Find 5 rational numbers between 25 and 35.

Step-by-step solution

Idea: The numerators 2 and 3 have no whole number between them. Multiply top and bottom by 5 + 1 = 6 to make room for exactly 5.

1. 25 = 2 × 65 × 6 = 1230 and 35 = 1830.1 mark
2. Numerators 13, 14, 15, 16, 17 lie between: 1330, 1430 = 715, 1530 = 12, 1630 = 815, 1730.1 mark

Check: Decimals: 0.4 < 0.433 < 0.467 < 0.5 < 0.533 < 0.567 < 0.6 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Multiplying only the numerators by 6.
• Giving 2.55 as an answer. Its value (12) is between, but in the form pq both p and q must be integers: write 510 or 12.
• Multiplying by 5 instead of 6, which gives only 4 numbers between (1125 to 1425).

How this can come in the exam

Try one yourself

Find 3 rational numbers between 49 and 59.

More questions like this

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• Without performing division, determine whether the decimal expansion of 18125 is terminating or non-terminating. If it terminates, state the number of decimal places.

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