The Notion of Letter-Numbers

Class 7 Maths · Chapter 4: Expressions using Letter-Numbers · NCERT Ganita Prakash section 4.1

Learn

Meher is 4 years older than her brother Kabir. When Kabir is 8, Meher is 12; when Kabir is 20, Meher is 24. The rule is always the same: Meher's age = Kabir's age + 4. Instead of writing the words, we use a letter: if k is Kabir's age, Meher's age is k + 4.

m = k + 4 · k = m − 4

Letters like k and m that stand for numbers are called letter-numbers, and expressions like k + 4 are algebraic expressions. To use one, replace the letter by a number: if k = 23, Meher is 23 + 4 = 27. Going the other way, Kabir's age is m − 4: if Meher is 20, Kabir is 16.

k = 23 → k + 4 = 27

Patterns: each "L" shape uses 2 matchsticks, so n Ls use 2 × n sticks. Coconuts cost ₹35 and jaggery ₹60 a kg: for c coconuts and j kg of jaggery the cost is c × 35 + j × 60. For 7 coconuts and 4 kg: 245 + 240 = ₹485. A rule written like this is a formula.

c × 35 + j × 60 → 7 × 35 + 4 × 60 = 485

Formulas for perimeters: a square with side q has perimeter 4 × q; an equilateral triangle with side a, 3 × a; a regular hexagon, 6 × a. Turning words into expressions: "5 more than a number" is n + 5; "4 less than a number" is n − 4; "2 less than 13 times a number" is 13 × n − 2.

13 × n − 2

Explore: words to expressions.

1. Match each phrase to its expression.

Remember

• A letter-number stands for a number; an expression like k + 4 is algebraic.
• Replace the letter by a number to find the value; a general rule written this way is a formula.

Quick check

A grinding mill takes 10 seconds to start and then 8 seconds for each kg. Which expression gives the time for y kg?

1. 10 + 8 × y
2. (10 + 8) × y
3. 10 × 8 × y
4. 10 × y + 8

Think about it

In a calendar, the date below w is w + 7. What are the dates to the left of w and above w?

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.