Fractions - Grade 5 Maths Questions With Solutions

Questions and Step-by-Step Solutions

1. Question 1: Write \(1\) as a fraction.

   1. \(\dfrac{1}{1}\) only
   2. \(\dfrac{2}{2}\) only
   3. \(\dfrac{3}{3}\) only
   4. Any fraction of the form \(\dfrac{n}{n}\) where \(n\) is a whole number
   ► View Step-by-Step Solution

   Use any whole number \(n\) to write 1 as a fraction as follows:
   If \(n = 1\), \(\quad 1 = \dfrac{1}{1}\)
   If \(n = 2\), \(\quad 1 = \dfrac{2}{2}\)
   If \(n = 11\), \(\quad 1 = \dfrac{11}{11}\)
   and so on.
   Note: We cannot write \(1 = \dfrac{0}{0}\) because a fraction cannot have a denominator equal to zero.

   Therefore, option D is correct.

2. Question 2: Write 5 as a reduced fraction.

   1. \(\dfrac{5}{5}\)
   2. \(\dfrac{1}{5}\)
   3. \(\dfrac{5}{1}\)
   4. \(\dfrac{1}{1}\)
   ► View Step-by-Step Solution

   Any whole number \(n\) may be written as a reduced fraction over 1: \(\dfrac{n}{1}\).
   Hence \(5\) may be written as \(\dfrac{5}{1}\).

   Therefore, option C is correct.

3. Question 3: \[ \dfrac{1}{4} + \dfrac{2}{4} = ? \]

   1. \(\dfrac{3}{4}\)
   2. \(\dfrac{3}{8}\)
   3. \(\dfrac{7}{8}\)
   4. \(3\)
   ► View Step-by-Step Solution

   When adding fractions with a common denominator, add the numerators directly while keeping the denominator the same:
   \[ \dfrac{1}{4} + \dfrac{2}{4} = \dfrac{1+2}{4} = \dfrac{3}{4} \]

   Therefore, option A is correct.

4. Question 4: \[ \dfrac{4}{7} - \dfrac{2}{7} = ? \]

   1. \(\dfrac{2}{14}\)
   2. \(\dfrac{6}{7}\)
   3. \(\dfrac{2}{7}\)
   4. \(\dfrac{4}{7}\)
   ► View Step-by-Step Solution

   When subtracting fractions with a common denominator, subtract the numerators directly while keeping the denominator the same:
   \[ \dfrac{4}{7} - \dfrac{2}{7} = \dfrac{4 - 2}{7} = \dfrac{2}{7} \]

   Therefore, option C is correct.

5. Question 5: \[ \dfrac{1}{5} + \dfrac{2}{3} = ? \]

   1. \(\dfrac{3}{8}\)
   2. \(\dfrac{2}{15}\)
   3. \(\dfrac{1}{8}\)
   4. \(\dfrac{13}{15}\)
   ► View Step-by-Step Solution

   Step 1: Find a common denominator by multiplying the denominators: \(5 \times 3 = 15\).
   Step 2: Rewrite the fractions with the common denominator:
   \(\dfrac{1}{5} = \dfrac{1 \times 3}{5 \times 3} = \dfrac{3}{15}\)
   \(\dfrac{2}{3} = \dfrac{2 \times 5}{3 \times 5} = \dfrac{10}{15}\)
   Step 3: Add the adjusted fractions:
   \[ \dfrac{3}{15} + \dfrac{10}{15} = \dfrac{3+10}{15} = \dfrac{13}{15} \]

   Therefore, option D is correct.

6. Question 6: \[ 3 \dfrac{1}{2} + 5 \dfrac{1}{3} = ? \]

   1. \(8\)
   2. \(8 \dfrac{2}{5}\)
   3. \(8 \dfrac{5}{6}\)
   4. \(\dfrac{2}{5}\)
   ► View Step-by-Step Solution

   Step 1: Add the whole parts: \(3 + 5 = 8\).
   Step 2: Add the fraction parts: \(\dfrac{1}{2} + \dfrac{1}{3}\).
   Step 3: Find a common denominator (6) for the fractions:
   \(\dfrac{1}{2} = \dfrac{3}{6}\) and \(\dfrac{1}{3} = \dfrac{2}{6}\).
   Step 4: Combine them:
   \[ 3 \dfrac{1}{2} + 5 \dfrac{1}{3} = (3+5) + \left(\dfrac{3}{6} + \dfrac{2}{6}\right) = 8 + \dfrac{5}{6} = 8 \dfrac{5}{6} \]

   Therefore, option C is correct.

7. Question 7: It takes Julia \(\dfrac{1}{2}\) hour to wash, comb her hair and put on her clothes, and \(\dfrac{1}{4}\) hour to have her breakfast. How much time does it take Julia to be ready for school?

