimals, and percentages.
• You can solve real-life problems quickly whenever you are out of the classroom.
• Be aware of the Sequences and Patterns followed by the Six Table.

Tips to Memorize 6 Times Table

Follow the below-listed tips & tricks to learn the Multiplication Table of Six easily. They are as follows

• Multiples of 6 are both multiples of 2 and 3
• Whenever you multiply an even number with 6 the result will have the same unit digit i.e. 682 = 12, 6*4 = 24, 6*6 =36, and so on.
• You can also learn the Multiplication Table of 6 using the skip counting process.

Solved Examples Involving Six Table

1. Using the table of 6, evaluate 3 times 5 times 6?

Solution:

Firstly, let us express the given statement in the form of a mathematical expression

= 3*5*6

= 90

Therefore, 3 times 5 times 6 is 90.

2. Using the 6 times table, find 6 groups of 4?

Solution:

6 groups of 4 = 6+6+6+6 = 24

6 times 4 = 6*4 = 24

Thus, 6 groups of 4 is 24.

3. Using numbers 4, 6, 5, and 12 and table of 6 complete the multiplication sentences _×_ = 30 and _×_ = 36?

Solution:

Since, we know that 6 times 5 = 30 and 6 times 6 = 36.

Therefore, the numbers are 6, 5, and 6, 6 respectively.

4. Find the value of ‘a’ using the table of 6, If a × 6 = 72?

Solution:

We know from the 12 Times Table 12*6 = 72

Thus, the value of a is 12.

Every student should memorize and learn the 0 Times Table as it is the most easiest multiplication table. Among all the Math Tables Zero Table can be easily remembered. You can perform your math calculations much quickly and effectively. Grasp the basic maths fundamentals by memorizing the Multiplication Table of 0 by heart. Learn How to Read and Write Zero Multiplication Table, Solved Examples Involving Zero Table in the later modules.

Zero Multiplication Chart

Below we have provided the Multiplication Table of 0 both in Image and Tabular Format. You can download it from here and prepare offline too whenever you need it. By downloading the 0 Times Table you can recite it regularly and remember it easily. We don’t charge any amount from you for this and you can make your mental math calculations quickly.

How to read 0 Times Table?

One time zero is 0

Two times zero is 0

Three times zero is 0

Four times zero is 0

Five times zero is 0

Six times zero is 0

Seven times zero is 0

Eight times zero is 0

Nine times zero is 0

Ten times zero is 0

Eleven times zero is 0

Twelve times zero is 0

Multiplication Table of 0 up to 20

Below is the list of Zero Table up to 20 natural numbers. Utilize the table whenever you need to perform math calculations and make your job simple. Try to Memorize the Zero Table by reciting them on a regular basis or writing them down on paper.

0	×	1	=	0
0	×	2	=	0
0	×	3	=	0
0	×	4	=	0
0	×	5	=	0
0	×	6	=	0
0	×	7	=	0
0	×	8	=	0
0	×	9	=	0
0	×	10	=	0
0	×	11	=	0
0	×	12	=	0
0	×	13	=	0
0	×	14	=	0
0	×	15	=	0
0	×	16	=	0
0	×	17	=	0
0	×	18	=	0
0	×	19	=	0
0	×	20	=	0

Get More Math Tables

1 Times Table	2 Times Table	3 Times Table
4 Times Table	5 Times Table	6 Times Table
7 Times Table	8 Times Table	9 Times Table
10 Times Table	11 Times Table	12 Times Table
13 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

Solved Examples on Zero Multiplication Table

1. What is 0 times seven plus 6?

Solution:

Expressing Given Statement in the form of a mathematical expression we have

= 0*7+6

= 6

Therefore, 0 times seven plus 6 is 6

2. What is 0 times 4 minus 2 plus 5?

Solution:

Expressing the given statement in the mathematical form we have

= 0*4-2+5

= 0-2+5

= 3

Therefore, 0 times 4 minus 2 plus 5 is 3.

3. What is the value of 0 times 8 plus nine minus 4?

Solution:

Expressing the given statement in the mathematical form we have

= 0*8+9-4

= 0+9-4

= 5

The angle of depression is created when the observer is higher than the object he is looking at. If a person looks at an object that is located at a distance lower than the person, the angle is formed below the horizontal line drawn with the level of the eye of the person and line joining object with the person’s eye. This angle is calculated by using the concept of trigonometry. Get the definition, formulas, and example questions with answers in the below sections.

Angle of Depression – Definition

The angle of depression is the angle formed between the horizontal line and the observation of the object from the horizontal line. This angle of depression is used to find the distance between the two objects when the angles, object’s distance from the ground are known parameters. It is also defined as the angle that is constructed with the horizontal line if the line of sight is downward from the horizontal line.

