Multiples of Sums and Differences

Class 7 Maths · Chapter 2: Arithmetic Expressions · NCERT Ganita Prakash section 2.2

Learn

Two friends each order a dosa (₹43) and a lassi (₹24). Is the total 2 × 43 + 24? No, that means 24 more than 2 × 43. We want double of (43 + 24), so we need brackets: 2 × (43 + 24) = 2 × 67 = ₹134. It is also two dosas plus two lassis: 2 × 43 + 2 × 24 = 86 + 48 = ₹134.

2 × (43 + 24) = 2 × 43 + 2 × 24

Rows in a parade: 4 rows of 5 scouts and 3 rows of 5 guides: 4 × 5 + 3 × 5 = 35. Or count rows first: (4 + 3) × 5 = 7 × 5 = 35. The multiple of a sum is the sum of the multiples: 10 × 98 + 3 × 98 = 13 × 98. It works for differences too: 14 × 10 − 6 × 10 = (14 − 6) × 10 = 80.

4 × 5 + 3 × 5 = (4 + 3) × 5 = 35

Quick products: 97 × 25 = (100 − 3) × 25 = 2500 − 75 = 2,425. And 104 × 15 = 1500 + 60 = 1,560. If you know 53 × 18 = 954, then 63 × 18 = 954 + 10 × 18 = 954 + 180 = 1,134. Split a number into an easy part plus (or minus) a little.

97 × 25 = 100 × 25 − 3 × 25 = 2,425

Careful: 5 × 4 + 3 is not the same as 5 × (4 + 3). The first is 23 (3 more than 20); the second is 35 (5 times 7). Brackets decide what gets multiplied. Also note (8 − 3) × 29 > (3 − 8) × 29, because 5 × 29 is positive and (−5) × 29 is negative.

5 × 4 + 3 = 23 but 5 × (4 + 3) = 35

Explore: quick ways to multiply.

1. Match each product to its quick form.

Remember

• a × (b + c) = a × b + a × c and a × (b − c) = a × b − a × c.
• Split a number near 10, 100 or 1000 to multiply quickly: 97 × 25 = 2500 − 75.

Quick check

Fill the blank: 3 × (5 + 8) = 3 × 5 + 3 × ___

1. 8
2. 5
3. 3
4. 13

Think about it

A boy reads a two-page story every day except Tuesdays and Saturdays. How many stories does he read in 8 weeks? Write it two ways.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.