Maths worksheets · lesson 55 of 64 · free

Rational numbers — Maths worksheet

A rational number is a fraction p/q of integers with q not zero, such as −3/4 or 5/(−7). In standard form the denominator is positive and the fraction is in lowest terms: 12/(−18) = −2/3. To compare or add rational numbers, give them the same positive denominator and then work with the numerators, using the rules of signs.

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The method

Common denominator, then signs — “make the denominators the same, then add the numerators with the rules of signs”

  1. Standard form: move any minus sign to the numerator and divide top and bottom by their HCF.
  2. Compare: same denominator, then the bigger numerator is bigger (−2/6 > −5/6).
  3. Add or subtract: common denominator, then add or subtract the numerators with the rules of signs.
  4. Additive inverse of a/b is −a/b; reciprocal of a/b is b/a (same sign).

Use it for: Temperatures and heights in fractions, money gained and lost, and the rational numbers chapter of Class 7 maths.

🧮 Check your own sums with the free Ratio calculator — it shows the working.

Worked example: What is (−3/4) + 1/2? → −1/4

  1. Common denominator 4: −3/4 + 2/4.
  2. −3 + 2 = −1, so the answer is −1/4.

Check: −1/4 − 1/2 = −1/4 − 2/4 = −3/4 ✓

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🏁 Lesson 55 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Class 7 Maths Worksheet: Rational Numbers

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