CBSE Class 5 Mathematics Fractions Worksheet Set 08

Q.1. Fill in the blanks.
(1) \(\frac{6}{7} \times 14 = 14 \times \frac{6}{7} = 12\)
Answer: \(\frac{6}{7}\) and 12
In simple words: Changing the order of numbers in multiplication does not change the answer (commutative property).
Exam Tip: Remember that \(a \times b = b \times a\) applies to fractions too.

(2) \(\frac{4}{5} \times \underline{\hspace{1cm}} = \frac{4}{5}\)
Answer: 1
In simple words: Any number multiplied by 1 gives the same number back.

Exam Tip: 1 is the multiplicative identity.

(3) \(0 \times \frac{71}{3} = \underline{\hspace{1cm}}\)
Answer: 0
In simple words: Multiplying any fraction by 0 always results in 0.

Exam Tip: The zero property of multiplication states that anything times zero is zero.

(4) \(\frac{3}{8} \div \frac{3}{8} = \underline{\hspace{1cm}}\)
Answer: 1
In simple words: Any non-zero number divided by itself is 1.

Exam Tip: Dividing a number by itself always yields 1.

(5) \(\underline{\hspace{1cm}} \div \frac{4}{9} = 1\)
Answer: \(\frac{4}{9}\)
In simple words: A number must be divided by itself to get 1.

(6) \(\frac{9}{11} \times \frac{4}{5} \times 0 \times \frac{3}{7} = \underline{\hspace{1cm}}\)
Answer: 0
In simple words: Because 0 is multiplied in the string of numbers, the entire product becomes 0.
Exam Tip: Look out for zero in long multiplication chains to save time.

(7) \(\frac{1}{3} \times \frac{1}{2} = \frac{1}{2} \times \underline{\hspace{1cm}} = \underline{\hspace{1cm}}\)
Answer: \(\frac{1}{3}\) and \(\frac{1}{6}\)
In simple words: Order does not matter in multiplication, and \(\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}\).

Exam Tip: Multiply numerators together and denominators together.

(8) \(\underline{\hspace{1cm}} \div 87\frac{1}{49} = \underline{\hspace{1cm}}\) (Note: based on standard worksheet patterns, dividing a number by itself or similar property applies, but let us complete it as \(87\frac{1}{49} \div 87\frac{1}{49} = 1\))
Answer: \(87\frac{1}{49}\) and 1
In simple words: A number divided by itself equals 1.

Exam Tip: Check for identical terms on both sides of division.

(9) \(10\frac{1}{7} \div 1 = \underline{\hspace{1cm}}\)
Answer: \(10\frac{1}{7}\)
In simple words: Dividing any number by 1 leaves it unchanged.

Exam Tip: 1 is the divisor identity.

(10) \(\frac{6}{13} \div \underline{\hspace{1cm}} = 1\)
Answer: \(\frac{6}{13}\)
In simple words: A number divided by itself gives 1.

Exam Tip: To get 1 from division, dividend and divisor must be equal.

Q.2. Find the value of each of the following.
(1) \(\frac{1}{9}\) of 27
Answer:
\(= \frac{1}{9} \times 27\)
\(= \frac{27}{9} = 3\)
In simple words: "Of" means multiplication, so find one-ninth of 27.
Exam Tip: Replace the word "of" with a multiplication sign.

(2) \(\frac{1}{6}\) of 42
Answer:
\(= \frac{1}{6} \times 42\)
\(= \frac{42}{6} = 7\)
In simple words: Divide 42 by 6 to get 7.

Exam Tip: Simplify by dividing the whole number by the denominator.

(3) \(\frac{2}{5}\) of 50
Answer:
\(= \frac{2}{5} \times 50\)
\(= 2 \times 10 = 20\)
In simple words: Multiply 50 by 2 and divide by 5.

Exam Tip: Cancel out common factors before multiplying.

(4) \(\frac{3}{7}\) of 84
Answer:
\(= \frac{3}{7} \times 84\)
\(= 3 \times 12 = 36\)
In simple words: Divide 84 by 7 to get 12, then multiply by 3.

Exam Tip: Always perform division first to keep numbers small.

(5) \(\frac{2}{3}\) of 90
Answer:
\(= \frac{2}{3} \times 90\)
\(= 2 \times 30 = 60\)
In simple words: Divide 90 by 3 to get 30, then multiply by 2.

Exam Tip: \(90 \div 3 = 30\), and \(30 \times 2 = 60\).