If the object observed by the observer is below the level of the observer, then the angle created between the horizontal line and the observer’s line of sight is called the angle of depression. In the above figure, θ is the angle of depression.

Angle of Depression Formulas

With the angle of elevation, if you know two sides of the right triangle are known, then the formula of the angle of depression is

tan θ = \(\frac { Opposite Side }{ Adjacent Side } \)

θ = tan^-1 (\(\frac { Opposite Side }{ Adjacent Side } \))

Also, check

• Angle of Elevation
• Angles
• Pairs of Angles

Angle of Elevation and Angle of Depression

The angle of elevation and angle of depression are opposite to each other. The elevation angle is formed when it is between the line of sight and the horizontal line. And if the line of sight is above the horizontal line, then the angle is called the angle of elevation. In the angle of depression, the line of sight is downwards to the horizontal line.

∠ABO = ∠O = θ

Angle of Depression Problems

Example 1:

The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 60° and 30° respectively. Find (i) The height of the lamp post. (ii) The difference between the height of the lamp post and the apartment. (iii) The distance between the lamp post and the apartment.

Solution:

Triangle AED forms a right triangle

So, tan 60° = \(\frac { ED }{ AD } \)

√3 = \(\frac { ED }{ AD } \)

AD = \(\frac { ED }{ √3 } \) —- (i)

In trinagle ABC,

tan 30° = \(\frac { AB }{ BC } \)

\(\frac { 1 }{ √3 } \) = \(\frac { 66 }{ BC }\)

BC = 66√3 —- (ii)

Equating both equations

\(\frac { ED }{ √3 } \) = 66√3

ED = 66√3 (√3 )

ED = 66(3)

ED = 198

(i) Height of lamp post = ED + DC

= 198 + 66

= 264 m

(ii) The difference between height of the lamp post and the apartment

= 364 – 66

= 198 m

(iii) The distance between the lamp post and the apartment

BC = 66√3

= 66(1.732)

= 114.31 m

Example 2:

An airplane is flying at a height of 2 miles above level ground. The angle of depression from the plane to the foot of the tree is 15°. What is the distance the plane must fly to be directly above the tree?

Solution:

To find the distance BA use the tangent function

tan 15° = \(\frac { 2 }{ BA } \)

0.26794919243 = \(\frac { 2 }{ BA } \)

BA = \(\frac { 2 }{ 0.26794919243 } \)

BA = 7.464

So, the plane must fly 7.464 ft horizontally to be directly over the tree.

Example 3:

A buoy in the ocean is observed from the top of a 40-meter-high oil rig. The angle of depression from the top of the tower to the buoy is 6°. How far is the buoy from the base of the oil rig?

Solution:

Given that,

The angle of depression from the top of the tower to the buoy = 6°

A buoy in the ocean is observed from the top of a 40-meter-high oil rig.

Tan 6° = \(\frac { 40 }{ h } \)

h = \(\frac { 40 }{ tan 6° } \)

h = \(\frac { 40 }{ 0.105104 } \)

h = 380.6

It is approximately 380.6 m from the buoy to the base of the oil rig.

Example 4:

A lift in a building of height 90 feet with transparent glass walls is descending from the top of the building. At the top of the building, the angle of depression to a fountain in the garden is 60°. Two minutes later, the angle of depression reduces to 30°. If the fountain is 30√3 feet from the entrance of the lift, find the speed of the lift which is descending.

Solution:

In the diagram above, in the right triangle ABC,

tan 30° = \(\frac { Opposite side }{ adjacent side } \)

\(\frac { 1 }{ √3 } \) = \(\frac { BC }{ 30√3 } \)

1 x 30√3 = √3 x BC

BC = 30

DC = DB – CB

DC = 90 – 30

DC = 60 feet

So, the left has descended 60 ft in 2 minutes.

Speed = \(\frac { Distance }{ Time } \)

Speed = \(\frac { 60 }{ 2 } \)

Speed = 30 ft/min

Speed = \(\frac { 30 ft }{ 60 sec } \)

Speed = 0.5 ft/sec

So, the speed of the lift which is descending is 0.5 ft/sec.

In geometry, line, line segment, and ray are one-dimensional figures that have no thickness. All these have a set of points connected. We draw different shapes triangle, square, rectangle using these lines, line segments, and rays. Let us discuss the definitions of each one of them and the differences between them in the below sections of this page.

What is Line?

A line can be defined as a straight set of points that extend in opposite directions. It is a one-dimensional figure and does not have a thickness, end in both directions.

The different types of lines are horizontal lines, vertical lines, parallel lines, and perpendicular lines. The images of these types are provided here for a better understanding of the concept.

If a line moves from left to right in a straight direction, it is a horizontal line.

If a line moves from top to bottom in a straight direction, then it is called the vertical line.

When two or more straight lines do not intersect each other at any point, then those are called parallel lines. The points A, B, C, D are called the points on the lines.

