Find 5 rational numbers between 16 and 25.

Step-by-step solution

Idea: Give both fractions the common denominator 30. The numerators 5 and 12 have 6 whole numbers between them, which is enough for 5.

1. 16 = 530 and 25 = 1230.1 mark
2. Numerators between 5 and 12: 6, 7, 8, 9, 10, 11. Take five: 630 = 15, 730, 830 = 415, 930 = 310, 1030 = 13.1 mark

Check: Decimals: 0.167 < 0.2 < 0.233 < 0.267 < 0.3 < 0.333 < 0.4 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Converting 25 to 1230 but 16 to 630 (wrong: 16 = 530).
• Keeping denominator 6 and just counting up the numerators (26, 36, 46, …) without checking: 36 = 12 is already bigger than 25.
• Including 1230 (= 25), which is an end point, not between.

How this can come in the exam

Try one yourself

Find 3 rational numbers between 18 and 13.

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