CBSE Class 7 Mathematics Working with Fractions Practice Paper Assignment Set 02 with Answers

Class 7 Maths Ganita Prakash Chapter 8 Working with Fractions Practice Paper 22 is a 40-mark test of 20 questions in Sections A to E, and every question is solved step by step below. It tests finding a fraction of a quantity, dividing a length into equal fractional pieces, reciprocals of mixed numbers, simplifying products by cancelling, and when a product or quotient becomes bigger or smaller, through problems on milk packets, ribbons, a pipe filling a tank, packing sweet boxes and carpeting a hall.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Convert \( 3\frac{1}{2} \) into an improper fraction.
(b) Find its reciprocal.
Answer:
(a) \( 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} \) = \( \frac{7}{2} \).
(b) Swap the numerator and the denominator: reciprocal of \( \frac{7}{2} \) = \( \frac{2}{7} \).
Check: \( \frac{7}{2} \times \frac{2}{7} = 1 \).
In simple words: 3 1/2 is 7 halves, and its reciprocal is 2/7.

Teacher's Note:
1. Improper fraction = (whole × denominator + numerator) over the same denominator.
2. A number multiplied by its reciprocal always gives 1.

Question 12. (a) Simplify \( \frac{8}{9} \times 9 \)
(b) Name the property used.
Answer:
(a) \( \frac{8}{9} \times 9 = \frac{8 \times 9}{9} \) = 8.
(b) We can write it as \( 8 \times (\frac{1}{9} \times 9) \). A number multiplied by its reciprocal gives 1 (\( \frac{1}{9} \times 9 = 1 \)), and then 8 × 1 = 8 because 1 is the multiplicative identity.
So the properties used are “a number × its reciprocal = 1” (with regrouping) and multiplicative identity (a × 1 = a).
In simple words: Nine ninths make one whole, so 8/9 of 9 is exactly 8.

Teacher's Note:
1. Multiplying a fraction by its own denominator always gives the numerator.
2. The source answer named only “multiplicative identity”; the key step is actually 9 × 1/9 = 1.

Question 13. (a) Write the division expression for cutting pieces.
(b) Evaluate: \( \frac{7}{8} \div \frac{1}{4} \)
Answer:
(a) Number of pieces = Total length ÷ Length of one piece.
(b) Dividing by \( \frac{1}{4} \) is the same as multiplying by its reciprocal 4.
\( \frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times 4 = \frac{28}{8} \) = \( \frac{7}{2} \) = \( 3\frac{1}{2} \).
In simple words: Divide the total by the size of one piece; 7/8 ÷ 1/4 = 3 1/2.

Teacher's Note:
1. To divide by a fraction, multiply by its reciprocal.
2. Check: 7/2 × 1/4 = 7/8.

Question 14. (a) Is \( \frac{4}{5} \times \frac{6}{5} \) greater than \( \frac{4}{5} \)?
(b) Give reason.
Answer:
(a) \( \frac{4}{5} \times \frac{6}{5} = \frac{24}{25} \) and \( \frac{4}{5} = \frac{20}{25} \). Since 24 > 20, yes, the product is greater than \( \frac{4}{5} \).
(b) \( \frac{6}{5} \) is greater than 1 (an improper fraction). Multiplying a number by a fraction greater than 1 makes it bigger.
In simple words: Multiplying by 6/5, which is more than 1, makes 4/5 grow to 24/25.

Teacher's Note:
1. Compare the multiplier with 1 to know whether the answer grows or shrinks.
2. Writing both fractions with denominator 25 makes the comparison easy.

Section C: Short Answer Questions (3 Marks Each)

Question 15. A ribbon of length \( \frac{9}{10} \) m is cut into pieces each of length \( \frac{1}{10} \) m.
(a) Operation used
(b) Number of pieces
(c) Reason
Answer:
(a) We need how many equal pieces fit into the ribbon, so the operation is division.
(b) \( \frac{9}{10} \div \frac{1}{10} = \frac{9}{10} \times \frac{10}{1} = \frac{90}{10} \) = 9 pieces.
(c) \( \frac{9}{10} \) m is 9 tenths of a metre and each piece is 1 tenth, so the piece of \( \frac{1}{10} \) m fits into the ribbon exactly 9 times.
In simple words: Nine tenths split into one-tenth pieces gives 9 pieces.

Teacher's Note:
1. Same denominators: just divide the numerators, 9 ÷ 1 = 9.
2. Check: 9 × 1/10 = 9/10 m.

Question 16. Find the area of a rectangle with sides \( 2\frac{1}{3} \) m and \( \frac{3}{7} \) m.
(a) Convert mixed fraction
(b) Multiply
(c) Write answer
Answer:
(a) \( 2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \).
(b) Area = length × breadth = \( \frac{7}{3} \times \frac{3}{7} = \frac{21}{21} \) = 1.
(c) Area of the rectangle = 1 m².
In simple words: 7/3 and 3/7 are reciprocals, so their product is exactly 1 m².