If two lines meet at a point at right angles, then they are perpendicular to each other.

Also, Read:

Lines and Angles

Line Segment – Definition

A line segment is a part of a line that has two endpoints. geometric shapes such as triangle, polygon, square, pentagon, and others are made up of a different number of line segments. The measurement of the line segment is called the length. As the line segment has two endpoints, it can not be extended and it is easy to measure its length. The below picture shows the line segment with points x, y.

What is Ray?

Ray is a combination of line and line segments that has an infinitely extending en and the other is terminating end. Its length can not be measured because one end is non-terminating. It is represented by \(\overrightarrow{AB}\).

Differences Between Line Segment, Ray and Line

From the below table you can get acquainted with the key differences between Line, Line Segment and Ray. They are as follows

Line Segment	Line	Ray
The line segment has two endpoints.	The line has no endpoints.	It has one starting point and another near the arrowhead.
The length of the line segment is definite. So, it can be measured.	As it has no endpoints, the length cannot be measured.	Its length can’t be measured as one point has no endpoint.
The symbol is ______.	The symbol is ↔.	The symbol of the ray is →.

Learning tables from 1 to 20 is the most important part of elementary education. Every student is supposed to study 13 table as mathematics have most of the problems depending on it. Become perfect with all math tables by going through our complete article. Some of the students may feel it is very difficult to remember the multiplication table of 13 as the values are hard to remember. Get the tricks and tips to memorize the 13 times table, know how to read and write Thirteen Times Table.

13 Times Table Chart

13 times multiplication tables in table format and image format is given here. So, it makes it easy for you to remember the values. Download 13 table charts for free and prepare well. The 13th table is helpful to perform the multiplication of numbers easily. You can save your time in competitive eams by learning these multiplication tables.

How to Read 13 Table?

Check the reading of the 13 multiplication table here.

One time thirteen is 13.

Two times thirteen is 26.

Three times thirteen is 39.

Four times thirteen is 52.

Five times thirteen is 65.

Six times thirteen is 78.

Seven times thirteen is 91.

Eight times thirteen is 104.

Nine times thirteen is 117.

Ten times thirteen is 130.

Importance of Multiplication Tables

Multiplication tables play an essential role in mathematics. It is the foundation of elementary maths. By learning the table chart, you will get self-confidence while doing multiplications. You can keep the information at your fingertips that help you to solve the questions quickly. Multiplication tables will enhance your memory power and improve the calculations speed.

Tables from 2 to 20 help in performing the simple arithmetic operations. So that you can save time and do calculations easily. Without learning the 13 times table, you can also calculate the multiplicative of 13 by performing the arithmetic multiplication operations.

Multiplication Table of 13 up to 20

Studying 13 Multiplication Table is an essential skill to solve the division and multiplication questions. Check out the below table to know how to write a 13 times table chart.

13	x	1	=	13
13	x	2	=	26
13	x	3	=	39
13	x	4	=	52
13	x	5	=	65
13	x	6	=	78
13	x	7	=	91
13	x	8	=	104
13	x	9	=	117
13	x	10	=	130
13	x	11	=	143
13	x	12	=	156
13	x	13	=	169
13	x	14	=	182
13	x	15	=	195
13	x	16	=	208
13	x	17	=	221
13	x	18	=	234
13	x	19	=	247
13	x	20	=	260

Tips and Tricks to Learn 13 Times Table

Here we are giving the easy tips that are helpful to remember the 13th table. Follow the below tricks and learn the multiplication tables quickly.

• To remember the 13 times table, first, we need to memorize the 3 times table. So, the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, . . .
• For getting the multiples of 13, add natural numbers to the ten’s digit of the 3 multiples. Therefore, 13 times table is obtained as (1 + 0)3 = 13, (2 + 0)6 = 26 , (3 + 0)9 = 39, (4 + 1)2 = 52, (5 + 1)5 = 65, (6 + 1)8 = 78, (7 + 2)1 = 91, (8 + 2)4 = 104, (9 + 2)7 = 117, (10 + 3)0 = 130, . . .
• 13 does not have any rules that make the multiplication of 13 table easier to memorize, then there is a structure for every 10 multiples of 13. They are 13, 26, 39, 52, 65, 78, 91, 104, 117, 130. In all these multiples, the last digit i.e units place digit is repeating. So, one can remember this logic to memorize the table.

Get More Math Tables:

0 Times Table	1 Times Table	2 Times Table
3 Times Table	4 Times Table	5 Times Table
6 Times Table	7 Times Table	8 Times Table
9 Times Table	10 Times Table	11 Times Table
12 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

Solved Examples on 13 Times Table Multiplication

Example 1:

Using the table of 13, calculate 13 times 13 plus 13?

