Fractions - Grade 4 Math Questions With Answers

This page is designed to help students, parents, and teachers master the topic of fractions through carefully selected practice questions and step-by-step solutions with explanations. Each solution provides the reasoning behind every step, helping learners build a strong foundation in understanding parts of a whole, equivalent fractions, and ordering.

The questions on this page cover essential topics related to fractions, including:

Questions and Step-by-Step Solutions

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

    Fraction diagram with shaded parts

    1. \(\dfrac{3}{8}\)
    2. \(\dfrac{8}{3}\)
    3. \(\dfrac{1}{8}\)
    4. \(\dfrac{1}{2}\)
    ► Solution to Question 1

    Explanation: A fraction represents part of a whole, written as \(\dfrac{\text{shaded parts}}{\text{total equal parts}}\). By counting the shaded segments versus total segments in the provided diagram, 3 parts are shaded out of 8 equal total parts.

    Therefore, the fraction is \(\dfrac{3}{8}\), making option A correct.

  2. Question 2: Which figure is shaded to show a fraction equal to \(\dfrac{2}{5}\) of its whole?

    Multiple fraction diagrams

    ► Solution to Question 2

    Explanation: To find a fraction equal to \(\dfrac{2}{5}\), look for a figure divided into 5 equal parts where 2 parts are shaded, or an equivalent fraction where 2 out of every 5 sections are shaded. Figure C correctly displays this proportion.

    Therefore, option C is correct.

  3. Question 3: Which two fractions are equivalent?

    1. \(\dfrac{1}{2}\) and \(\dfrac{1}{3}\)
    2. \(\dfrac{1}{2}\) and \(\dfrac{2}{4}\)
    3. \(\dfrac{1}{4}\) and \(\dfrac{1}{6}\)
    4. \(\dfrac{2}{3}\) and \(\dfrac{1}{3}\)
    ► Solution to Question 3

    Explanation: Equivalent fractions represent the exact same value or proportion. If you multiply the numerator and denominator of \(\dfrac{1}{2}\) by 2, you get \(\dfrac{1 \times 2}{2 \times 2} = \dfrac{2}{4}\).

    Therefore, \(\dfrac{1}{2}\) and \(\dfrac{2}{4}\) are equivalent, making option B correct.

  4. Question 4: The figures below show that:

    Comparing fractions visually

    1. \(\dfrac{1}{5} = \dfrac{1}{4}\)
    2. \(\dfrac{2}{5} = \dfrac{2}{4}\)
    3. \(\dfrac{2}{5} > \dfrac{2}{4}\)
    4. \(\dfrac{2}{5} < \dfrac{2}{4}\)
    ► Solution to Question 4

    Explanation: When numerators are the same, the fraction with the smaller denominator represents larger pieces because the whole is divided into fewer parts. Since fifths are smaller than fourths, \(\dfrac{2}{5}\) is less than \(\dfrac{2}{4}\).

    Therefore, \(\dfrac{2}{5} < \dfrac{2}{4}\), making option D correct.

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

    1. \(\dfrac{1}{2}\)
    2. \(\dfrac{1}{4}\)
    3. \(\dfrac{2}{4}\)
    4. \(\dfrac{3}{4}\)
    ► Solution to Question 5

    Explanation: "Half" is written as \(\dfrac{1}{2}\). Finding half of a half means multiplying \(\dfrac{1}{2}\) by \(\dfrac{1}{2}\):

    \(\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}\)

    Therefore, option B is correct.

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

    1. \(N = 2\)
    2. \(N = 1\)
    3. \(N = 4\)
    4. \(N = 3\)
    ► Solution to Question 6

    Explanation: To convert the denominator 3 to 6, multiply it by 2. To keep the fraction equivalent, do the same to the numerator:

    \(\dfrac{2 \times 2}{3 \times 2} = \dfrac{4}{6}\)

    Comparing \(\dfrac{N}{6}\) to \(\dfrac{4}{6}\), we find \(N = 4\). Therefore, option C is correct.

  7. Question 7: Which two figures have shaded parts that represent equivalent fractions?

    Equivalent fraction diagrams

    ► Solution to Question 7

    Explanation: Examining the shaded areas across the multiple choices shows that the figures in option D represent the same proportional shaded area (equivalent fractions).

    Therefore, option D is correct.

  8. Question 8: Order from greatest to least: \(\dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{2}, \dfrac{1}{7}\)

    1. \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{7}\)
    2. \(\dfrac{1}{7}, \dfrac{1}{6}, \dfrac{1}{3}, \dfrac{1}{2}\)
    3. \(\dfrac{1}{2}, \dfrac{1}{6}, \dfrac{1}{3}, \dfrac{1}{7}\)
    4. \(\dfrac{1}{7}, \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{6}\)
    ► Solution to Question 8

    Explanation: When unit fractions have a numerator of 1, the fraction with the smallest denominator is the largest value because the whole is divided into fewer pieces. Sorting by size from largest to smallest:

    • \(\dfrac{1}{2}\) (greatest)
    • \(\dfrac{1}{3}\)
    • \(\dfrac{1}{6}\)
    • \(\dfrac{1}{7}\) (least)

    Therefore, the correct order is \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{7}\), making option A correct.

  9. Question 9: What value of \(N\) makes \(\dfrac{N}{3} < \dfrac{1}{2}\) true?

    1. \(N = 3\)
    2. \(N = 2\)
    3. \(N = 1\)
    4. \(N = 4\)
    ► Solution to Question 9

    Explanation: Let's test the values of \(N\):

    • If \(N = 3\), \(\dfrac{3}{3} = 1\) (not less than \(\dfrac{1}{2}\))
    • If \(N = 2\), \(\dfrac{2}{3} \approx 0.67\) (not less than \(\dfrac{1}{2}\))
    • If \(N = 1\), \(\dfrac{1}{3} \approx 0.33\), which is less than \(\dfrac{1}{2} (0.5)\)

    Therefore, \(N = 1\), making option C correct.

  10. Question 10: John, Sarah, Tom and Joane bought 2 pizzas of the same size. John ate \(\dfrac{2}{4}\) of a pizza. Tom, Sarah and Joane each ate \(\dfrac{1}{4}\) of a pizza. How much pizza was left?

    1. \(\dfrac{1}{4}\) of a pizza
    2. 1 pizza
    3. \(\dfrac{1}{2}\) of a pizza
    4. \(\dfrac{3}{4}\) of a pizza
    ► Solution to Question 10

    Explanation: Calculate the total pizza eaten:

    • John: \(\dfrac{2}{4}\)
    • Tom: \(\dfrac{1}{4}\)
    • Sarah: \(\dfrac{1}{4}\)
    • Joane: \(\dfrac{1}{4}\)

    Total eaten = \(\dfrac{2}{4} + \dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4} = \dfrac{5}{4}\) pizzas (or \(1\dfrac{1}{4}\) pizzas).

    Since they started with 2 pizzas (\(\dfrac{8}{4}\)), subtract what was eaten:

    \(\dfrac{8}{4} - \dfrac{5}{4} = \dfrac{3}{4}\) of a pizza left.

    Therefore, option D is correct.

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