Q.3. Find the product of each of the following.
(1) \(3\frac{1}{3} \times 2\frac{2}{5}\)
Answer:
Convert mixed fractions to improper fractions:
\(3\frac{1}{3} = \frac{10}{3}\)
\(2\frac{2}{5} = \frac{12}{5}\)
Multiply:
\(= \frac{10}{3} \times \frac{12}{5}\)
\(= \frac{10 \times 12}{3 \times 5} = \frac{120}{15} = 8\)
In simple words: Convert mixed numbers to improper fractions first, then multiply.
Exam Tip: Cross-cancel numbers diagonally to simplify calculation.

(2) \(2\frac{2}{7} \times 4\frac{1}{5}\)
Answer:
Convert mixed fractions:
\(2\frac{2}{7} = \frac{16}{7}\)
\(4\frac{1}{5} = \frac{21}{5}\)
Multiply:
\(= \frac{16}{7} \times \frac{21}{5}\)
Cancel 7 and 21: \(21 \div 7 = 3\)
\(= \frac{16 \times 3}{5} = \frac{48}{5} = 9\frac{3}{5}\)
In simple words: Convert, cancel common factors, and multiply straight across.

Exam Tip: Express final improper fractions as mixed numbers if required.

(3) \(6 \times \frac{1}{2} \times 2\frac{1}{2}\)
Answer:
Convert mixed fraction:
\(2\frac{1}{2} = \frac{5}{2}\)
Multiply:
\(= \frac{6}{1} \times \frac{1}{2} \times \frac{5}{2}\)
\(= \frac{6 \times 1 \times 5}{1 \times 2 \times 2} = \frac{30}{4} = \frac{15}{2} = 7\frac{1}{2}\)
In simple words: Write whole numbers as fractions over 1, convert mixed numbers, and multiply.

Exam Tip: Reduce fractions to their lowest terms.

(4) \(3\frac{1}{3} \times \frac{3}{5} \times 3\frac{1}{2}\)
Answer:
Convert mixed fractions:
\(3\frac{1}{3} = \frac{10}{3}\)
\(3\frac{1}{2} = \frac{7}{2}\)
Multiply:
\(= \frac{10}{3} \times \frac{3}{5} \times \frac{7}{2}\)
Cancel 3 with 3, and \(10 \div (5 \times 2) = 1\):
\(= \frac{10 \times 3 \times 7}{3 \times 5 \times 2} = \frac{210}{30} = 7\)
In simple words: Convert all to improper fractions and simplify before multiplying.

Exam Tip: Look for vertical and diagonal cancellation.

(5) \(\frac{3}{4} \times \frac{12}{15} \times 2\frac{2}{9}\)
Answer:
Convert mixed fraction:
\(2\frac{2}{9} = \frac{20}{9}\)
Multiply:
\(= \frac{3}{4} \times \frac{12}{15} \times \frac{20}{9}\)
Simplify numerators and denominators:
\(= \frac{3 \times 12 \times 20}{4 \times 15 \times 9} = \frac{720}{540} = \frac{4}{3} = 1\frac{1}{3}\)
In simple words: Multiply all numerators together and all denominators together, then simplify.

Exam Tip: Step-by-step reduction prevents arithmetic errors.

Q.4. Solve the following.
(1) In a class of 60 students, \(\frac{2}{3}\) of it are boys. How many girls and boys are there?
Answer:
Total students = 60
Fraction of boys = \(\frac{2}{3}\)
Number of boys = \(\frac{2}{3} \times 60 = 2 \times 20 = 40\)
Number of girls = Total students - Number of boys
Number of girls = \(60 - 40 = 20\)
There are 40 boys and 20 girls.
In simple words: Find the number of boys by taking two-thirds of 60, then subtract from 60 to find the girls.
Exam Tip: Always label your final answer units clearly (boys and girls).

(2) A boy ate \(\frac{1}{5}\) of a box of 20 chocolates. How many chocolates did he eat?
Answer:
Total chocolates = 20
Fraction eaten = \(\frac{1}{5}\)
Chocolates eaten = \(\frac{1}{5} \times 20 = \frac{20}{5} = 4\)
He ate 4 chocolates.
In simple words: Calculate one-fifth of 20 by dividing 20 by 5.

Exam Tip: Word problems involving "of" require multiplication.

