Category: Maths Notes PPT

The lateral faces (triangles) of a pyramid meet at a common point known as the vertex. A pyramid’s name is derived from the name of the polygon that defines its base. A square pyramid, a rectangular pyramid, a triangular pyramid, a pentagonal pyramid, a hexagonal pyramid, and so on are examples of pyramids.

Let’s discuss the hexagonal pyramid in details,

A hexagonal pyramid is a pyramid with a hexagonal base and six isosceles triangular faces that intersect at a point in geometry (the apex). It is self-dual, just like any other pyramid. C6v symmetry is found in a right hexagonal pyramid with a regular hexagon base. A right regular pyramid has a regular polygon as its base and an apex that is “above” the centre of the base, creating a right triangle with the apex, the centre of the base, and every other vertex. It is also known as Heptahydron.

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Hexagonal Pyramid Formula

A  pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height (h) is a special case of the formula for a regular n-gonal pyramid with n = 6.

The formula of the base area of a hexagonal pyramid is,

b = 3 x a x b

where a is the length of a side of the base. The hexagon volume formula is,

V = a x b x h

and the hexagonal surface area formula is,

S = (3 x a x b) + (3 x b x s)

Where,

a is apothem length of the pyramid.

b is the base length of the pyramid.

s is the slant height of the pyramid.

h is the height of the pyramid.

Examples for Hexagonal Pyramid

Ex.1.  Find The Base Area, The Surface Area of Hexagon And Volume of A Hexagonal Pyramid of Apothem Length 3 Cm, Base Length 6 Cm, Height 8 Cm And Slant Height 14 Cm?

Answer: 

Given,

a = 3 cm

b = 6 cm

h = 8 cm

s = 14 cm

Base area of a hexagonal pyramid

b = 3 x a x b

= 3 × 3 cm × 6 cm

= 54 cm²

Surface area of hexagon pyramid

S = (3 x a x b) + (3 x b x s)

= (3 × 3 cm × 6 cm) + (3 × 6 cm × 14 cm)

= 54 cm² + 252 cm²

= 304 cm²

Hexagon volume formula is,

V = a x b x h

= 3 cm × 6 cm × 8 cm

= 144 cm³

Hence, the Base area of a hexagonal pyramid is 54 cm²

The  surface area of hexagon pyramid is 304 cm²

The volume of a hexagonal pyramid is 144 cm³

Ex.2. Find The Height of A Hexagonal Pyramid When The Volume (V) of A Pyramid is 169 cm³, the base (b) length of the pyramid is 9cm and the apothem (a) length of the pyramid is 7cm?

Answer: 

Given,

a = 7 cm

b = 9 cm

h = ? 

V = 169 cm³

Now, use the volume formula to find the height of a hexagonal pyramid.

V = a x b x h

169 = 7 x 9 x h

Hence,

h = 169/63

h = 2.68 cm 

The height of a hexagonal pyramid is 2.68cm.

S.No

Inverse Trigonometry Class 12 Formulas

1

sin-1 (-x) = -sin-1(x), x ∈ [-1, 1]

2

cos-1(-x) = π -cos-1(x), x ∈ [-1, 1]

3

tan-1(-x) = -tan-1(x), x ∈ R

4

cot-1(-x) = π – cot-1(x), x ∈ R

5

sec-1(-x) = π -sec-1(x), |x| ≥ 1

6

cosec-1(-x) = -cosec-1(x), |x| ≥ 1

7

sin-1x + cos-1x = π/2 , x ∈ [-1, 1]

8

sin-1(1/x) = cosec-1(x), if x ≥ 1 or x ≤ -1

9

cos-1(1/x) = sec-1(x), if x ≥ 1 or x ≤ -1

10

tan-1x + cot-1x = π/2 , x ∈ R

11

tan-1(1/x) = cot-1(x), x > 0

12

tan-1 x + tan-1 y = tan-1((x+y)/(1-xy)), if the value xy < 1

13

tan-1 x – tan-1 y = tan-1((x-y)/(1+xy)), if the value xy > -1

14

2 tan-1 x = sin-1(2x/(1+x2)), |x| ≤ 1

15

sec-1x + cosec-1x = π/2 ,|x| ≥ 1

16

3sin-1x = sin-1(3x-4x3)

17

sin(sin-1(x)) = x, -1≤ x ≤1

18

3cos-1x = cos-1(4x3-3x)

