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Mathematics · Grades 4–7

Fraction reasoning and common mistakes

Comparisons require the same whole. Equal-sized parts give the denominator meaning.

Make a worksheet

Understand the idea

Think about the whole

Comparisons require the same whole. Equal-sized parts give the denominator meaning.

Choose a check

Use a number line, an equivalent fraction or a benchmark such as one half.

Check the operation

Addition does not add denominators; multiplying by a fraction below one can make a positive value smaller.

Worked examples

Which fraction is closest to one half: 1/8, 4/9, 7/8 or 1/10?

4/9 differs from 1/2 by only 1/18.

4/9

A learner writes 2/5 + 1/5 = 3/10. What is the correct sum?

The equal fifths stay fifths: (2 + 1)/5 = 3/5.

3/5

Try it yourself

  1. Which pair names the same point on a number line?

    1. 2/5 and 4/5
    2. 1/3 and 1/6
    3. 3/4 and 9/12
    4. 3/4 and 3/8

  2. Nia eats half of a small cake and Jo eats half of a large cake. Must they eat equal amounts? Explain.

  3. What fraction remains after 3/8 of a ribbon is cut away?

  4. For a positive quantity x, which expression is smaller than x?

    1. x ÷ 2/3
    2. x × 3/2
    3. x × 2/3
    4. x + 2/3

Answers and marking notes

Answers and marking notes
  1. 3/4 and 9/12

    Multiplying numerator and denominator by 3 preserves the fraction.

  2. No. Their fractions are equal, but the wholes can have different sizes.

    Credit the distinction between equal proportions and unequal whole sizes.

  3. 5/8

    The whole is 8/8; subtract 3/8.

  4. x × 2/3

    Multiplying by a positive factor below one makes a positive quantity smaller.

Further reading and review references

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Preview material · independent educational review required. Grade bands are approximate, not official curriculum alignment.