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Summaries · Grade 7 Maths › Fractions
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Fractions

Numerator and denominator, comparing, equivalent fractions and adding and subtracting fractions. Read one part at a time and tap “I know this”. Then test yourself in the quiz.

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What is a fraction?

A fraction is part of a whole. The denominator (bottom) says into how many equal parts the whole is cut; the numerator (top) says how many parts we have.

1 whole½²⁄₄½ = ²⁄₄: the same amount
½ = ²⁄₄
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Compare, equivalent and simplify

  • Same denominator: bigger numerator = bigger fraction: ⅗ > ⅖.
  • Same numerator: bigger denominator = smaller pieces: ⅓ > ⅕.
  • Equivalent fractions: multiply or divide top and bottom by the same number: ½ = ²⁄₄ = ³⁄₆.
  • Simplify: divide top and bottom by the same factor: ⁶⁄₈ = ¾.
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Adding and subtracting

Rule

First make the denominators the same, then add only the numerators: ½ + ¼ = ²⁄₄ + ¼ = ¾.

Watch out

Never add the denominators: ½ + ¼ is not ²⁄₆.

Multiply: top × top, bottom × bottom: ⅔ × ¾ = ⁶⁄₁₂ = ½. Divide: flip the second fraction and multiply: ½ ÷ ¼ = ½ × ⁴⁄₁ = 2.

Subtracting mixed numbers: 2½ − 1⅔ = ⁵⁄₂ − ⁵⁄₃ = ¹⁵⁄₆ − ¹⁰⁄₆ = ⁵⁄₆. Fraction of an amount: ⅗ of 40 = 40 ÷ 5 × 3 = 24.

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Grade 7: unlike denominators and multiplying

  • Unlike denominators: find the LCM of the denominators. ⅔ + ¼ = ⁸⁄₁₂ + ³⁄₁₂ = ¹¹⁄₁₂.
  • Mixed number to improper fraction: 2¾ = (2 × 4 + 3)⁄4 = ¹¹⁄₄.
  • Multiply: numerator × numerator and denominator × denominator. ⅔ × ¾ = ⁶⁄₁₂ = ½.
  • With mixed numbers: first make them improper fractions. 1½ × ⅔ = ³⁄₂ × ⅔ = ⁶⁄₆ = 1.
  • Write the answer in its simplest form: divide numerator and denominator by their HCF.
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Remember this and test yourself

Remember this: your summary
  • Denominator = number of equal parts; numerator = how many we have.
  • Bigger denominator = smaller pieces.
  • Equivalent: multiply top and bottom by the same number.
  • Adding: make the denominators the same first.
  • Simplify by dividing top and bottom.

Write these points in your book. Read them again the night before the test.

Memory trick

The denominator names the kind of piece; the numerator counts how many you have.

Flash cards · Tap to turn over

Important words

First say the answer yourself, then turn the card over.

Test yourself · Part 2

True or false?

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