   1. \(\dfrac{3}{4}\) hour
   2. 1 hour
   3. \(\dfrac{2}{4}\) hour
   4. 1 and \(\dfrac{1}{4}\) hours
   ► View Step-by-Step Solution

   Total time = \(\dfrac{1}{2}\text{ hour} + \dfrac{1}{4}\text{ hour} = \left(\dfrac{1}{2} + \dfrac{1}{4}\right)\text{hour}\).
   Convert \(\dfrac{1}{2}\) to fourths: \(\dfrac{1}{2} = \dfrac{2}{4}\).
   \[ \dfrac{2}{4} + \dfrac{1}{4} = \dfrac{3}{4}\text{ hour} \]

   Therefore, option A is correct.

8. Question 8: Which two fractions are equivalent?

   1. \(\dfrac{5}{2}\) and \(\dfrac{2}{5}\)
   2. \(\dfrac{4}{3}\) and \(\dfrac{8}{6}\)
   3. \(\dfrac{1}{4}\) and \(\dfrac{2}{4}\)
   4. \(\dfrac{2}{3}\) and \(\dfrac{1}{3}\)
   ► View Step-by-Step Solution

   Let's check option B: Write \(\dfrac{4}{3}\) with denominator 6 by multiplying numerator and denominator by 2:
   \[ \dfrac{4}{3} = \dfrac{4 \times 2}{3 \times 2} = \dfrac{8}{6} \]
   Therefore, \(\dfrac{4}{3}\) and \(\dfrac{8}{6}\) are equivalent fractions.

   Therefore, option B is correct.

9. Question 9: \[ 5 \dfrac{2}{3} - 3 \dfrac{1}{2} = ? \]

   1. \(2\)
   2. \(1 \dfrac{2}{5}\)
   3. \(2 \dfrac{7}{6}\)
   4. \(2 \dfrac{1}{6}\)
   ► View Step-by-Step Solution

   Step 1: Convert mixed numbers to improper fractions:
   \(5 \dfrac{2}{3} = \dfrac{17}{3}\) and \(3 \dfrac{1}{2} = \dfrac{7}{2}\).
   Step 2: Find a common denominator (6):
   \(\dfrac{17}{3} = \dfrac{34}{6}\) and \(\dfrac{7}{2} = \dfrac{21}{6}\).
   Step 3: Subtract:
   \[ \dfrac{34}{6} - \dfrac{21}{6} = \dfrac{13}{6} = 2 \dfrac{1}{6} \]

   Therefore, option D is correct.

10. Question 10: Billy ate \(1 \dfrac{1}{4}\) of a pizza and John ate \(1 \dfrac{2}{3}\) pizzas. How much more pizza did John eat than Billy?

    1. \(\dfrac{2}{3}\)
    2. \(\dfrac{5}{12}\)
    3. \(\dfrac{1}{4}\)
    4. \(\dfrac{7}{12}\)
    ► View Step-by-Step Solution

    Difference = \(1 \dfrac{2}{3} - 1 \dfrac{1}{4} = \left(1 - 1\right) + \left(\dfrac{2}{3} - \dfrac{1}{4}\right) = \dfrac{2}{3} - \dfrac{1}{4}\).
    Using common denominator 12:
    \(\dfrac{2}{3} = \dfrac{8}{12}\) and \(\dfrac{1}{4} = \dfrac{3}{12}\).
    \[ \dfrac{8}{12} - \dfrac{3}{12} = \dfrac{5}{12} \]

    Therefore, option B is correct.

11. Question 11: \[ \dfrac{5}{2} \div \dfrac{3}{4} = ? \]

    1. \(\dfrac{10}{3}\)
    2. \(\dfrac{10}{8}\)
    3. \(\dfrac{13}{4}\)
    4. \(1\)
    ► View Step-by-Step Solution

    To divide fractions, multiply by the reciprocal of the second fraction:
    \[ \dfrac{5}{2} \div \dfrac{3}{4} = \dfrac{5}{2} \times \dfrac{4}{3} = \dfrac{20}{6} = \dfrac{10}{3} \]

    Therefore, option A is correct.

12. Question 12: \[ 5 \div \dfrac{1}{7} = ? \]

    1. \(\dfrac{5}{7}\)
    2. \(\dfrac{6}{7}\)
    3. \(\dfrac{1}{35}\)
    4. \(35\)
    ► View Step-by-Step Solution

    Multiply 5 by the reciprocal of \(\dfrac{1}{7}\):
    \[ 5 \div \dfrac{1}{7} = \dfrac{5}{1} \times \dfrac{7}{1} = 35 \]

    Therefore, option D is correct.