Solution:

From the given data

We can express the given data in the form of Mathematical Expression

= (13 x 13) + 13

= 169 + 13

= 182

Therefore, 13 times 13 plus 13 is 182.

Example 2:

If David’s father has to pay the amount “12 less than 13 times 15” in dollars. Using the table of 13, find how much he needs to pay?

Solution:

From the given data,

The mathematical expression of 12 less than 13 times 15 = (13 x 15) – 12

= 195 – 12

= 183

therefore, David’s father is required to pay $183.

Example 3: 

Families in a colony are going on a picnic. If 13 people ride in each car and there are 5 cars, then how many people are going on a picnic?

Solution:

Given that,

The number of people going on picnic = 13

Number of cars = 5

Then, multiply the number of people on each car, total number of cars on the picnic to get the total number of persons going for the picnic.

The number of persons going on the picnic = 13 x 5

= 65

Therefore, 65 people going on a picnic.

Example 4:

Using the 13 times table, check whether 13 times 7 minus 1 plus 10 is 100?

Solution:

Firstly, let us express the given statement in the form of mathematical expression

13 times 7 minus 1 plus 10 = (13 x 7) – 1 + 10

= (91) + 9

= 100

Hence, 13 times 7 minus 1 plus 10 is 100.

Memorizing the Math Tables 0 to 25 you can do quick computations and save a lot of time. It is advised for Students to by heart the Multiplication Tables to have a stronger foundation of basics right from an early age. Refer to the complete guide and learn the Tips & Tricks to Memorize the Multiplication Tables. Know why one should learn these Math Tables as a part of their learning.

Multiplication Tables for 0 to 25

Below is the list of Math Tabes for 0 to 25 to make your math calculations easier and faster. These Time Tables from 0 to 25 help your child to skillfully tackle complex problems too with ease. Remembering the Multiplication Tables not just brings out self-confidence in you but also keeps information prepared at your fingertips so that you can use it whenever required. On Mastering the 0 to 25 Multiplication Charts children can enhance their speed and accuracy.

Maths Tables 0 to 25
0 Times Table	1 Times Table
2 Times Table	3 Times Table
4 Times Table	5 Times Table
6 Times Table	7 Times Table
8 Times Table	9 Times Table
10 Times Table	11 Times Table
12 Times Table	13 Times Table
14 Times Table	15 Times Table
16 Times Table	17 Times Table
18 Times Table	19 Times Table
20 Times Table	21 Times Table
22 Times Table	23 Times Table
24 Times Table	25 Times Table

Importance of Math Tables or Multiplication Tables

Math Tables are the basic blocks of arithmetic calculations. Learning these Multiplication Tables can stimulate the memory power in kids and develop observation skills. Things learned at an early age can be retained for a long time. Refer to the below modules to know why one should learn Maths Tables and they are as such

• Multiplication Tables are quite important as they support in student’s mathematical learning.
• Students can get a strong grasp of facts associated with multiplication.
• Makes it easier to solve problems in Mathematics.
• The one who tends to be good at these Times Tables will be self-confident while learning new math concepts.

Tips to Memorize Multiplication Times Tables

Most of you might struggle to memorize the math tables. However, we have curated few effective tips that help you to learn the Math Times Tables easily. They are in the following fashion

• Practice Skip Counting i.e. if you start with a number 2 keep adding 2 every time you count. That is you would say 2, 4, 6, 8, 10, 12, 14…..
• Recite the multiplication tables in order at least once a day until you remember them. Also, learn reverse recitation of tables.
• If you have any difficulty in remembering you can always opt for writing and memorizing. Make it a habit in your daily routine and try to memorize once.
• Apply multiplication tables to real life and try to understand them using real-life scenarios.
• Identify the Multiplication Table Patterns so that you can remember them much faster.

Learn 2 to 9 Times Multiplication Tricks

FAQs on Maths Times Tables

1. What is the easiest way to memorize the multiplication tables?

One of the easiest ways to memorize the Math Tables is through addition. We know the number of times a number is multiplied with another number it is added to itself the same number of times repeatedly.

2. How to memorize Multiplication Times Table?

In order to memorize the Multiplication Times Table start reciting it verbally on a regular basis or write it down on paper. In fact, you can solve questions involving multiplication charts to retain them for a long time.

 3. How Can I Learn Tables Fast?

Start with the easiest ones and then work on them until you feel confident. Learn the Tips & Tricks to memorize the Math Tables easily. Recite them as many times as possible or write to remember them fast.

Students are advised to learn the Multiplication Table of 3 for quick calculations. 3 Times Table is the multiplication table of prime number 3 with other whole numbers. Table of 3 can be easily found using the repeated addition. Math Tables proves to be an excellent brain activity for kids right from an early age. Check How to Read and Write 3 Times Multiplication Chart, Tips to Remember the Three Table. Learn to solve problems involving Multiplication Table of 3 by referring to the complete article.

