Fractions online worksheet for GRade 5/ Year 6 - Free Printable

Problem Analysis and Solution

The provided worksheet focuses on fractions, covering topics such as equivalent fractions, comparing fractions, simplifying fractions, and solving word problems. Below is a detailed solution for each question.

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Q1. Write the equivalent fraction

#### Instructions:
Write the missing numerator or denominator to make the fractions equivalent.

#### Solutions:
1. \( \frac{3}{3} = \frac{\_\_}{9} \)
- To find the missing numerator, notice that the denominator changes from 3 to 9 (multiplied by 3). Therefore, the numerator must also be multiplied by 3.
- \( 3 \times 3 = 9 \)
- Answer: \( \frac{3}{3} = \frac{9}{9} \)

2. \( \frac{2}{8} = \frac{\_\_}{32} \)
- The denominator changes from 8 to 32 (multiplied by 4). Therefore, the numerator must also be multiplied by 4.
- \( 2 \times 4 = 8 \)
- Answer: \( \frac{2}{8} = \frac{8}{32} \)

3. \( \frac{4}{7} = \frac{\_\_}{28} \)
- The denominator changes from 7 to 28 (multiplied by 4). Therefore, the numerator must also be multiplied by 4.
- \( 4 \times 4 = 16 \)
- Answer: \( \frac{4}{7} = \frac{16}{28} \)

4. \( \frac{4}{9} = \frac{\_\_}{45} \)
- The denominator changes from 9 to 45 (multiplied by 5). Therefore, the numerator must also be multiplied by 5.
- \( 4 \times 5 = 20 \)
- Answer: \( \frac{4}{9} = \frac{20}{45} \)

5. \( \frac{4}{12} = \frac{\_\_}{3} \)
- The denominator changes from 12 to 3 (divided by 4). Therefore, the numerator must also be divided by 4.
- \( 4 \div 4 = 1 \)
- Answer: \( \frac{4}{12} = \frac{1}{3} \)

6. \( \frac{4}{6} = \frac{\_\_}{3} \)
- The denominator changes from 6 to 3 (divided by 2). Therefore, the numerator must also be divided by 2.
- \( 4 \div 2 = 2 \)
- Answer: \( \frac{4}{6} = \frac{2}{3} \)

7. \( \frac{3}{6} = \frac{1}{\_\_} \)
- The numerator changes from 3 to 1 (divided by 3). Therefore, the denominator must also be divided by 3.
- \( 6 \div 3 = 2 \)
- Answer: \( \frac{3}{6} = \frac{1}{2} \)

8. \( \frac{9}{12} = \frac{\_\_}{4} \)
- The denominator changes from 12 to 4 (divided by 3). Therefore, the numerator must also be divided by 3.
- \( 9 \div 3 = 3 \)
- Answer: \( \frac{9}{12} = \frac{3}{4} \)

9. \( \frac{4}{10} = \frac{\_\_}{5} \)
- The denominator changes from 10 to 5 (divided by 2). Therefore, the numerator must also be divided by 2.
- \( 4 \div 2 = 2 \)
- Answer: \( \frac{4}{10} = \frac{2}{5} \)

10. \( \frac{5}{10} = \frac{\_\_}{2} \)
- The denominator changes from 10 to 2 (divided by 5). Therefore, the numerator must also be divided by 5.
- \( 5 \div 5 = 1 \)
- Answer: \( \frac{5}{10} = \frac{1}{2} \)

11. \( \frac{4}{16} = \frac{1}{\_\_} \)
- The numerator changes from 4 to 1 (divided by 4). Therefore, the denominator must also be divided by 4.
- \( 16 \div 4 = 4 \)
- Answer: \( \frac{4}{16} = \frac{1}{4} \)

12. \( \frac{8}{8} = \frac{\_\_}{2} \)
- The denominator changes from 8 to 2 (divided by 4). Therefore, the numerator must also be divided by 4.
- \( 8 \div 4 = 2 \)
- Answer: \( \frac{8}{8} = \frac{2}{2} \)

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Q2. Use < / > / =

#### Instructions:
Compare the given fractions using \( < \), \( > \), or \( = \).

#### Solutions:
1. \( \frac{3}{7} \, \square \, \frac{10}{14} \)
- Simplify \( \frac{10}{14} \): \( \frac{10 \div 2}{14 \div 2} = \frac{5}{7} \)
- Compare \( \frac{3}{7} \) and \( \frac{5}{7} \): Since the denominators are the same, compare the numerators.
- \( 3 < 5 \)
- Answer: \( \frac{3}{7} < \frac{10}{14} \)

2. \( \frac{2}{3} \, \square \, \frac{8}{15} \)
- Find a common denominator: The least common multiple of 3 and 15 is 15.
- Convert \( \frac{2}{3} \) to a fraction with denominator 15: \( \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \)
- Compare \( \frac{10}{15} \) and \( \frac{8}{15} \): Since the denominators are the same, compare the numerators.
- \( 10 > 8 \)
- Answer: \( \frac{2}{3} > \frac{8}{15} \)

