CBSE Class 7 Mathematics Working with Fractions Practice Paper Worksheet Set 03 with Answers

Working with Fractions Practice Paper 25 for Class 7 Maths Ganita Prakash (Chapter 8) is a full 40-mark, 20-question paper in Sections A to E, given here with a clear worked answer for every question. It covers taking a fraction of a quantity of sugar, counting equal ribbon pieces, products greater than 1, cancelling in 33/40 × 8/11, the reciprocal of 9 7/11, dividing by 5/6, and the time a worker needs to finish a task, ending with case studies on filling coffee sachets and the floor area of a community hall.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Convert \( 13\frac{3}{8} \) into an improper fraction.
(b) Find its reciprocal.
Answer:
(a) \( 13\frac{3}{8} = \frac{13 \times 8 + 3}{8} = \frac{104 + 3}{8} \) = \( \frac{107}{8} \).
(b) Reciprocal = \( \frac{8}{107} \).
In simple words: 13 3/8 is 107 eighths; flipping it gives 8/107.

Teacher's Note:
1. 13 × 8 = 104, then add 3.
2. Check: 107/8 × 8/107 = 1.

Question 12. (a) Simplify \( \frac{23}{24} \times 24 \)
(b) State the property used.
Answer:
(a) \( \frac{23}{24} \times 24 = \frac{23 \times 24}{24} \) = 23.
(b) \( \frac{23}{24} \times 24 = 23 \times (\frac{1}{24} \times 24) = 23 \times 1 = 23 \). A number times its reciprocal is 1, and multiplying by 1 leaves 23 unchanged (multiplicative identity).
Properties used: “number × reciprocal = 1” and multiplicative identity.
In simple words: 24 twenty-fourths make one whole, so 23/24 of 24 is 23.

Teacher's Note:
1. Multiplying a fraction by its own denominator gives the numerator.
2. The source names only the multiplicative identity; the reciprocal step is the key one.

Question 13. (a) Write the expression to find number of equal pieces.
(b) Evaluate: \( \frac{21}{22} \div \frac{1}{22} \)
Answer:
(a) Number of equal pieces = Total quantity ÷ Size of one piece.
(b) \( \frac{21}{22} \div \frac{1}{22} = \frac{21}{22} \times 22 \) = 21.
In simple words: There are 21 pieces of 1/22 in 21/22.

Teacher's Note:
1. Same denominator: divide the numerators, 21 ÷ 1 = 21.
2. Check: 21 × 1/22 = 21/22.

Question 14. (a) Is \( \frac{12}{13} \times \frac{15}{12} \) greater than \( \frac{12}{13} \)?
(b) Give reason.
Answer:
(a) \( \frac{12}{13} \times \frac{15}{12} = \frac{15}{13} \) (the 12s cancel). \( \frac{15}{13} \gt \frac{12}{13} \), so yes.
(b) \( \frac{15}{12} \) is greater than 1, so multiplying by it increases the value.
In simple words: Multiplying by 15/12, which is more than 1, makes 12/13 bigger.

Teacher's Note:
1. Compare the multiplier with 1 to predict the result.
2. 15/13 is even more than 1 whole.

Section C: Short Answer Questions (3 Marks Each)

Question 15. A rope of length \( \frac{26}{27} \) m is cut into pieces of length \( \frac{1}{27} \) m.
(a) Operation used
(b) Number of pieces
(c) Explanation
Answer:
(a) Division.
(b) \( \frac{26}{27} \div \frac{1}{27} = \frac{26}{27} \times 27 \) = 26 pieces.
(c) The rope contains 26 parts of \( \frac{1}{27} \) m, so the unit fraction \( \frac{1}{27} \) fits into it 26 times.
In simple words: A 26/27 m rope gives 26 pieces of 1/27 m.

Teacher's Note:
1. Number of pieces = total length ÷ length of one piece.
2. Check: 26 × 1/27 = 26/27 m.

Question 16. Find area of rectangle: sides \( 6\frac{2}{5} \) m and \( \frac{5}{32} \) m.
(a) Convert mixed fraction
(b) Multiply
(c) Area
Answer:
(a) \( 6\frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{32}{5} \).
(b) \( \frac{32}{5} \times \frac{5}{32} = \frac{160}{160} \) = 1.
(c) Area = 1 m².
In simple words: 32/5 and 5/32 are reciprocals, so the area is 1 square metre.