3 Times Multiplication Chart

Learning Table of 3 is quite essential to do your math calculations in a much faster way. Utilize the Table of 3 to understand and gain a deeper insight into the multiplication operation. For your idea, we have given the 3 Times Multiplication Table in image format. You can download and save it without paying us a single penny. Use this Table of 3 Chart for quick reference and try to recite it every day and memorize it easily.

How to Read Three Times Multiplication Table?

One time three is 3

Two times three is 6

Three times three is 9

Four times three is 12

Five times three is 15

Six times three is 18

Seven times three is 21

Eight times three is 24

Nine times three is 27

Ten times three is 30

Eleven times three is 33

Twelve times three is 36

How to write a Multiplication Table of 3? | Three Times Table upto 20

Learn how to write Table of 3 by checking out the below table. We have outlined the 3 Times Table up to 20 natural numbers so that you can get deeper knowledge on the multiplication which would be beneficial in the long run.

3	x	1	=	3
3	x	2	=	6
3	x	3	=	9
3	x	4	=	12
3	x	5	=	15
3	x	6	=	18
3	x	7	=	21
3	x	8	=	24
3	x	9	=	27
3	x	10	=	30
3	x	11	=	33
3	x	12	=	36
3	x	13	=	39
3	x	14	=	42
3	x	15	=	45
3	x	16	=	48
3	x	17	=	51
3	x	18	=	54
3	x	19	=	57
3	x	20	=	60

Why should you Learn the Multiplication Table of 3?

Go through the below lines to know the importance of the Three Table. They are along the lines

• Learning the Table of 3 is a necessary skill to solve problems on long division and multiplication.
• You can perform your metal math calculations right in your head and improve your problem-solving skills.
• By Learning the Multiplication Table of 3, you can understand the pattern of multiples.
• Ensures faster calculations and saves a lot of time.

Tips to Memorize 3 Times Table

Follow the below-listed tips & tricks to keep in mind to learn and memorize the Multiplication Table of 3. They are in the below fashion

• • • • Apparently, there are any rules that make the table of 3 easy to remember. However, there is a pattern for every 10 multiples of 3 i.e. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
      • The last digit of these multiples will always repeat. You can remember these digits to memorize the multiples of 3 easily.
      • Another way to learn 3 up to 10 is through skip counting.

    

By referring to the above image you can understand that the units digit are nothing but counting numbers written three in one column in descending order from right to left. 0 is left outside the grid. Later, place the digit 0 before the units digit in row 1 and digit 1 in the second row and digit 2 in the third row. Also, place 3 before the digit 0 outside the grid. That’s it you have got the first ten multiples of 3.

Get More Math Tables:

0 Times Table	1 Times Table	2 Times Table
4 Times Table	5 Times Table	6 Times Table
7 Times Table	8 Times Table	9 Times Table
10 Times Table	11 Times Table	12 Times Table
13 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

Solved Examples Involving 3 Times Table

1. Using 3 times table, evaluate 3 times 6 minus 3?

Solution:

From the given statement we can write the mathematical expression as follows

= 3*6-3

= 18-3

=15

Thus, 3 times 6 minus 3 is 15

2. Using the table of 3, Find the value of 3 plus 3 times 7 minus 5?

Solution:

First, let us write 3 plus 3 times 7 minus 5 mathematically

= 3+3*7-5

= 3+21-5

= 24-5

= 19

Hence, 3 plus 3 times 7 minus 5 is 19

3. Find the value of 4 plus 3 times 6?

Solution:

Let us write the given statement mathematically

= 4+3*6

= 4+18

= 22

Hence, 4 plus 3 times 6 is 22

4. Using the table of 3, find the value of 3 times 5 minus 3 times 2?

Solution:

Let us write the given statement mathematically

= 3*5-3*2

= 15-6

=9

Hence, 3 times 5 minus 3 times 2 is 9.

Maths is completely tips and tricks and Multiplication Table of Two is no more different. Learning Multiplication Chart of 2 is important as it makes mental maths easier. You can attempt complex problems too easily with confidence if you know the Table of Two. Learn the Tips & Tricks to Memorize the Multiplication Table of 2, How to Read and Write 2 Times Table. Also, Read Solved Examples Involving 2 Table for a better understanding of the concept.

Multiplication Table of 2

Here is the Multiplication Chart of Two in image format. Use it as a quick reference to make your mental math calculations much easier. Learning Table of 2 Promotes a better understanding of the multiplication operation. Knowing the basic math tables you can solve the maths problems in no time. You can save a lot of time in your competitive exams by learning the 2 Times Multiplication Table.

How to Read Table of Two?

One time two is 2

Two times two is 4

Three times two is 6

Four times two is 8

Five times two is 10

Six times two is 12

Seven times two is 14

Eight times two is 16

Nine times two is 18

Ten times two is 20

Eleven times two is 22

Twelve times two is 24

Multiplication Table of Two upto 20 | How to Write 2 Times Table?

