Master Chapter 8 Class 7 - Working with Fractions (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
Start Learning NowWelcome to Chapter 8, Working with Fractions, from your Class 7 Maths book, Ganita Prakash.
In the last chapter, we learned about the rules for arithmetic, and in earlier classes, you've learned what fractions are and how to add and subtract them. Now, we're going to tackle the next logical step: how do you multiply and divide fractions?
This chapter will give you the complete set of tools for working with fractions. We'll start with simple, real-world examples and build up to a powerful, universal rule that works for all fraction operations.
This chapter is broken down into two main parts: multiplication and division.
We'll start with what you already know: multiplying by a whole number. If Aaron walks 3 km in 1 hour, he walks 5 × 3 = 15 km in 5 hours.
We'll use this same logic for fractions:
Whole Number × Fraction: If a tortoise walks 1/4 km in 1 hour, how far does it walk in 3 hours? It's simply 3 × 1/4. We can think of this as repeated addition:
Fraction × Whole Number: What if Aaron (who walks 3 km in 1 hour) only walks for 2/5 of an hour? This would be 2/5 × 3. To understand this, we first find 1/5 of his distance (1/5 × 3 = 3/5 km) and then multiply by 2, which gives us 6/5 km.
Fraction × Fraction (The Big Idea): This is the most important new concept. What does 1/2 × 1/4 actually mean? It helps to read "×" as "of". So, the problem is asking: "What is 1/2 of 1/4?"
We'll learn to visualize this using an area model, like a square.
First, we take a whole square and find 1/4 of it (a horizontal slice).
Next, we find 1/2 of that slice (by cutting it in half vertically).
This new, smaller piece is 1/8 of the original whole square.
Therefore, 1/2 × 1/4 = 1/8.
Brahmagupta's Formula: This visual method reveals a simple, universal rule for all multiplication: multiply the numerators and multiply the denominators.
Division can be tricky, so we'll learn to think about it as a "missing number" multiplication problem.
We know that 12 ÷ 4 = 3 because 4 × 3 = 12.
So, what is 1 ÷ 2/3? This is the same as asking: 2/3 × ? = 1.
The Reciprocal: This leads us to a new key idea: the reciprocal. The reciprocal of a fraction is the number you multiply it by to get 1. The reciprocal of 2/3 is 3/2, because 2/3 × 3/2 = 6/6 = 1.
Brahmagupta's Formula: This gives us a simple, powerful rule for all division: to divide by a fraction, you multiply by its reciprocal.
Finally, this chapter will challenge what you think you know about multiplication and division.
Does multiplying always make a number bigger? No! When you multiply by a fraction that is less than 1 (like 1/2), you are taking a part of the number, so the result is smaller.
Does dividing always make a number smaller? No! When you divide by a fraction that is less than 1 (like 1/4), you are asking "how many of this tiny piece fit into the whole?" The answer will be bigger.
This chapter gives you the final, essential rules for mastering fractions. Understanding why we multiply across and why we flip and multiply for division is key. At Teachoo, we walk you through every example, from the area models to the reciprocal, to make sure these concepts click.
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