Q.1. Divide each of the following.
(1) \(\frac{18}{24}\) by 12
Answer:
\(= \frac{18}{24} \div 12\)
\(= \frac{18}{24} \times \frac{1}{12}\)
\(= \frac{18}{288} = \frac{1}{16}\)
In simple words: Multiply the fraction by the reciprocal of the whole number.
Exam Tip: Reciprocal of 12 is \(\frac{1}{12}\).

(2) \(\frac{5}{9}\) by 10
Answer:
\(= \frac{5}{9} \div 10\)
\(= \frac{5}{9} \times \frac{1}{10}\)
\(= \frac{5}{90} = \frac{1}{18}\)
In simple words: Change division to multiplication by the reciprocal and simplify.

Exam Tip: Always reduce fractions to lowest terms.

(3) \(\frac{11}{2}\) by 33
Answer:
\(= \frac{11}{2} \div 33\)
\(= \frac{11}{2} \times \frac{1}{33}\)
\(= \frac{11}{66} = \frac{1}{6}\)
In simple words: Multiply \(\frac{11}{2}\) by \(\frac{1}{33}\) and simplify.

Exam Tip: Cancel 11 and 33 to get 3 in the denominator.

(4) \(\frac{3}{11}\) by 9
Answer:
\(= \frac{3}{11} \div 9\)
\(= \frac{3}{11} \times \frac{1}{9}\)
\(= \frac{3}{99} = \frac{1}{33}\)
In simple words: Multiply the fraction by the reciprocal of 9.

Exam Tip: Divide numerator and denominator by 3.

(5) \(\frac{6}{7}\) by 3
Answer:
\(= \frac{6}{7} \div 3\)
\(= \frac{6}{7} \times \frac{1}{3}\)
\(= \frac{6}{21} = \frac{2}{7}\)
In simple words: Multiply by \(\frac{1}{3}\) and simplify the fraction.

Exam Tip: \(6 \div 3 = 2\), so the numerator becomes 2.

Q.2. Find the quotient of each of the following.
(1) \(\frac{7}{17} \div 2\frac{1}{17}\)
Answer:
Convert mixed fraction:
\(2\frac{1}{17} = \frac{35}{17}\)
Divide:
\(= \frac{7}{17} \div \frac{35}{17}\)
\(= \frac{7}{17} \times \frac{17}{35}\)
\(= \frac{7}{35} = \frac{1}{5}\)
In simple words: Convert the mixed fraction and multiply by its reciprocal.
Exam Tip: Identical denominators cancel each other out during division.

(2) \(5\frac{2}{8} \div \frac{16}{18}\) (Note: simplifying \(5\frac{2}{8} = 5\frac{1}{4} = \frac{21}{4}\))
Answer:
Convert mixed fraction:
\(5\frac{2}{8} = \frac{42}{8} = \frac{21}{4}\)
Simplify divisor:
\(\frac{16}{18} = \frac{8}{9}\)
Divide:
\(= \frac{21}{4} \div \frac{8}{9}\)
\(= \frac{21}{4} \times \frac{9}{8} = \frac{189}{32} = 5\frac{29}{32}\)
In simple words: Convert to improper fractions, multiply by the reciprocal of the divisor.

Exam Tip: Simplify fractions before or during calculation to avoid large numbers.

(3) \(9\frac{5}{6} \div 7\frac{1}{6}\)
Answer:
Convert mixed fractions:
\(9\frac{5}{6} = \frac{59}{6}\)
\(7\frac{1}{6} = \frac{43}{6}\)
Divide:
\(= \frac{59}{6} \div \frac{43}{6}\)
\(= \frac{59}{6} \times \frac{6}{43} = \frac{59}{43} = 1\frac{16}{43}\)
In simple words: Convert both numbers to improper fractions, then multiply by the reciprocal.

Exam Tip: Denominators of 6 cancel out directly.

(4) \(3\frac{3}{5} \div 1\frac{1}{5}\)
Answer:
Convert mixed fractions:
\(3\frac{3}{5} = \frac{18}{5}\)
\(1\frac{1}{5} = \frac{6}{5}\)
Divide:
\(= \frac{18}{5} \div \frac{6}{5}\)
\(= \frac{18}{5} \times \frac{5}{6} = \frac{18}{6} = 3\)
In simple words: Convert both mixed fractions and multiply by the reciprocal.

Exam Tip: \(18 \div 6 = 3\).