Below is the Table of 2 up to 20 Natural Numbers. You can avail the Multiplication Table of Two here and use it whenever you need to perform quick calculations. Refer to the 2 Times Table over here to memorize it quickly and recite it on a regular basis so that you can retain it for a long time.

2	x	1	=	2
2	x	2	=	4
2	x	3	=	6
2	x	4	=	8
2	x	5	=	10
2	x	6	=	12
2	x	7	=	14
2	x	8	=	16
2	x	9	=	18
2	x	10	=	20
2	x	11	=	22
2	x	12	=	24
2	x	13	=	26
2	x	14	=	28
2	x	15	=	30
2	x	16	=	32
2	x	17	=	34
2	x	18	=	36
2	x	19	=	38
2	x	20	=	40

Get More Math Tables:

0 Times Table	1 Times Table	3 Times Table
4 Times Table	5 Times Table	6 Times Table
7 Times Table	8 Times Table	9 Times Table
10 Times Table	11 Times Table	12 Times Table
13 Times Table	14 Times Table	15 Times Table
16 Times Table	17 Times Table	18 Times Table
19 Times Table	20 Times Table	21 Times Table
22 Times Table	23 Times Table	24 Times Table
25 Times Table

How to Learn Multiplication Table of Two?

Table of 2 is quite basic and one of the easiest tables to learn and memorize. Let us learn how to obtain and memorize the multiplication table of 2 in the below sections. Basic things to observe in the Multiplication Table of Two are as such

• 2 Times Table follows the pattern 2, 4, 6, 8, 0 in the units place.
• It will always have even numbers
• It is simple as we can learn using skip counting i.e. 2, 4, 6, 8, 10, 12……

Tips to Memorize Two Times Table

Follow the tips & tricks to memorize the multiplication table of 2 by referring to the below modules. They are along the lines

• Two Times Table always follows the pattern of the even numbers i.e. 2, 4, 6, 8, 10, ….
• Another simple way to memorize the Table of Two is through addition.
• You can memorize the Two Table taking the help of the 1 Times Table. All you have to do is simply add the natural numbers to multiples of 1 to get the Two Table.
  • 1×1+1 = 2
  • 1×2+2 =4
  • 1×3+3 =6
  • 1×4+4 =8
  • 1×5+5=10
  • 1×6+6 =12
  • 1×7+7=14
  • 1×8+8=16
  • 1×9+9=18
  • 1×10+10=20 and so on.

Solved Examples Involving Multiplication Table of 2

1. If Reethu eats 2 chocolates per day, Using the table of 2 find how many chocolates will she have eaten at the end of the 5th day?

Solution:

Reetu eats a number of chocolates per day = 2

Number of Chocolates Reethu eats at the end of the 5th day = 2*5

= 10

Therefore, Reethu eats 10 chocolates at the end of the 5th day.

2. Using 2 times table, find 2 times 3 times 4 times 2?

Solution:

Expressing the given statement in the form of mathematical expression we have

= 2*3*4*2

= 48

Therefore, 2 times 3 times 4 times 2 is 48.

3. James wants to buy 6 Pencils. If the cost of one Pencil is $2, using the table of 2, find the cost of 6 Pencils?

Solution:

The Cost of one Pencil is $2

No. of Pencils James wants to buy = 6

Cost of 6 Pencils = $2*6

= $12

Therefore, the cost of 6 Pencils is $12.

Need instant homework help in calculating the Mass and Weight unit conversions? Don’t get stress as we have come up with a helpful article ie., Units of Mass and Weight Conversion Chart. We all know how conversions are important in calculating the unit of measurements in real-life things. So, to make you learn thoroughly about the Mass and Weight Unit Conversions, we have shared the conversion chart table below.

Take a look at the table and calculate all kinds of mass and weight conversion problems. Also, you can learn more about unit conversions such as length, capacity, time, etc. from our article ie., Math Conversion Chart. Moreover, you can also find some worked-out examples and faqs on the Units of Mass and Weight Conversion Table.

Conversion Chart for Units of Mass and Weight

Different Units of Mass and Weight Conversions are tabulated here that you can make use of the most while calculating the mass and weight unit conversions. Have a glance at the below-tabulated Units of Mass and Weight Conversion Chart and utilize them as per your requirements.

