Find 6 rational numbers between 3 and 4.

Step-by-step solution

Idea: To get 6 numbers between, write both as fractions with denominator 6 + 1 = 7; the numerators then have exactly 6 whole numbers between them.

1. Write with denominator 7: 3 = 217 and 4 = 287.1 mark
2. Numerators 22, 23, 24, 25, 26, 27 lie between 21 and 28, giving 227, 237, 247, 257, 267, 277.1 mark

Check: 227 ≈ 3.14 and 277 ≈ 3.86 both lie between 3 and 4 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Saying there are no numbers between 3 and 4 because they are consecutive integers. There are no integers between them, but infinitely many rational numbers.
• Including 3 or 4 themselves (e.g. 217 or 287).
• Using denominator 6, which gives only 5 numbers between (196 to 236).

How this can come in the exam

Try one yourself

Find 4 rational numbers between 5 and 6.

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