19

cos(cos-1(x)) = x, -1≤ x ≤1

20

3tan-1x = tan-1((3x-x3)/(1-3x2)

21

tan(tan-1(x)) = x, – ∞ < x < ∞

22

sec(sec-1(x)) = x,- ∞ < x ≤ 1 or 1 ≤ x < ∞

23

cosec(cosec-1(x)) = x, – ∞ < x ≤ 1 or -1 ≤ x < ∞

24

cot(cot-1(x)) = x, – ∞ < x < ∞

25

sin-1(sin θ) = θ, -π/2 ≤ θ ≤π/2

26

cos-1(cos θ) = θ, 0 ≤ θ ≤ π

27

tan-1(tan θ) = θ, -π/2 < θ < π/2

28

sec-1(sec θ) = θ, 0 ≤ θ ≤ π/2 or π/2< θ ≤ π

29

cosec-1(cosec θ) = θ, – π/2 ≤ θ < 0 or 0 < θ ≤ π/2

30

cot-1(cot θ) = θ, 0 < θ < π

Tips and Tricks to Memorise Table of 3

• The foremost tip is to read the Table Chart of 3 out loud and repeat the same until you have achieved a stage where you can see the numbers 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 in that order by closing your eyes.

• To remember the 3’s table pattern up to 10, look at the numbers given in the box below. You can recognise that in tables written in 3 × 3 or 3 × 4, the tens digit (blue coloured number) is increased by 1 and the unit digit (black coloured number)  is decreased by 1.

For example: 12, 15, 18 or 30, 33, 36.

How to Solve Questions Based on Table 3?

In this section, we are going to solve a few questions that can appear in the form of word problems, multiple choice, or numericals.

Word Problems on Table 3 with Practice Questions

Question 1: Bittu reads 3 pages a day, how many pages can he read in a week?

Solution:       

Here, in a day Bittu reads 3 pages.

So, 1(day) × 3(pages)= 3(pages)

Number of days in a week is 7.

So, in 7 days, Bittu can read 7(days) × 3(pages) = 21 pages.

Hence, Bittu can read 21 pages in a week.

Question 2: Solve the given puzzle using Table of 3.

A number is part of the Table of 3, which is greater than 10 and less than 20. If we sum 6 three times the number will be _______.

Solution:

From the table chart of 3, 6 times 3 is 18.

Hence, the number is 18.

Practice Questions

Question 1: If 1 basket contains 3 apples, how many apples will be there in 15 baskets?

Answers: 45.

Question 2: Find the 2 digit numbers, which are present in Table of 3 and they are less than 18.

Answer: 12, 15

MCQs on Table 3 with Practice Questions

Question: 

1. What is 7 times 3?

1. 20

2. 31

3. 17

4. 21

Solution: (d)

7 times 3 is 3 x 7 = 21.

Practice Question

Question:

1. Jack drives his bike 10 km per day to his office. What is the total distance he covers from his home to the office for the next 3 days?

1. 33 kms

2. 27 kms

3. 30 kms

4. 41 kms

Answer: (c)

 

Table Chart of 3 from 11 to 20

To keep the multiple of 3 on your tips, it is useful if you can remember the table from 11 to 20 as well. Refer to the image given below, the same is provided in the PDF, which can be easily downloaded and printed.

For Parent/Teacher: How to Read the Table to Your Kid?

A kid can easily remember his/her name due to repetition or occurrence of the name multiple times throughout the day. Similarly, there is a way the table should be read to your kid. 

It can become a new rhyme/song that you repeat in the morning or play on your devices.

Read the table in front of your kid and ask them to repeat after you.

Considering the importance of Table of 3, we have provided the PDF containing multiplication table up to 20. To access the PDF, students can click on ‘Download PDF’ and use it whenever they need it.

This will certainly  help students in keeping the table of 3 at their fingertips and improve their efficiency at mathematical calculations.

Remember the trick to master the multiplication table is repetition and practice.

Multiplication is nothing but the process of repetitive addition. 

For example,

• 2 times 19 is 39 which is equal to 19 + 19.

• Similarly, when we add 19 five times, the result will be 95, i.e., 19+19+19+19+19.

• Also, the number 19 is a prime number which is only divisible by 1 and the number itself. 

Tips and Tricks to Memorise Table of 19

Though reading a table aloud is the best way to learn any table. But, as we promise, here are some tricks to remember the table easily. 