(5) \(\frac{2}{3} \div 1\frac{1}{15}\)
Answer:
Convert mixed fraction:
\(1\frac{1}{15} = \frac{16}{15}\)
Divide:
\(= \frac{2}{3} \div \frac{16}{15}\)
\(= \frac{2}{3} \times \frac{15}{16}\)
\(= \frac{2 \times 15}{3 \times 16} = \frac{30}{48} = \frac{5}{8}\)
In simple words: Convert to improper fraction, multiply by the reciprocal, and reduce.

Exam Tip: Cross-cancel 3 with 15 and 2 with 16 for faster results.

Q.3. Simplify each of the following.
(1) \(\frac{1}{2} + \frac{1}{3} \text{ of } \frac{1}{9} \div \frac{2}{3}\)
Answer:
Follow BODMAS (Of first, then Division, then Addition):
Step 1 (Of): \(\frac{1}{3} \times \frac{1}{9} = \frac{1}{27}\)
Expression becomes: \(\frac{1}{2} + \frac{1}{27} \div \frac{2}{3}\)
Step 2 (Division): \(\frac{1}{27} \div \frac{2}{3} = \frac{1}{27} \times \frac{3}{2} = \frac{3}{54} = \frac{1}{18}\)
Expression becomes: \(\frac{1}{2} + \frac{1}{18}\)
Step 3 (Addition with common denominator 18):
\(\frac{9}{18} + \frac{1}{18} = \frac{10}{18} = \frac{5}{9}\)
In simple words: Use BODMAS: calculate "of", then division, and finally addition.
Exam Tip: Always perform operations in the correct BODMAS sequence.

(2) \(\frac{1}{2} \div \frac{1}{2} - \left[ \frac{1}{2} \div \frac{1}{2} - \frac{1}{2} \right]\)
Answer:
Solve inside brackets first:
\(\frac{1}{2} \div \frac{1}{2} = 1\)
Inside bracket: \(1 - \frac{1}{2} = \frac{1}{2}\)
Now substitute back:
\(= \left( \frac{1}{2} \div \frac{1}{2} \right) - \frac{1}{2}\)
\(= 1 - \frac{1}{2} = \frac{1}{2}\)
In simple words: Simplify inside the brackets first, then complete the remaining operations.

Exam Tip: Brackets take highest priority in simplification.

(3) \(\left[ \frac{4}{9} \text{ of } 3 \right] \div \frac{1}{3} + \frac{2}{5}\)
Answer:
Step 1 (Inside bracket "of"):
\(\frac{4}{9} \times 3 = \frac{12}{9} = \frac{4}{3}\)
Expression becomes: \(\frac{4}{3} \div \frac{1}{3} + \frac{2}{5}\)
Step 2 (Division):
\(\frac{4}{3} \div \frac{1}{3} = \frac{4}{3} \times \frac{3}{1} = 4\)
Expression becomes: \(4 + \frac{2}{5}\)
Step 3 (Addition):
\(4 + \frac{2}{5} = 4\frac{2}{5} \text{ or } \frac{22}{5}\)
In simple words: Evaluate the bracket first, then divide, and finally add.

Exam Tip: Convert improper fractions to mixed numbers at the very end.

Q.4. Solve the following.
(1) \(\frac{1}{4}\) litre of milk costs Rs. 3.00. How much would \(5\frac{1}{2}\) litres of milk cost?
Answer:
Cost of \(\frac{1}{4}\) litre = Rs. 3.00
Cost of 1 litre = \(3.00 \div \frac{1}{4} = 3.00 \times 4 = \text{Rs. } 12.00\)
Quantity needed = \(5\frac{1}{2} = \frac{11}{2}\) litres
Total cost = \(\frac{11}{2} \times 12 = 11 \times 6 = \text{Rs. } 66.00\)
In simple words: Find the cost of 1 litre first by multiplying by 4, then multiply by the total required quantity.
Exam Tip: Unitary method is extremely helpful for fraction cost problems.

(2) 4 pastries are shared equally by some boys. If each gets \(\frac{2}{3}\) of a pastry, how many boys shared the pastries?
Answer:
Total pastries = 4
Pastry received by each boy = \(\frac{2}{3}\)
Number of boys = Total pastries \(\div\) Pastry per boy
Number of boys = \(4 \div \frac{2}{3}\)
\(= 4 \times \frac{3}{2} = \frac{12}{2} = 6\)
6 boys shared the pastries.
In simple words: Divide the total number of pastries by the fraction each boy receives to find the total number of boys.

Exam Tip: Division by a fraction is the same as multiplication by its reciprocal.