NCERT Solutions Class 7 Maths Chapter  8 Working with Fractions Exercise 8.2

Designed for the purpose of mastering the difficult operation of dividing fractions, this conceivable exercise 8.2 for the NCERT Solutions Class 7 Maths Chapter 8: Working with Fractions drives home the operation of dividing fractions. This follows upon the knowledge gained on multiplication (discussed in Exercise 8.1) and introduces the most crucial concept in this operation: the Reciprocal and the practice of using a three-step procedure for the operation of dividing fractions.

Mastery at this level is essential because, typically in the real world, when you divide fractions, you will probably be converting a unit rate problem, or scaling a mixture, or dealing with ratios. These types of issues will typically occur when packing different items together, figuring out meals, or measuring. Generally, any time you are dealing with fractions, there will be occasions to convert, mix, and measure. Exercise 8.2 presents problems involving the situation of dividing a whole number by a fraction, a fraction by a fraction, and simplifying (adding/subtracting, multiplying/dividing) expressions with mixed fractions.

1.0Download Class 7 Maths Chapter 8 Ex 8.2 NCERT Solutions PDF

Sharpen your skills in dividing fractions! Download the complete solutions for this entire exercise, including step-by-step NCERT Solutions for Class 7 Maths. You can use this to understand the reciprocal method and practice increasing the part of your calculation. 

2.0Key Concepts of Exercise 8.2 Class 7 Chapter 8 - Working with Fractions

• Reciprocal: Knowing that the reciprocal of the fraction  a/b is b/a and that multiplying a fraction by its reciprocal will always give you the result of 1. 
• Division Rule: The basic idea here is to know that when you divide by a fraction, you are effectively multiplying it by the reciprocal of that fraction. 

a/b  ÷ c/d   = a/b  × d/c

• Mixed Fraction: The important first step in any division question is to convert mixed fractions into improper fractions; you cannot divide mixed fractions directly.
• Reciprocal identification: You want to identify if the reciprocal of a fraction is a proper fraction (numerator < denominator); improper fraction (numerator ≥ denominator); or a whole number. 
• Whole Number Divided by a Fraction: This involves dividing a whole number by either a proper or improper fraction. 
• Fraction Divided by Fraction: The main type of problem that has us using the concept of the reciprocal.
• Mixed Operations: These problems require us to divide whole numbers, proper fractions, and mixed fractions.

3.0NCERT Solutions Class 7 Maths Chapter 8 Working with Fractions : Other Exercises

4.0Detailed CBSE Class 7 Chapter 8 Exercise 8.2 Solutions

1. Find the following products.

(a) 1/3 x 1/5

(b) 1/4 x 1/3

(c) 1/5 x 1/2

(d) 1/6 x 1/5

Now, find 1/12 x 1/18

Sol. Use formula: 1/b x 1/d = 1/(b x d)

(a) 1/3 x 1/5 = 1/(3 x 5) = 1/15

(b) 1/4 x 1/3 = 1/(4 x 3) = 1/12

(c) 1/5 x 1/2 = 1/(5 x 2) = 1/10

(d) 1/6 x 1/5 = 1/(6 x 5) = 1/30

Now, 1/12 x 1/18 = 1/(12 x 18) = 1/216

2. Find the following products.

(a) 2/3 x 4/5

(b) 1/4 x 2/3

(c) 3/5 x 1/2

(d) 4/6 x 3/5

Sol. Use formula: a/b x c/d = (a x c)/(b x d)

(a) 2/3 x 4/5 = (2 x 4) / (3 x 5) = 8/15

(b) 1/4 x 2/3 = (1 x 2) / (4 x 3) = 2/12. Simplified form is 1/6. (The original solution had an error, as 2/12 simplifies to 1/6, not 1/6 directly from the product step.)

Note on (b): The original problem text's solution shows 1/6, which is the simplified answer, but the step 4x3 in the denominator is 12, so 2/12 is the unsimplified answer.x

Using the provided solution's final answer:x 1/4 x 2/3 = (1 x 2) / (4 x 3) = 2/12 = 1/6

(c) 3/5 x 1/2 = (3 x 1) / (5 x 2) = 3/10

(d) 4/6 x 3/5 = (4 x 3) / (6 x 5) = 12/30. Simplified form is 2/5. (The original solution simplifies 12/30 to 2/5)

5.0Key Features of Class 7 Maths Chapter 8 Exercise 8.2

• Essential Math Skill: In later grades, fractions are an important step to ratios and proportions.
• Clear Conceptual Understanding: The answers clearly delineate turning a division problem into multiplication with the reciprocal.
• Manipulating Complex Numbers: Conversion of mixed numbers, practiced, ready for multi-step problem solvin.