Trick 1: Odd numbers and reversing method

Step 1: Write the odd numbers from 1-19 in the following manner:

 

Step 2: Next, we will write the numbers from 0 to 9 from bottom to top beside the numbers written in step 1:

 

So, this is our 19th table.

We have many other ways to write tables of 19, so let us try those:

Trick 2: Addition and Subtraction Method

Method 1: Addition: From table 17 and 18

 

Method 2: Subtraction: From 20 Times Table

How to Solve Questions Based on Table 19?

In this section, we are going to solve a few questions that can appear in the form of word problems and multiple choice.

Word Problems Based on Table 19 with Practice Questions

Example 1: Evaluate using 19 times table: 19 times 8 times 9

Solution:

First, we’ll do a mathematical calculation of 19 times 8 times 9.

We have: 19 times 8 times 9 = 19 x 8 x 9 = 1368 using the table of 19.

As a result, 19 times 8 times 9 equals 1368.

Example 2: If one coconut candy costs ten cents, how much would 19 coconut candies cost if you used the table of 19?

Solution: Because one candy equals ten cents, therefore 19 coconut candies cost = 19 candies x 10 cents = 190 cents 

As a result, 19 coconut candies cost 190 cents.

Example 3: Robert is attempting to add the first five multiples of 19 together. Let’s use the table of 19 to assist Robert in computing the same.

Solution: The first five multiples of 19 are given as follows:

19 × 1 = 19

19 × 2 = 38

19 × 3 = 57

19 × 4 = 76

19 × 5 = 95

Therefore, by adding the multiples 19 + 38 + 57 + 76 + 95, we get the result as 285. Thus, the sum is 285.

Practice Questions

Question 1: If 1 basket contains 3 bananas, how many bananas will be there in 19 baskets?

Question 2: Tappu reads 3 pages a day, how many pages can he read in a week?

MCQs on Table 19 with Practice Questions

Question: 

What is 7 times 19?
a) 201
b) 133
c) 104
D) 145

Solution: (b)

7 times 19 is 7 x 19 = 133

Practice Question

Question:

Bhide drives his scooter 10 km per day to take tuition. What is the total distance he covers from his home to the tuition centre for the next 19 days?

a) 330 km
b) 190 km
c) 100 km

d)109 km

Table Chart of 19 from 11 to 20

It is useful if you can remember the table of 19 from 11 to 20. Refer to the image given below, the same is provided in the PDF, which can be easily downloaded and printed.

For Parents/Teachers: Way to Read the Table out to Your Kids

The contents of the multiplication table of 19 can be read out to children in a simple way. The more children hear themselves talk, the better they will recall the knowledge, and the table of 19 will become easier for them to remember. The following chart will make the articulation of the table easier for your kids.

Multiplication games are a pleasant and enjoyable way for kids to learn the multiplication table of 19 in a fun and engaging way. Play hide and seek with your child, but instead of numbering sequentially, have them skip count in 19s. Alternatively, you and your child can play a table of 19 matching games. On one set of flashcards, write the questions for the 19 times table, and on the other set, write the answers. Ask your child to shuffle both flashcards and match the correct table of 19 answers to the questions.

Conclusion

It may appear that learning the multiplication table of 19 is time demanding. If you remember the multiplication table of 19, you will be able to use the results quickly instead of wasting time calculating each and every result each time.

In rupees, one billion equals 10,000 lakhs. 1,000,000,000 is a natural number that equals one billion. The number 999,999,999 comes before 1 billion, and 1,000,000,001 comes after it. The concept of place value is used in mathematics to describe quantities. There are two ways to interpret the place value of the digits in a number. The Indian System and the International System are the two. The place value charts are used to determine the number’s positional values. With the support of positions, numbers in the general form can be extended.

 

The place value is ordered from right to left. Starting with the unit location (one’s place), the place value progresses to tens, hundreds, thousands, and so on. Let us look at the value of 1 billion in rupees of the Indian scheme of place value and 1 billion dollars in rupees in words. We’ll also look at the position value chart for both the Indian and International systems.

Overview of the Topic

The place value is ordered from right to left. Starting with the unit location (one’s place), the place value progresses to tens, hundreds, thousands, and so on. Let us look at the value of 1 billion in rupees of the Indian scheme of place value and 1 billion dollars in rupees in words. We’ll also look at the position value chart for both the Indian and International systems.

