Solutions and Explanations to Grade 4 Questions on Fractions

Solutions and detailed explanations to Grade 4 maths questions on fractions are presented.

Questions and Solutions

  1. Use fractions to write the part of the whole shape that is shaded.

    fraction question 1

    Solution

    The whole shape has 8 equal parts and 3 parts are shaded. The shaded fraction is:

    \[ \frac{3}{8} \]

  2. Which figure is shaded to show a fraction equal to \( \tfrac{2}{5} \)?

    fraction question 2

    Solution

    Figure C shows:

    \[ \frac{4}{10} \]

    Divide numerator and denominator by 2 to get an equivalent fraction:

    \[ \frac{2}{5} \]

  3. Which two fractions are equivalent?
    1. \( \tfrac{1}{2} \) and \( \tfrac{1}{3} \)
    2. \( \tfrac{1}{2} \) and \( \tfrac{2}{4} \)
    3. \( \tfrac{1}{4} \) and \( \tfrac{1}{6} \)
    4. \( \tfrac{2}{3} \) and \( \tfrac{1}{3} \)

    Solution

    \( \tfrac{1}{2} \) and \( \tfrac{2}{4} \) are equivalent because multiplying numerator and denominator of \( \tfrac{1}{2} \) by 2 gives \( \tfrac{2}{4} \).

  4. The figures below show that:

    fraction question 4

    1. \( \tfrac{1}{5} = \tfrac{1}{4} \)
    2. \( \tfrac{2}{5} = \tfrac{2}{4} \)
    3. \( \tfrac{2}{5} > \tfrac{2}{4} \)
    4. \( \tfrac{2}{5} < \tfrac{2}{4} \)

    Solution

    The whole parts have the same size. The shaded part in the first figure is smaller than in the second, so:

    \( \tfrac{2}{5} < \tfrac{2}{4} \)

  5. Half of half is the same as the fraction:

    Solution

    Half of half is:

    \[ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]

  6. If the fractions \( \tfrac{N}{6} \) and \( \tfrac{2}{3} \) are equivalent, what is the value of \(N\)?

    Solution

    To go from denominator 3 to 6, multiply by 2. Multiply the numerator the same way:

    \[ N = 2 \times 2 = 4 \]

  7. Which two figures represent equivalent fractions?

    fraction question 7

    Solution

    The only pair with equal shaded fractions is in option D. Each figure shows \( \tfrac{1}{2} \).

  8. Order the fractions \( \tfrac{1}{3}, \tfrac{1}{6}, \tfrac{1}{2}, \tfrac{1}{7} \) from greatest to least.

    Solution

    From the model, the order is:

    \[ \frac{1}{2} > \frac{1}{3} > \frac{1}{6} > \frac{1}{7} \]

    fraction question 8 solution

  9. What value of \(N\) makes \( \tfrac{N}{3} < \tfrac{1}{2} \)?
    1. \( N=3 \)
    2. \( N=2 \)
    3. \( N=1 \)
    4. \( N=4 \)

    Solution

    \( \tfrac{1}{3} < \tfrac{1}{2} \), so the correct value is:

    \[ N = 1 \]

  10. John, Sarah, Tom, and Joane bought 2 equal pizzas. John ate \( \tfrac{2}{4} \). Each of the others ate \( \tfrac{1}{4} \). How much pizza was left?

    Solution

    One pizza has 4 quarters, so two pizzas contain 8 quarters:

    \[ \frac{2}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{5}{4} \]

    The remaining pizza amount is:

    \[ \frac{8}{4} - \frac{5}{4} = \frac{3}{4} \]

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