Teacher's Note:
1. Spot reciprocal pairs: their product is always 1.
2. Always write the unit m² for area.

Question 17. Show multiplying a fraction by its reciprocal = 1.
(a) Choose fraction
(b) Multiply
(c) Result
Answer:
(a) Take \( \frac{8}{15} \); its reciprocal is \( \frac{15}{8} \).
(b) \( \frac{8}{15} \times \frac{15}{8} = \frac{8 \times 15}{15 \times 8} = \frac{120}{120} \).
(c) The result is 1.
In simple words: A fraction multiplied by its flipped form always gives 1.

Teacher's Note:
1. The reciprocal of a/b is b/a (when a is not 0).
2. This fact is the reason we multiply by the reciprocal when dividing.

Section D: Long Answer Question (5 Marks)

Question 18. A worker completes \( \frac{15}{32} \) of a task in one hour.
(a) Work done in 6 hours
(b) Work done in \( \frac{5}{6} \) hour
(c) Time required to complete task
(d) Operations involved
(e) Conclusion
Answer:
(a) Work in 6 hours = \( 6 \times \frac{15}{32} = \frac{90}{32} \) = \( \frac{45}{16} \) = \( 2\frac{13}{16} \) tasks (if he goes on to similar tasks).
(b) Work in \( \frac{5}{6} \) hour = \( \frac{5}{6} \times \frac{15}{32} = \frac{75}{192} \) = \( \frac{25}{64} \) of the task (divide by 3).
(c) Time for one whole task = \( 1 \div \frac{15}{32} = \frac{32}{15} \) = \( 2\frac{2}{15} \) hours, i.e. 2 hours 8 minutes.
(d) Multiplication of fractions in (a) and (b); division of fractions in (c).
(e) The worker finishes the task in \( 2\frac{2}{15} \) hours; working 6 hours, he could do the work of \( 2\frac{13}{16} \) such tasks.
In simple words: Multiply 15/32 by the hours worked, and divide 1 by 15/32 to get the time for the full task.

Teacher's Note:
1. 2/15 hour = 2/15 × 60 = 8 minutes.
2. Always reduce answers such as 75/192 to lowest terms (25/64).
3. Check (c): 32/15 × 15/32 = 1 whole task.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: Packing Coffee Powder
A coffee company produces \( \frac{4}{7} \) kg of coffee powder daily. The powder is packed into small sachets, each weighing \( \frac{1}{14} \) kg. The supervisor calculates how many full sachets can be filled so that no powder is wasted. This situation represents division of fractions in real-life application.
Answer the following questions:
(a) Write the expression
(b) Find number of sachets
(c) Reciprocal used
(d) Name the operation
Answer:
(a) Number of sachets = \( \frac{4}{7} \div \frac{1}{14} \).
(b) \( \frac{4}{7} \times 14 = \frac{56}{7} \) = 8 sachets.
(c) Reciprocal of \( \frac{1}{14} \) = 14.
(d) Division of fractions.
In simple words: 4/7 kg of coffee filled 1/14 kg at a time makes 8 sachets.

Teacher's Note:
1. Cancel 14 with 7: 4 × 2 = 8.
2. Check: 8 × 1/14 = 8/14 = 4/7 kg.

Question 20. Case Study 2: Laying a Carpet
A rectangular community hall has a length of \( \frac{19}{20} \) m and a width of \( \frac{5}{19} \) m. To plan flooring, the manager calculates the area. This demonstrates multiplication of fractions with fractional dimensions to find area in real-life scenarios.
Answer the following questions:
(a) Area formula
(b) Substitute values
(c) Find area
(d) Concept applied
Answer:
(a) Area = length × breadth.
(b) Area = \( \frac{19}{20} \times \frac{5}{19} \).
(c) Cancel 19 with 19 and 5 with 20: Area = \( \frac{5}{20} \) = \( \frac{1}{4} \) m².
(d) Multiplication of fractions.
In simple words: 19/20 × 5/19 = 1/4, so the area is a quarter of a square metre.

Teacher's Note:
1. Cancel before multiplying to keep the numbers small.
2. Area is measured in square metres (m²).