3. \( \frac{1}{2} \, \square \, \frac{12}{20} \)
- Simplify \( \frac{12}{20} \): \( \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \)
- Convert \( \frac{1}{2} \) to a fraction with denominator 10: \( \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \)
- Convert \( \frac{3}{5} \) to a fraction with denominator 10: \( \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \)
- Compare \( \frac{5}{10} \) and \( \frac{6}{10} \): Since the denominators are the same, compare the numerators.
- \( 5 < 6 \)
- Answer: \( \frac{1}{2} < \frac{12}{20} \)

4. \( \frac{4}{5} \, \square \, \frac{16}{20} \)
- Simplify \( \frac{16}{20} \): \( \frac{16 \div 4}{20 \div 4} = \frac{4}{5} \)
- Compare \( \frac{4}{5} \) and \( \frac{4}{5} \):
- \( \frac{4}{5} = \frac{4}{5} \)
- Answer: \( \frac{4}{5} = \frac{16}{20} \)

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Q3. Simplify each fraction

#### Instructions:
Simplify the given fractions to their lowest terms.

#### Solutions:
a. \( \frac{28}{49} \)
- Find the greatest common divisor (GCD) of 28 and 49: GCD(28, 49) = 7
- Simplify: \( \frac{28 \div 7}{49 \div 7} = \frac{4}{7} \)
- Answer: \( \frac{4}{7} \)

b. \( \frac{12}{20} \)
- Find the GCD of 12 and 20: GCD(12, 20) = 4
- Simplify: \( \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \)
- Answer: \( \frac{3}{5} \)

c. \( \frac{24}{42} \)
- Find the GCD of 24 and 42: GCD(24, 42) = 6
- Simplify: \( \frac{24 \div 6}{42 \div 6} = \frac{4}{7} \)
- Answer: \( \frac{4}{7} \)

d. \( \frac{13}{39} \)
- Find the GCD of 13 and 39: GCD(13, 39) = 13
- Simplify: \( \frac{13 \div 13}{39 \div 13} = \frac{1}{3} \)
- Answer: \( \frac{1}{3} \)

e. \( \frac{32}{36} \)
- Find the GCD of 32 and 36: GCD(32, 36) = 4
- Simplify: \( \frac{32 \div 4}{36 \div 4} = \frac{8}{9} \)
- Answer: \( \frac{8}{9} \)

f. \( \frac{9}{15} \)
- Find the GCD of 9 and 15: GCD(9, 15) = 3
- Simplify: \( \frac{9 \div 3}{15 \div 3} = \frac{3}{5} \)
- Answer: \( \frac{3}{5} \)

g. \( \frac{16}{48} \)
- Find the GCD of 16 and 48: GCD(16, 48) = 16
- Simplify: \( \frac{16 \div 16}{48 \div 16} = \frac{1}{3} \)
- Answer: \( \frac{1}{3} \)

h. \( \frac{15}{55} \)
- Find the GCD of 15 and 55: GCD(15, 55) = 5
- Simplify: \( \frac{15 \div 5}{55 \div 5} = \frac{3}{11} \)
- Answer: \( \frac{3}{11} \)

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Q4. Answer the following

#### Instructions:
Raneem completed \( \frac{5}{6} \) of the math homework, and Sara completed \( \frac{4}{5} \) of the math homework. Who did more of the homework?

#### Solution:
To determine who completed more homework, compare the fractions \( \frac{5}{6} \) and \( \frac{4}{5} \).

1. Find a common denominator for \( \frac{5}{6} \) and \( \frac{4}{5} \):
- The least common multiple of 6 and 5 is 30.

2. Convert both fractions to have the denominator 30:
- \( \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \)
- \( \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \)

3. Compare \( \frac{25}{30} \) and \( \frac{24}{30} \):
- Since the denominators are the same, compare the numerators.
- \( 25 > 24 \)

4. Conclusion:
- Raneem completed \( \frac{25}{30} \) of the homework, and Sara completed \( \frac{24}{30} \) of the homework.
- Therefore, Raneem completed more homework.

#### Final Answer:
\[ \boxed{\text{Raneem}} \]

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Final Answers Summary

1. Equivalent fractions:
- 1) \( \frac{9}{9} \)
- 2) \( \frac{8}{32} \)
- 3) \( \frac{16}{28} \)
- 4) \( \frac{20}{45} \)
- 5) \( \frac{1}{3} \)
- 6) \( \frac{2}{3} \)
- 7) \( \frac{1}{2} \)
- 8) \( \frac{3}{4} \)
- 9) \( \frac{2}{5} \)
- 10) \( \frac{1}{2} \)
- 11) \( \frac{1}{4} \)
- 12) \( \frac{2}{2} \)

2. Comparisons:
- 1) \( < \)
- 2) \( > \)
- 3) \( < \)
- 4) \( = \)

3. Simplified fractions:
- a) \( \frac{4}{7} \)
- b) \( \frac{3}{5} \)
- c) \( \frac{4}{7} \)
- d) \( \frac{1}{3} \)
- e) \( \frac{8}{9} \)
- f) \( \frac{3}{5} \)
- g) \( \frac{1}{3} \)
- h) \( \frac{3}{11} \)

4. Word problem:
- \( \boxed{\text{Raneem}} \)