13. Question 13: \[ \dfrac{2}{5} \times \dfrac{3}{7} = ? \]

    1. \(\dfrac{14}{15}\)
    2. \(\dfrac{6}{35}\)
    3. \(\dfrac{35}{6}\)
    4. \(\dfrac{15}{14}\)
    ► View Step-by-Step Solution

    Multiply numerators together and denominators together:
    \[ \dfrac{2}{5} \times \dfrac{3}{7} = \dfrac{2 \times 3}{5 \times 7} = \dfrac{6}{35} \]

    Therefore, option B is correct.

14. Question 14: To have \(a + 1 \dfrac{3}{4} = 2\), \(a\) must be equal to:

    1. \(1\)
    2. \(\dfrac{3}{4}\)
    3. \(\dfrac{1}{2}\)
    4. \(\dfrac{1}{4}\)
    ► View Step-by-Step Solution

    Subtract \(1 \dfrac{3}{4}\) from both sides:
    \(a = 2 - 1 \dfrac{3}{4} = 1 - \dfrac{3}{4} = \dfrac{4}{4} - \dfrac{3}{4} = \dfrac{1}{4}\)

    Therefore, option D is correct.

15. Question 15: What fraction or mixed number is the shaded part?
    

    

    1. \(\dfrac{3}{4}\)
    2. \(\dfrac{6}{4}\)
    3. \(2 \dfrac{3}{4}\)
    4. \(1 \dfrac{3}{4}\)
    ► View Step-by-Step Solution

    There are two whole shaded items and one shaded at \(\dfrac{3}{4}\). Hence the mixed number representing the shaded parts is \(2 \dfrac{3}{4}\).

    Therefore, option C is correct.

16. Question 16: True or false: \[ 2 \dfrac{1}{2} = 2 \times \dfrac{1}{2} \]

    ► View Step-by-Step Solution

    False: \(2 \dfrac{1}{2}\) is a mixed number equal to \(2 + \dfrac{1}{2}\), not \(2 \times \dfrac{1}{2}\).

17. Question 17: Tina works 15 hours a week (Monday to Friday). Last week she worked \(3 \dfrac{1}{2}\) hours on Monday, 4 hours on Tuesday, \(2 \dfrac{1}{6}\) hours on Wednesday, and \(1 \dfrac{1}{2}\) hours on Thursday. How many hours did she work on Friday?

    1. \(4\)
    2. \(\dfrac{5}{6}\)
    3. \(3 \dfrac{5}{6}\)
    4. \(2 \dfrac{5}{6}\)
    ► View Step-by-Step Solution

    Let \(n\) be the hours worked on Friday:
    \(3 \dfrac{1}{2} + 4 + 2 \dfrac{1}{6} + 1 \dfrac{1}{2} + n = 15\)
    Combine whole numbers and fractions:
    \((3 + 4 + 2 + 1) + \left(\dfrac{1}{2} + \dfrac{1}{6} + \dfrac{1}{2}\right) + n = 15\)
    \(10 + \left(1 + \dfrac{1}{6}\right) + n = 15 \implies 11 \dfrac{1}{6} + n = 15\)
    \(n = 15 - 11 \dfrac{1}{6} = 3 \dfrac{5}{6}\text{ hours}\).

    Therefore, option C is correct.

18. Question 18: Which point on the number line represents \(1 \dfrac{7}{10}\)?
    

    

    1. S
    2. R
    3. W
    4. K
    ► View Step-by-Step Solution

    \(1 \dfrac{7}{10} = 1.7\), which corresponds to point W on the graph.

    Therefore, option C is correct.

19. Question 19: Write \(2 \dfrac{1}{3}\) as an improper fraction.

    1. \(\dfrac{2}{3}\)
    2. \(\dfrac{7}{3}\)
    3. \(\dfrac{1}{3}\)
    4. \(\dfrac{3}{3}\)
    ► View Step-by-Step Solution

    \(2 \dfrac{1}{3} = 2 + \dfrac{1}{3} = \dfrac{6}{3} + \dfrac{1}{3} = \dfrac{7}{3}\).

    Therefore, option B is correct.

20. Question 20: Write the fraction \(\dfrac{31}{8}\) as a mixed number.

    1. \(4\)
    2. \(4 \dfrac{7}{8}\)
    3. \(3 \dfrac{1}{8}\)
    4. \(3 \dfrac{7}{8}\)
    ► View Step-by-Step Solution

    \(31 \div 8 = 3\) with a remainder of 7.
    \[ \dfrac{31}{8} = \dfrac{3 \times 8 + 7}{8} = 3 + \dfrac{7}{8} = 3 \dfrac{7}{8} \]

    Therefore, option D is correct.