Unit Name	Relation to kilogram [kg]
assay ton [AT][long]	0.0326666666666667 [kg]
assay ton [AT][short]	0.0291666666666667 [kg]
atomic unit of mass	9.10938E-31 [kg]
bag [Portland cement, Canada]	39.689332375 [kg]
bag [Portland cement, US]	42.63768278 [kg]
bag coffe	60 [kg]
barge	2.041166E+4 [kg]
carat [kt]	2.591956E-4 [kg]
carat [metric]	2E-4 [kg]
cental	45.359237 [kg]
chalder	2692.52 [kg]
clove	3.62873896 [kg]
crith	8.9885E-5 [kg]
dram [dr][apothecary]	0.0038879346 [kg]
dram [dr][apothecary]	0.0017718451953125 [kg]
firkin	25.40117272 [kg]
flask	34.7 [kg]
gamma	1E-9 [kg]
geepound	14.5939 [kg]
grain [gr]	6.479891E-5 [kg]
gram [g]	0.001 [kg]
milligram [mg]	1E-6 [kg]
kilogram [kg]	1 [kg]
gros	0.0102 [kg]
hundredweight [long]	50.80234544 [kg]
hundredweight [short]	45.359237 [kg]
hyl [cgs]	9.80665 [kg]
international unit [ui]	1.515152E-9 [kg]
jin [China]	0.5 [kg]
kip [kip]	453.59237 [kg]
last [General]	1814.36948 [kg]
last [US]	1981.29147216 [kg]
liang [China]	0.05 [kg]
mark	0.2488278144 [kg]
metric ton	1000 [kg]
mic	1E-9 [kg]
millier	1000 [kg]
mite	3.239946E-6 [kg]
mite [metric]	5E-5 [kg]
myriagram [myrg]	10 [kg]
ounce [oz][apothecary]	0.0311034768 [kg]
ounce [oz av][avoirdupois]	0.028349523125 [kg]
ounce [oz][troy]	0.0311034768 [kg]
pennyweight [pwt]	0.00155517384 [kg]
point	2E-6 [kg]
pound [lb av][avoirdupois]	0.45359237 [kg]
pound [lb][metric]	0.5 [kg]
pound [lb t][troy]	0.3732417216 [kg]
quarter [informal]	254.0117272 [kg]
quarter [imperial]	12.70058636 [kg]
quartern	1.587573295 [kg]
quintal [q][metric]	100 [kg]
quintal [q]	45.36 [kg]
rebah	0.00408233133 [kg]
sack [Canada]	39.689332375 [kg]
sack [US]	42.63768278 [kg]
sack of flour	45.36 [kg]
scruple [s ap][apothecary]	0.0012959782 [kg]
sheet	6.479891E-4 [kg]
shekel	0.01632932532 [kg]
slinch	175.1268 [kg]
slug	14.5939 [kg]
stone [st]	6.35029318 [kg]
ton [t]	1000 [kg]
tonne [long]	1016.0469088 [kg]
tonne [metric]	1000 [kg]
tonne [short]	907.18474 [kg]
troy	0.3732417216 [kg]
truss	25.40117272 [kg]
wey	114.30527724 [kg]

Mass Metric Conversion Chart

Mass is used to measure the weight of an object. In the metric system of measurement, the most common units of mass are the gram and kilogram.

Metric		US or Imperial
1 milligram [mg]		0.0154 grain
1 gram [g]	1,000 mg	0.0353 oz
1 kilogram [kg]	1,000 g	2.2046 lb
1 tonne [t]	1,000 kg	1.1023 short ton
1 tonne [t]	1,000 kg	0.9842 long ton

Solved Examples on Mass and Weight Unit Conversions

1. Calculate the conversion of 650 g into kilograms.

Solution:

We know 1 Gram = \(\frac { 1 }{ 1000 } \) Kilogram

650 g = \(\frac { 650 }{ 1000 } \) kg

650 g = 0.65 kg

Hence, 650 g converted to kilograms if 0.65 kg.

2. Convert 87 decigram into grams.

Solution:

87 dg = \(\frac { 87 }{ 10 } \) g

= 8.7 g

3. Find the conversion of 6.9 kg into dag.

Solution:

6.9 kg = 6 kg + 900 g

We know, 1 dag = 10 g

So, 6900 g = \(\frac { 6900 }{ 10 } \) dg

= 690 dag

4. Convert 75 cg into dg.

Solution:

We know 1 dg = 10 cg

So, 75 cg = \(\frac { 6900 }{ 10 } \) dg

= 7.5 dg

Therefore, 75 cg converts into 7.5 dg

FAQs on Units of Mass and Weight Conversion Chart

1. What are the units of measurement for mass and weight?

In the International System of Units (SI), the basic unit of mass is the kilogram. The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton.

2. What is the weight of a 200g mass?

The Weight of a 100 G Mass has a magnitude (0.2 Kg)(9.8 M/s). Hence, the result is 2 N.

3. How do you calculate mass from weight?

In order to calculate the mass of an object using its weight, the formula is M = W ÷ G (where W is weight and G is Acceleration of Gravity).