Students get scared by seeing big numbers but nothing to get scared of. It is important that students must understand how to identify big numbers. They must have proper knowledge and information about the rules for identifying big numbers. There are different ways to identify the numbers. Mainly, students are taught about two different systems of place value. One is the Indian system of place value and the other is the International System of place value. It is important that students must have knowledge of both the Indian and the International System of place values to identify big numbers easily. Students must know how to convert international numbers in the Indian system. The names given to different numbers in the Indian and international system are different and students must know this concept for excelling in higher classes. 

1 Billion is a big number and it is equal to 10,000 lakhs in Indian money.  One billion can be written as 1,000,000,000. Students can remember this by counting the zeroes. There are nine zeros in one billion. Similarly, if students want to remember other big numbers they can count the zeroes. For example, one million will have six zeros and it is written as 1000,000. Thus, in a similar manner students can remember other big numbers. 

One Billion in Rupees

Consider 1 dollar = 73.80 rupees

 

Value of 1 billion = 1,000,000,000 rupees

 

So 1 billion dollars in rupees = 73.80 x 1,000,000,000 =7.38 x 1010¹⁰

 

Similarly

 

5 billion dollars in rupees =73.80 x 5,000,000,000 = 369 x 1011¹¹

1 Billion in Indian Rupees

The International System uses billions based on position value charts. The equivalent value of  1 billion in Indian rupees (according to the Indian System) is

 

1 billion in rupees = 1,000,000,000 Rupees

 

We can write it as:

 

1 Billion = 10,000 Lakhs (As we know 1 lakh = 1,00,000)

 

As a result, a billion in lakhs equals 10,000 lakhs. It means that one billion lakhs equals ten million lakhs.

 

In other words, 1 billion equals 100 crores (as 1 lakh equals 1,00,00,000).

Conversion from Billion to Lakhs

Multiply the given billion value by ten thousand lakhs to convert the given billion value to lakhs (10,000 Lakhs)

 

Multiply 7 by 10,000 lakhs, for example, to convert 7 billion to lakhs.

 

(i.e.,) 7 Billion = 7 x 10,000 lakhs

 

70,000 lakhs = 7 billion

 

As a result, 7 billion equals 70,000 lakhs.

 

1 billion dollar to inr is 73,80,00,50,000

Conversion from Billion to Crores

Multiply the given billion value by 100 crores to convert the given billion value to crores.

 

To convert 9 billion to crores, multiply 9 by 100 crores, as an example.

 

(To put it another way,) 9 billion is equal to 9 x 100 crores.

 

900 crores = 9 billion dollars

 

As a result, 9 billion equals 900 crores.

 

Similarly, any billion value can be converted to values in the Indian numbering system, such as lakhs, crores, and so on.

How Many Zeros in a Billion?

There are nine (9) zeros in a billion. 

 

1 billion = 1,000,000,000
 

How Many Millions is a Billion?

1 million = 1000,000

 

One million is equal to 1000 thousand.

 

1 billion = 1000 million = 1000,000,000

 

Therefore, one billion is equal to 1000 million.

Place Value Chart for Indian System

The sequence of the position value of the digit in the Indian system is as follows:

 

The Hindu-Arabic method of numeration is also known as the Indian system of numeration. The comma symbol “,” is used to differentiate the intervals in this scheme. The first comma appears after three digits from the right hand, followed by two digits, two digits, and then every two digits.

International System Place Value Chart:

The sequence of a digit’s position value in the International System is as follows:

 

Ones

 

Thousands

 

Millions

 

Billions

 

How to Use the Calculator to Convert Billion to Rupees?

The following is the protocol for using the billion to rupees conversion calculator:

Step 1: In the input region, type the number of billions.

 

Step 2: To get the conversion value, press the “Convert” button.

 

Step 3: Finally, in the output sector, the value of the conversion from billions to rupees will be shown.

What Does Billion to Rupees Conversion Mean?

In the Indian and International (more precisely the US) numeral systems, the place value of digits is referred to in various ways. Digits in the Indian system have place values of Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores, and so on. The position values of digits in the International system are in the order Ones, Tens, Hundreds, Thousands, Ten Thousand, Hundred Thousands, Millions, Billions, and so on. As a result, 1 billion is converted to 100 crores in the conversion from billions to rupees.

