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Equivalent fractions

Numerator and denominator, comparing, equivalent fractions and adding and subtracting with the same denominator. 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

When the denominators are the same, add or subtract only the numerators; the denominator stays the same: ⅖ + ⅕ = ⅗; ⅞ − ⅜ = ⁴⁄₈ = ½.

Watch out

Never add the denominators: ⅖ + ⅕ is not ³⁄₁₀.

Mixed numbers: add or subtract the whole numbers first, then the fractions: 2⅓ + 1⅓ = 3⅔; 3¾ − 1¼ = 2²⁄₄ = 2½. If the fraction part is 1 or more, make a whole from it: 1⅗ + 2⅘ = 3⁷⁄₅ = 4⅖.

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Counting in fractions and comparing to twelfths

  • Count on in quarters: ¼; ½; ¾; 1; 1¼; 1½ …
  • Compare ⅔ and ¾: make both twelfths. ⅔ = ⁸⁄₁₂ and ¾ = ⁹⁄₁₂, so ¾ is bigger.
  • Order from small to big: ⁵⁄₁₂; ½; ⅔; ¾ (that is ⁵⁄₁₂; ⁶⁄₁₂; ⁸⁄₁₂; ⁹⁄₁₂).
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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 and subtracting with the same denominator: only the numerators change.
  • 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

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Test yourself · Part 2

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