21. Question 21: \[ 3 \times \dfrac{1}{4} = ? \]

    1. \(3 \dfrac{1}{4}\)
    2. \(\dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4}\)
    3. \(\dfrac{1}{4}\)
    4. \(12\)
    ► View Step-by-Step Solution

    \(3 \times \dfrac{1}{4} = (1 + 1 + 1) \times \dfrac{1}{4} = \dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4}\).

    Therefore, option B is correct.

22. Question 22: \[ 3 \dfrac{1}{4} = ? \]

    1. \(3 \times \dfrac{1}{4}\)
    2. \(\dfrac{3}{4}\)
    3. \(3 + \dfrac{1}{4}\)
    4. \(\dfrac{4}{3}\)
    ► View Step-by-Step Solution

    A mixed number represents the sum of its whole number part and fractional part: \(3 \dfrac{1}{4} = 3 + \dfrac{1}{4}\).

    Therefore, option C is correct.

23. Question 23: True or false: \[ \dfrac{2}{5} > \dfrac{3}{8} \]

    ► View Step-by-Step Solution

    Using a common denominator (40):
    \(\dfrac{2}{5} = \dfrac{16}{40}\) and \(\dfrac{3}{8} = \dfrac{15}{40}\).
    Since \(\dfrac{16}{40} > \dfrac{15}{40}\), the statement is True.

24. Question 24: Order from least to greatest the fractions: \[ \dfrac{3}{5}, \; \dfrac{7}{6}, \; \dfrac{1}{3}, \; \dfrac{4}{9} \]

    1. \(\dfrac{1}{3}, \; \dfrac{4}{9}, \; \dfrac{3}{5}, \; \dfrac{7}{6}\)
    2. \(\dfrac{4}{9}, \; \dfrac{1}{3}, \; \dfrac{3}{5}, \; \dfrac{7}{6}\)
    3. \(\dfrac{1}{3}, \; \dfrac{4}{9}, \; \dfrac{7}{6}, \; \dfrac{3}{5}\)
    4. \(\dfrac{1}{3}, \; \dfrac{3}{5}, \; \dfrac{4}{9}, \; \dfrac{7}{6}\)
    ► View Step-by-Step Solution

    \(\dfrac{7}{6} > 1\), while the others are less than 1.
    Using common denominator 45 for the remaining three fractions:
    \(\dfrac{3}{5} = \dfrac{27}{45}\), \(\dfrac{1}{3} = \dfrac{15}{45}\), \(\dfrac{4}{9} = \dfrac{20}{45}\).
    Ordering from least to greatest: \(\dfrac{1}{3}, \; \dfrac{4}{9}, \; \dfrac{3}{5}, \; \dfrac{7}{6}\).

    Therefore, option A is correct.

25. Question 25: Write \(\dfrac{2}{3}\) of \(4\) as a mixed number.

    1. \(4 \dfrac{2}{3}\)
    2. \(1 \dfrac{2}{3}\)
    3. \(2 \dfrac{2}{3}\)
    4. \(\dfrac{8}{3}\)
    ► View Step-by-Step Solution

    \(\dfrac{2}{3} \times 4 = \dfrac{8}{3} = \dfrac{6+2}{3} = 2 + \dfrac{2}{3} = 2 \dfrac{2}{3}\).

    Therefore, option C is correct.

26. Question 26: How many minutes are there in \(\dfrac{2}{3}\) of an hour?

    1. 40 minutes
    2. 60 minutes
    3. 20 minutes
    4. 100 minutes
    ► View Step-by-Step Solution

    \(\dfrac{2}{3} \times 60\text{ minutes} = \dfrac{120}{3} = 40\text{ minutes}\).

    Therefore, option A is correct.

27. Question 27: In the figure below, a large square was divided into 16 smaller squares of equal sides. Find the fraction of the large square for each color.
    

    

    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: \(\dfrac{3}{16}\)
    ► View Step-by-Step Solution

    Each small square represents \(\dfrac{1}{16}\) of the large square.
    - Red: 4 small squares = \(\dfrac{4}{16} = \dfrac{1}{4}\).
    - Blue: 1 small square = \(\dfrac{1}{16}\).
    - Orange: Half a small square = \(\dfrac{1}{2} \times \dfrac{1}{16} = \dfrac{1}{32}\).
    - Green: 1 and a half small squares = \(\dfrac{1}{16} + \dfrac{1}{32} = \dfrac{3}{32}\).
    - Black: 3 small squares = \(\dfrac{3}{16}\).
    - Yellow: 3 small squares = \(\dfrac{3}{16}\).

    Therefore, option D is correct.

More References and Links

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