Fractions and Mixed Numbers

Grade 6 Maths Questions and Problems With Answers

Practice Grade 6 math multiple choice questions on fractions and mixed numbers. Each problem comes with answers, and detailed step-by-step solutions and explanations to help students, parents, and teachers build strong fraction skills.
The first three questions review the basic concepts of fractions and mixed numbers, while the remaining problems focus on applying these skills through more challenging practice.

Questions

  1. What fraction of the large square is red?
    What fraction of the large square is blue?
    What fraction of the large square is orange?
    What fraction of the large square is green?
    What fraction of the large square is black?
    What fraction of the large square is yellow?
    fraction, question 1.
    1. red: \( \dfrac{1}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{16} \) , green: \( \dfrac{3}{16} \) , black: \( \dfrac{3}{16} \) , yellow: \( \dfrac{3}{16} \)
    2. red: \( \dfrac{4}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{16} \) , green: \( \dfrac{3}{32} \) , black: \( \dfrac{3}{16} \) , yellow: \( \dfrac{3}{16} \)
    3. red: \( \dfrac{1}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{16} \) , green: \( \dfrac{3}{16} \) , black: \( \dfrac{3}{16} \) , yellow: \( \dfrac{3}{16} \)
    4. red: \( \dfrac{1}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{32} \) , green: \( \dfrac{3}{32} \) , black: \( \dfrac{3}{16} \) , yellow: \( \dfrac{3}{16} \)

  2. What fraction is the shaded part?
    fraction, question 2.
    1. \(2 \dfrac{1}{2}\)
    2. \(2\)
    3. \(2 \dfrac{3}{4}\)
    4. \(2 \dfrac{1}{4}\)

  3. Which point on the number line represents \( 1 \dfrac{1}{5} \) ?
    fraction, question 3.
    1. \( S \)
    2. \( R \)
    3. \( W \)
    4. \( K \)

  4. \[ 3 \dfrac{1}{2} + 5 \dfrac{1}{2} = \]
    1. \(8\)
    2. \(8 \dfrac{1}{2}\)
    3. \(9\)
    4. \(9 \dfrac{1}{2}\)

  5. \[ \dfrac{1}{2} + \dfrac{1}{14} = \]
    1. \(\dfrac{4}{7}\)
    2. \(\dfrac{8}{7}\)
    3. \(\dfrac{2}{16}\)
    4. \(\dfrac{2}{14}\)

  6. \[ \dfrac{1}{3} - \dfrac{1}{12} = \]
    1. \(0\)
    2. \(\dfrac{1}{4}\)
    3. \(-\dfrac{1}{9}\)
    4. \(\dfrac{1}{9}\)


  7. one half is the same as?
    1. one quarter
    2. two quarters
    3. three quarters
    4. four quarters


  8. Which two fractions are not equivalent?
    1. \(\dfrac{1}{2}\) and \(\dfrac{2}{4}\)
    2. \(\dfrac{4}{3}\) and \(\dfrac{8}{6}\)
    3. \(\dfrac{1}{5}\) and \(\dfrac{3}{15}\)
    4. \(\dfrac{2}{3}\) and \(\dfrac{8}{9}\)

  9. \[ 5 \dfrac{2}{3} + 5 \dfrac{1}{2} = \]
    1. \( 10 \dfrac{3}{5} \)
    2. \( 10 \dfrac{1}{6} \)
    3. \( 11 \dfrac{1}{6} \)
    4. \( 10 \)

  10. Order from least to greatest: \( \dfrac{8}{9}, \dfrac{17}{18}, \dfrac{2}{3}, \dfrac{7}{6} \)

    1. \( \dfrac{8}{9}, \dfrac{17}{18}, \dfrac{2}{3}, \dfrac{7}{6} \)
    2. \( \dfrac{2}{3}, \dfrac{8}{9}, \dfrac{17}{18}, \dfrac{7}{6} \)
    3. \( \dfrac{8}{9}, \dfrac{2}{3}, \dfrac{17}{18}, \dfrac{7}{6} \)
    4. \( \dfrac{2}{3}, \dfrac{7}{6}, \dfrac{8}{9}, \dfrac{17}{18} \)

  11. Which fraction is closest to 1?

    1. \(\dfrac{10}{11}\)
    2. \(\dfrac{11}{10}\)
    3. \(\dfrac{9}{11}\)
    4. \(-\dfrac{9}{10}\)

  12. \[ \dfrac{5}{2} \div \dfrac{2}{5} = \]
    1. \(1\)
    2. \(\dfrac{4}{25}\)
    3. \(25\)
    4. \(6 \dfrac{1}{4}\)

  13. \[ 5 \div \dfrac{1}{5} = \]
    1. \(\dfrac{1}{25}\)
    2. \(25\)
    3. \(1\)
    4. \(\dfrac{6}{5}\)