 

1 billion rupees = 1,000,000,000 rupees

 

Since 1 lakh equals Rs. 100000, 1 billion equals 10,000 lakhs.

 

100 Crores = 1 Billion

Solved Examples

1. What is the Rupee Equivalent of 5 Billion? 

Solution: We know that a billion rupees equal 1,000,000,000 rupees.

 

As a result, the rupee value of 5 billion is estimated as follows:

 

5 Billion = 5 x 1,000,000,000

 

5 Billion = 5,000,000,000 rupees

 

We may also assume that 5 billion equals 500 crores.

 

2. In Crores, What is the Worth of 4.6 Billion?

Solution: We know that

 

1 Billion = 100 crores

 

Therefore, 4.6 Billion = 4.6 x 100 crores

 

4.6 Billion = 460 crores

 

Hence, the value of 4.6 billion is 460 crores.

Overview of Place Value

Place value is an important concept in mathematics. It helps to determine the position of a digit in the given number. Each digit in a number has a position. A number can be expanded depending on the position of different digits. We count the place value of digits from right to left. The position will start from the unit’s place and move on to tens, hundreds, thousands, ten thousand, etc.

The place value of every digit in a given number is different. A number may have two same digits but both digits in the number will have a different position or place value. For example, 5456 in this number 5 will have a different place value. The number on the right will have a place value of tens and the number on the left will have a place value of ten thousand.

Solved Examples

1. What is 3 billion equal to the Indian rupee?

You know that one billion is equal to 1,000,000,000 rupees.

Thus, the value of 3 billion can be calculated as follows:

3 Billion = 3 x 1, 000,000,000

3 Billion = 3,000,000, 000 rupees.

We can also say that 3 million is equal to 300 crores.

Convert 4 billion to lakhs

We know that one Billion is equal to = 10,000 lakhs

Thus the value of 4 billion can be calculated as follows

1 billion = 10,000 lakhs

4 billion = 4 x 10,000

4 billion = 40,000 lakhs

Thus, we can say that the value of 4 billion is 40,000 lakhs

A fraction can be defined as a part of a whole number which can be represented numerically.

For example:

Bheem drank two and a half glass of milk i.e. 2 ½ and Indu drank one and a half glass of milk

i.e. 1 ½ .In this example, the half glass of milk is represented as a numerical quantity.

Introduction to Addition and Subtraction of Fraction

From the above example the question arises, what is the total amount of milk that they drank? In this case, the addition and subtraction of fractions take place to find the total quantity of an item. How do we add fraction? How to subtract fractions? What are the steps to add or subtract?  Let us learn about Addition and Subtraction of Fractions.

Methods for Adding and Subtracting Fractions

Unlike whole numbers adding and subtracting fraction is not easy it requires different methods for different types of fraction. The following methods will guide you through addition and subtraction of fractions.

• Addition and subtraction of Like fraction

• Addition and subtraction of unlike fraction

• Addition and Subtraction of Mixed fraction

Addition and Subtraction of Like Fraction

The fractions which have the same denominators are known as Like fractions.  Additional and subtraction of like fraction is quite easy, as the denominator of the fractions are same.

Example 1:

1/4 + 2/4 =?

In the above example the denominator of the fraction is the same.

                1/4 =      2/4 = 

The above diagram gives the pictorial representation of the fractions. The circle is divided into 4 parts which is the denominator and the colored part represents the numerator.

Steps for Addition of Like Fractions:

Step1: check the denominators of the fraction, If the denominator is the same or not. 

Step2: If the denominators are the same, add the numerators of the fraction keeping the denominator as it is.

Step3: Solution 

         1/4 + 2/4 = 3/4 

Example 2:  6/8 – 2/8 =?

Steps for Subtraction of Like Fractions:

Step1: Check the denominators of the fraction, If the denominator is the same or not.

Step2: Subtract the smaller numerator with the larger one keeping the denominator as it is.

Step3: Solution

 6/8 – 2/8 = 4/8 

Addition and Subtraction of Unlike Fraction

The fractions which have the different denominators are known as unlike fractions. For addition and subtraction of fraction the denominators of the fraction should be the same. So we need to make them the same by taking LCM of the denominators.

Example 3: 4/6 + 2/8 =?

Steps for Addition of Unlike Fractions:

Step 1: Take LCM of the denominators of the given fractions.In this example the LCM of  6 and 8 is 24.

