Revisiting Arithmetic Expressions

Class 7 Maths · Chapter 4: Expressions using Letter-Numbers · NCERT Ganita Prakash section 4.2–4.3

Learn

A quick recap from Chapter 2: write an expression as a sum of terms, then swap and group to make it easy. 83 + 28 − 13 + 32 = (83 − 13) + (28 + 32) = 70 + 60 = 130. And 68 − (18 + 13) = 68 − 18 − 13 = 37: a minus before brackets changes the signs inside.

83 + 28 − 13 + 32 = 130

Dropping the × sign: the multiples of 4 are 4, 8, 12, 16 … The 3rd term is 4 × 3 and the nth term is 4 × n. We usually write this as 4n: the number first, then the letter, with no × sign. So 7k means 7 × k, and when k = 4, 7k = 28.

4n = 4 × n · 7k = 28 when k = 4

Finding values: for 5m + 3 when m = 2, first 5m = 5 × 2 = 10, then + 3 = 13. With brackets: 3(m + 1) when m = −6 is 3 × (−5) = −15. With two letters: 2f − 2g when f = 3 and g = 1 is 6 − 2 = 4.

m = 2: 5m + 3 = 13

Mind the mistake: "If d = 6, then 3d = 36" is wrong: 3d means 3 × 6 = 18, not the digits 3 and 6 side by side. "If a = −4, then 10 − a = 6" is also wrong: 10 − (−4) = 14. Always put the number in brackets when you replace a letter, especially a negative number.

Explore: values when m = 2.

1. Match each expression to its value when m = 2.

Remember

• 4n means 4 × n: write the number first and leave out the × sign.
• To find a value, put the number in place of the letter (in brackets), then use brackets–terms–add.

Quick check

What is the value of 3s − 2 when s = 7?

1. 19
2. 15
3. 35
4. 21

Think about it

Why is it a mistake to say that if r = 8 then 2r + 1 = 29?

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.