CBSE Class 5 Mathematics Fractions Worksheet Set 04

Fractions

Question 1. Circle the proper fractions.
Answer: Proper fractions are fractions where the numerator is strictly less than the denominator. Let us check each given fraction:
- \(\frac{22}{3}\): Numerator 22 is greater than denominator 3. (Improper fraction)
- \(\frac{4}{8}\): Numerator 4 is less than denominator 8. (Proper fraction)
- \(\frac{2}{10}\): Numerator 2 is less than denominator 10. (Proper fraction)
- \(\frac{16}{9}\): Numerator 16 is greater than denominator 9. (Improper fraction)
- \(\frac{7}{3}\): Numerator 7 is greater than denominator 3. (Improper fraction)
- \(\frac{3}{5}\): Numerator 3 is less than denominator 5. (Proper fraction)
- \(\frac{36}{6}\): Numerator 36 is greater than denominator 6. (Improper fraction)
- \(\frac{4}{12}\): Numerator 4 is less than denominator 12. (Proper fraction)
- \(\frac{13}{2}\): Numerator 13 is greater than denominator 2. (Improper fraction)
Thus, the proper fractions are \(\frac{4}{8}, \frac{2}{10}, \frac{3}{5}, \frac{4}{12}\).
In simple words: A proper fraction always has a smaller top number than the bottom number.

Exam Tip: Remember that proper fractions represent a value less than 1, so the numerator must be smaller than the denominator.

Question 2. Convert into mixed fractions.
a. \(\frac{44}{5} = 8\frac{4}{5}\)
b. \(\frac{97}{4} = 24\frac{1}{4}\)
c. \(\frac{153}{5} = 30\frac{3}{5}\)
d. \(\frac{89}{14} = 6\frac{5}{14}\)
Answer: To convert an improper fraction into a mixed fraction, divide the numerator by the denominator. The quotient becomes the whole number part, the remainder becomes the numerator, and the denominator remains the same.
a. Divide 44 by 5: Quotient = 8, Remainder = 4. So, \(\frac{44}{5} = 8\frac{4}{5}\)
b. Divide 97 by 4: Quotient = 24, Remainder = 1. So, \(\frac{97}{4} = 24\frac{1}{4}\)
c. Divide 153 by 5: Quotient = 30, Remainder = 3. So, \(\frac{153}{5} = 30\frac{3}{5}\)
d. Divide 89 by 14: Quotient = 6, Remainder = 5. So, \(\frac{89}{14} = 6\frac{5}{14}\)
In simple words: Divide the top number by the bottom number to get a whole number and a remainder fraction.

Exam Tip: Always double check your mixed fraction by multiplying the whole number by the denominator and adding the numerator to get back the original improper fraction.

Question 3. Convert each into an improper fraction.
a. \(7\frac{2}{5} = \frac{37}{5}\)
b. \(4\frac{6}{9} = \frac{42}{9}\)
c. \(5\frac{3}{10} = \frac{53}{10}\)
d. \(1\frac{2}{6} = \frac{8}{6}\)
Answer: To convert a mixed fraction into an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.
a. \(\frac{(7 \times 5) + 2}{5} = \frac{35 + 2}{5} = \frac{37}{5}\)
b. \(\frac{(4 \times 9) + 6}{9} = \frac{36 + 6}{9} = \frac{42}{9}\)
c. \(\frac{(5 \times 10) + 3}{10} = \frac{50 + 3}{10} = \frac{53}{10}\)
d. \(\frac{(1 \times 6) + 2}{6} = \frac{6 + 2}{6} = \frac{8}{6}\)
In simple words: Multiply whole number with denominator and add numerator to form the new top number.

Exam Tip: Never change the denominator when converting between mixed and improper fractions.

Question 4. Complete the following equivalent fractions.
a. \(\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18}\)
b. \(\frac{4}{7} = \frac{8}{14} = \frac{12}{21} = \frac{16}{28} = \frac{20}{35} = \frac{24}{42}\)
Answer: To find equivalent fractions, multiply both the numerator and the denominator by the same non-zero whole number.
a. Given base fraction is \(\frac{1}{3}\).
- Second term: \(\frac{1 \times 2}{3 \times 2} = \frac{2}{6}\)
- Third term: \(\frac{1 \times 3}{3 \times 3} = \frac{3}{9}\)
- Fourth term: \(\frac{1 \times 4}{3 \times 4} = \frac{4}{12}\)
- Fifth term: \(\frac{1 \times 5}{3 \times 5} = \frac{5}{15}\)
- Sixth term: \(\frac{1 \times 6}{3 \times 6} = \frac{6}{18}\)
b. Given base fraction is \(\frac{4}{7}\).
- First term: \(\frac{4}{7}\)
- Second term: \(\frac{4 \times 2}{7 \times 2} = \frac{8}{14}\)
- Third term: \(\frac{4 \times 3}{7 \times 3} = \frac{12}{21}\)
- Fourth term: \(\frac{4 \times 4}{7 \times 4} = \frac{16}{28}\)
- Fifth term: \(\frac{4 \times 5}{7 \times 5} = \frac{20}{35}\)
- Sixth term: \(\frac{4 \times 6}{7 \times 6} = \frac{24}{42}\)
In simple words: Multiply the top and bottom numbers by 2, then 3, then 4, and so on.

Exam Tip: Whatever you multiply the numerator by, you must multiply the denominator by the exact same number.

Question 5. Reduce the following fractions to their lowest terms.
a. \(\frac{9}{81} = \frac{1}{9}\)
b. \(\frac{35}{150} = \frac{7}{30}\)
c. \(\frac{6}{36} = \frac{1}{6}\)
d. \(\frac{50}{100} = \frac{1}{2}\)
e. \(\frac{8}{64} = \frac{1}{8}\)
f. \(\frac{24}{96} = \frac{1}{4}\)
Answer: To reduce a fraction to its lowest terms, divide both the numerator and the denominator by their Highest Common Factor (HCF).
a. HCF of 9 and 81 is 9. Dividing both by 9 gives \(\frac{9 \div 9}{81 \div 9} = \frac{1}{9}\)
b. HCF of 35 and 150 is 5. Dividing both by 5 gives \(\frac{35 \div 5}{150 \div 5} = \frac{7}{30}\)
c. HCF of 6 and 36 is 6. Dividing both by 6 gives \(\frac{6 \div 6}{36 \div 6} = \frac{1}{6}\)
d. HCF of 50 and 100 is 50. Dividing both by 50 gives \(\frac{50 \div 50}{100 \div 50} = \frac{1}{2}\)
e. HCF of 8 and 64 is 8. Dividing both by 8 gives \(\frac{8 \div 8}{64 \div 8} = \frac{1}{8}\)
f. HCF of 24 and 96 is 24. Dividing both by 24 gives \(\frac{24 \div 24}{96 \div 24} = \frac{1}{4}\)
In simple words: Divide the top and bottom numbers by the biggest number that divides both evenly.

Exam Tip: A fraction is in its lowest terms when the only common factor between the numerator and denominator is 1.