(LCM is the least common multiple of two numbers)

Step 2: To get the same denominator 8 and 12 should be converted into 24 by multiplying the suitable multiple to both numerator and denominator.

For  4/6 ,  4/4  will be multiplied  4/6 x 4/4 = 16/24

For  2/8 ,  3/3  will be multiplied  2/8 x 3/3 = 6/24

Step 3: Now, the denominators of the two fractions are the same .Add the numerator keeping the denominator as it is.

 16/24 + 6/24 

Step 4: Solution

16/24 + 6/24 = 22/24

Example 4:  4/6 – 2/8 =?

Steps for Subtraction of Unlike Fractions:

Step 1: Take LCM of the denominators of the given fractions. In this example the LCM of  6 and 8 is 24.

(LCM is the least common multiple of two numbers)

Step 2: To get the same denominator 8 and 12 should be converted into 24 by multiplying the suitable multiple to both numerator and denominator.

For  4/6 ,  4/4  will be multiplied  4/6 x 4/4 = 16/24

For  2/8 ,  3/3  will be multiplied  2/8 x 3/3 = 6/24

Step 3: Now, the denominators of the two fraction are the same .Subtract the numerator keeping the denominator as it is.

 16/24 – 6/24 

Step 4: Solution

16/24 – 6/24 = 10/24

Addition and Subtraction of Mixed Fraction

A mixed fraction can be defined  as a combination of a whole number and a fraction combined into one mixed number.

For example :  2 1/4   is a mixed fraction

2 1/4    =

In the above diagram the whole number is represented by the circle which is completely colored and the fraction is represented by the circle which is partially colored.

There are two methods for the addition and subtraction of mixed fraction.

1.  Addition and subtraction of like mixed fraction.

2.  Addition and subtraction of unlike mixed fraction.

Addition and Subtraction of Like Mixed Fraction

Example 5: 3 3/4 + 2 2/4 =?

Steps for Addition of Like Mixed Fraction 

Step1: First add the whole number of the mixed number

3+2= 5 – (1)

Step 2: Add the fractional part of the mixed number

3/4 + 2/4 =5/4     — (2)  

Step 3: Converting improper fraction into proper fraction

Equation (2)  —–> 5/4  = 1 1/4   — (2) 

Step 4: Solution 

Combining equation (1) and (2)

5+1 1/4   =6 1/4     

Example 6: 3 3/4 + 2 2/4 =?

Steps for Subtraction of Like Mixed Fraction 

Step1: First subtract the whole number of the mixed number

3-2= 1 – (1)

Step 2: Subtract the fraction part of the mixed number

3/4 – 2/4 =1/4     — (2)  

Step 3: Solution 

Combining equation (1) and (2)

1+1/4   =11/4     

Addition and Subtraction of Unlike Mixed Fraction

In Unlike mixed fraction the denominator of the fractional part is different which needs to be made the same using LCM.

Example 7: 3 3/4 + 2 2/6 =?

Steps for Addition of Unlike Mixed Fraction –

Step 1: First add the whole number of the mixed number

3+2= 5 – (1)

Step 2: Take the LCM of the fractional part and make the denominator same

The LCM of 4 and 6 is 12

For  3/4 ,  3/3  will be multiplied  3/4 x 3/3 = 9/12

For  2/6 ,  2/2  will be multiplied  2/6 x 2/2 = 4/12

Step 3: Adding the fraction with the same denominators 

9/12+ 4/12 =13/12     — (2)  

Step 4: Converting improper fraction into proper fraction

Equation (2) —–> 13/12  =  1 1/12     — (2)  

Step 5: Solution 

Combining equation (1) and (2)

5+11/12   =61/12   

Example 8: 3
3/4 – 22/6 =?

Steps for Subtraction of Unlike Mixed Fraction 

Step1: First subtract the whole number of the mixed number

3-2= 1 – (1)

Step 2: Take the LCM of the fractional part and make the denominator same

The LCM of 4 and 6 is 12

For  3/4 ,  3/3  will be multiplied  3/4 x 3/3 = 9/12

For  2/6 ,  2/2  will be multiplied  2/6 x 2/2 = 4/12

Step 3: Subtracting the fraction with the same denominators 

9/12 – 4/12 =5/12     — (2)  

Step 4: Solution 

Combining equation (1) and (2)

5+5/12   =51/12