In the earlier grades, you must have learned about the division of natural numbers and whole numbers. Fractions are expressed in ratios where numerator and denominator are integers and not equal to zero. Here, we have mentioned the Division of Fractions by using different methods along with examples. Fractions Division is a bit difficult so we have provided an easy and alternative method to perform Division of Fractions. Rather than doing division, you can perform multiplication as it is quite simple in comparison.

Refer to the procedures on how to divide fractions using different methods. For better understanding, we even provided solved examples for a better understanding of the concept.

What is meant by Dividing Fractions?

Dividing Fractions is simply a multiplication of fractions by reversing one of the two fractions or by writing the reciprocal of one of the fractions. If a fraction is given as a/b, then the reciprocal is b/a and is obtained by interchanging the numerator and denominator with each other.

How to Divide Fractions?

Division of Fractions are classified into three different ways and they are as such

• Dividing fractions by a fraction
• Dividing fractions by whole number
• Dividing fractions by mixed fraction

Continue reading the further modules to learn about all three procedures in a detailed way.

Dividing Fraction by a Fraction

Refer to the Procedure of dividing fractions by converting them into a multiplication of fractions. The procedure is as follows

• Write the Reciprocal of Second Fraction and then multiply with the first fraction number.
• Multiply the Numerators and Denominators of both the fractions.
• Simplify the fraction if possible.

If \(\frac { a }{ b } \), \(\frac { c }{ d } \) are two fractions then

\(\frac { a }{ b } \) ÷ \(\frac { c }{ d } \) = \(\frac { a }{ b } \)*\(\frac { d }{ c } \)

= \(\frac { (a×d) }{ (b×c) } \)

= \(\frac { (ad) }{ (bc) } \)

From the above expressions it is clear that we divided \(\frac { a }{ b } \) with \(\frac { c }{ d } \) and then rewrote the same as multiplication of reciprocal of second term i.e. \(\frac { c }{ d } \). Later multiply both the numerators a,d and denominators b,c.

Dividing Fraction by a Whole Number

Division of Fractions with the Whole Number is quite simple. Go through the procedure below to learn how to divide fractions with a whole number. They are along the lines

Step 1: In the first step, change the whole number to a fraction by placing the denominator value 1.

Step 2: Take the Reciprocal of a Number

Step 3: Multiply the fractional value with the given fraction.

Step 4: Simplify the obtained result if possible.

Example:

Divide 3/10 with 5?

Solution:

Given Whole Number is 5

Convert it to a fraction by placing the numerator value as it is  and the denominator as 1 i.e. \(\frac { 5 }{ 1 } \)

Take the reciprocal of it i.e. \(\frac { 1 }{ 5 } \)

Multiply \(\frac { 3 }{ 10 } \) and \(\frac { 1 }{ 5 } \) i.e. \(\frac { 3 }{ 10 } \) *\(\frac { 1 }{ 5 } \)

= \(\frac { 3 }{ 50 } \)

Dividing Fractions by a Mixed Fraction

Process of Dividing fractions by a mixed fraction is similar to dividing fraction by fraction. The Procedure to follow for fractions by a mixed fraction are given in the below modules. They are as such

Step 1: In the initial stage convert the given mixed fraction to improper fraction

Step 2: After that, take the reciprocal of the given improper fraction

Step 3: Multiply the obtained fraction with the given fraction

Step 4: Simplify the resultant fraction to possible extent.

Example:

Divide \(\frac { 3 }{ 4 } \) and 5 \(\frac { 1 }{ 2 } \)?

Solution:

Given Mixed Fraction is 5 \(\frac { 1 }{ 2 } \)

Convert it to Improper Fraction i.e. \(\frac { 11 }{ 2 } \)

Take the reciprocal of improper fraction \(\frac { 11 }{ 2 } \) i.e. \(\frac { 2 }{ 11 } \)

Multipy \(\frac { 3 }{ 4 } \) and \(\frac { 2 }{ 11 } \) i.e. \(\frac { (3*2) }{ (4*11) } \)

= \(\frac { 6 }{ 44 } \)

Simplifying it further we get \(\frac { 3 }{ 22 } \)

FAQs on Dividing Fractions

1. What are the basic arithmetic operations performed on Fractions?

The Basic Arithmetic Operations performed on Fractions are

• Addition
• Subtraction
• Multiplication
• Division

2. What is meant by dividing fractions?

Dividing a fraction by another fraction is the same as multiplying the fraction by the reciprocal (inverse) of the other.

3. What are the 3 Rules for Dividing Fractions?

The rules to keep in mind while dividing fractions are as follows

• Flip the divisor into a reciprocal.
• Change the division sign into a multiplication sign and multiply.
• Simplify if possible.

4. What are the different methods in Dividing Fractions?

Dividing Fractions are classified into three different methods and they are as follows

• Dividing fractions by a fraction
• Dividing fractions by whole number
• Dividing fractions by mixed fraction