Teacher's Note:
1. Always convert mixed numbers before multiplying.
2. Spotting reciprocals saves time: their product is always 1.

Question 17. Show with an example that multiplying by a whole number increases a fraction.
(a) Choose fraction
(b) Multiply
(c) Compare
Answer:
(a) Take the fraction \( \frac{5}{8} \) and the whole number 3.
(b) \( \frac{5}{8} \times 3 = \frac{15}{8} \) = \( 1\frac{7}{8} \).
(c) \( \frac{15}{8} \gt \frac{5}{8} \) (same denominator, larger numerator). So the product is greater than the original fraction.
In simple words: Three times 5/8 is 15/8, which is clearly more than 5/8.

Teacher's Note:
1. This works for any whole number greater than 1 (multiplying by 1 keeps it the same, and by 0 gives 0).
2. Multiplying by a whole number is repeated addition: 5/8 + 5/8 + 5/8.

Section D: Long Answer Question (5 Marks)

Question 18. A pipe fills \( \frac{5}{12} \) of a tank in one hour.
(a) Fraction filled in 2 hours
(b) Fraction filled in \( \frac{1}{3} \) hour
(c) Time to fill the tank completely
(d) Operation used
(e) Final conclusion
Answer:
(a) In 2 hours: \( 2 \times \frac{5}{12} = \frac{10}{12} \) = \( \frac{5}{6} \) of the tank.
(b) In \( \frac{1}{3} \) hour: \( \frac{1}{3} \times \frac{5}{12} \) = \( \frac{5}{36} \) of the tank.
(c) Time for the full tank = \( 1 \div \frac{5}{12} = 1 \times \frac{12}{5} = \frac{12}{5} \) = \( 2\frac{2}{5} \) hours.
\( \frac{2}{5} \) hour = \( \frac{2}{5} \) × 60 minutes = 24 minutes, so this is 2 hours 24 minutes.
(d) Multiplication of fractions in (a) and (b), and division of fractions in (c).
(e) The pipe fills \( \frac{5}{6} \) of the tank in 2 hours and the whole tank in \( 2\frac{2}{5} \) hours (2 hours 24 minutes).
In simple words: Multiply the hourly fraction by the time; divide 1 whole tank by 5/12 to get 2 2/5 hours.

Teacher's Note:
1. Part filled = rate × time; time for whole job = 1 ÷ rate.
2. Check (c): 12/5 × 5/12 = 1 full tank.
3. Converting 2/5 hour into minutes makes the answer easy to picture.

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

Question 19. Case Study 1: Packing Sweet Boxes
A sweet shop owner has \( \frac{10}{11} \) kg of sweets. He wants to pack the sweets into small boxes, each box holding \( \frac{2}{11} \) kg. Before packing, he calculates how many complete boxes can be prepared so that no sweets are wasted. This situation helps students understand the concept of division of fractions by applying real-life reasoning where a total quantity is divided by the quantity required for one unit.
Answer the following questions:
(a) Write the mathematical expression
(b) Find number of boxes
(c) Write the reciprocal used
(d) Name the operation
Answer:
(a) Number of boxes = total sweets ÷ sweets in one box = \( \frac{10}{11} \div \frac{2}{11} \).
(b) \( \frac{10}{11} \times \frac{11}{2} = \frac{110}{22} \) = 5 boxes.
(c) The reciprocal of \( \frac{2}{11} \), which is \( \frac{11}{2} \).
(d) Division of fractions.
In simple words: 10 elevenths of a kilogram packed 2 elevenths at a time fills 5 boxes.

Teacher's Note:
1. Check: 5 × 2/11 = 10/11 kg, so no sweets are wasted.
2. When the denominators match, the answer is simply 10 ÷ 2.

Question 20. Case Study 2: Laying a Carpet
A rectangular hall has a length of \( \frac{6}{7} \) m and a width of \( \frac{5}{12} \) m. The owner wants to calculate the area of the hall to purchase the correct amount of carpet. Students recall that the area of a rectangle, even with fractional dimensions, is found by multiplying length and breadth.
Answer the following questions:
(a) Write the formula
(b) Substitute values
(c) Find the area
(d) Concept used
Answer:
(a) Area of a rectangle = length × breadth.
(b) Area = \( \frac{6}{7} \times \frac{5}{12} \).
(c) Cancel 6 and 12 by 6: \( \frac{1}{7} \times \frac{5}{2} = \frac{5}{14} \). Area = \( \frac{5}{14} \) m².
(d) Multiplication of fractions.
In simple words: Multiply 6/7 by 5/12 to get an area of 5/14 square metre.

Teacher's Note:
1. Area is always in square units (m²).
2. Cancelling 6 with 12 first gives the lowest-terms answer directly.