  14. \(\dfrac{2}{5} \times \dfrac{7}{8} =\)
    1. \(\dfrac{14}{8}\)
    2. \(\dfrac{14}{5}\)
    3. \(\dfrac{7}{20}\)
    4. \(\dfrac{9}{40}\)

  15. Write the mixed number \(7 \dfrac{7}{8}\) as a fraction
    1. \(\dfrac{14}{8}\)
    2. 63
    3. \(\dfrac{49}{8}\)
    4. \(\dfrac{63}{8}\)

  16. Write the fraction \(\dfrac{31}{8}\) as a mixed number.
    1. \(3 \dfrac{7}{8}\)
    2. \(4 \dfrac{7}{8}\)
    3. \(31 \dfrac{1}{8}\)
    4. \(3 \dfrac{1}{8}\)


  17. \(3 \times \dfrac{1}{4} =\)
    1. \(3 \dfrac{1}{4}\)
    2. \(\dfrac{3}{4}\)
    3. 34
    4. \(\dfrac{1}{12}\)

  18. \[ 3 \dfrac{1}{4} \div 5 \dfrac{1}{3} = \]
    1. \(\dfrac{3}{5}\)
    2. \(\dfrac{3}{5} + \dfrac{3}{4}\)
    3. \(\dfrac{3}{4}\)
    4. \(\dfrac{39}{64}\)

  19. \(4 \dfrac{2}{7} \times 5 \dfrac{3}{5} = \)

    1. \(24\)
    2. \(20 \dfrac{6}{35}\)
    3. \(20\)
    4. \(\dfrac{6}{35}\)

  20. To have \[ F + 2 \dfrac{5}{7} = 4 \] , \( F \) must be equal to
    1. \(1\)
    2. \(2\)
    3. \(1 \dfrac{2}{7}\)
    4. \(2 \dfrac{2}{7}\)


  21. Tom runs \( \dfrac{3}{4} \) of an hour every Monday, 30 minutes every Tuesday, \( \dfrac{1}{2} \) an hour every Wednesday, \( 1 \dfrac{1}{4} \) hours every Thursday, and \( \dfrac{2}{3} \) of an hour on Friday. How many hours does Tom run from Monday to Friday?
    1. 4 hours and 40 minutes
    2. 3 hours and 30 minutes
    3. 3 hours and 50 minutes
    4. 3 hours and 40 minutes

  22. Order from least to greatest: \(5 \dfrac{3}{4},\; 3 \dfrac{4}{5},\; 3 \dfrac{1}{5},\; 4 \dfrac{5}{6}\).
    1. \(5 \dfrac{3}{4},\; 3 \dfrac{4}{5},\; 3 \dfrac{1}{5},\; 4 \dfrac{5}{6}\)
    2. \(3 \dfrac{1}{5},\; 3 \dfrac{4}{5},\; 4 \dfrac{5}{6},\; 5 \dfrac{3}{4}\)
    3. \(3 \dfrac{4}{5},\; 3 \dfrac{1}{5},\; 4 \dfrac{5}{6},\; 5 \dfrac{3}{4}\)
    4. \(3 \dfrac{1}{5},\; 3 \dfrac{4}{5},\; 5 \dfrac{3}{4},\; 4 \dfrac{5}{6}\)

  23. Order from least to greatest: \(7 \dfrac{2}{3}, \; 7 \dfrac{3}{5}, \; 7 \dfrac{3}{4}, \; 7 \dfrac{6}{11}\).

    1. \(7 \dfrac{3}{5}, \; 7 \dfrac{2}{3}, \; 7 \dfrac{6}{11}, \; 7 \dfrac{3}{4}\)
    2. \(7 \dfrac{3}{5}, \; 7 \dfrac{6}{11}, \; 7 \dfrac{3}{4}, \; 7 \dfrac{2}{3}\)
    3. \(7 \dfrac{6}{11}, \; 7 \dfrac{3}{5}, \; 7 \dfrac{2}{3}, \; 7 \dfrac{3}{4}\)
    4. \(7 \dfrac{3}{5}, \; 7 \dfrac{6}{11}, \; 7 \dfrac{2}{3}, \; 7 \dfrac{3}{4}\)

  24. What fraction of 1 hour is 50 minutes?

    1. \( \dfrac{1}{50} \)
    2. \( \dfrac{6}{5} \)
    3. \( \dfrac{5}{6} \)
    4. \( \dfrac{50}{1} \)

  25. \(\dfrac{1}{3}\) is \(\dfrac{1}{8}\) of what number?

    1. \(\dfrac{8}{3}\)
    2. \(\dfrac{3}{8}\)
    3. \(\dfrac{1}{2}\)
    4. \(\dfrac{3}{4}\)

Answers to the Above Questions

  1. D
  2. C
  3. B
  4. C
  5. A
  6. B
  7. B
  8. D
  9. C
  10. B
  11. A
  12. D
  13. B
  14. C
  15. D
  16. A
  17. B
  18. D
  19. A
  20. C
  21. D
  22. B
  23. C
  24. C
  25. A

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