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Working with Fractions Exercises

🎓 Class 7 Mathematics CBSE Theory Ch 8 — Working with Fractions ⏱ ~35 min
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This MCQ module is based on: Working with Fractions Exercises

This mathematics assessment will be based on: Working with Fractions Exercises
Targeting Class 7 level in Fractions, with Basic difficulty.

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Chapter 8 — End-of-Chapter Exercises

Work through these items using the rules from sections 8.1 and 8.2. For each question, try the pencil-and-paper calculation before tapping Show Answer.

Q1. Evaluate: (a) \(3\times\tfrac94=\tfrac{27}{4}\); (b) \(\tfrac{14}{7}\times 2=\tfrac{7}{4}\); (c) \(\tfrac{2}{3}\times\tfrac{2}{15}\div 1\); (d) \(\tfrac{14}{11}\div\tfrac73=1\tfrac{2}{3}\). Confirm each answer.
(a) \(\tfrac{27}{4}\). (b) \(\tfrac{28}{7}=4\). (c) \(\tfrac{2}{3}\times\tfrac{2}{15}=\tfrac{4}{45}\). (d) \(\tfrac{14}{11}\times\tfrac{3}{7}=\tfrac{42}{77}=\tfrac{6}{11}\).
Q2. Maria has 8 m of lace to decorate bags. She uses \(\tfrac14\) m per bag. How many bags can she decorate?
\(8\div\tfrac14 = 32\) bags.
Q3. \(\tfrac12\) m of ribbon is used to make 8 badges. What is the length of ribbon per badge?
\(\tfrac12\div 8 = \tfrac{1}{16}\) m = 6.25 cm per badge.
Q4. A baker needs \(\tfrac56\) kg of flour per loaf and has 5 kg. How many loaves? Compare with the answer if each loaf needs \(\tfrac12\) kg.
First: \(5\div\tfrac56 = 6\) loaves. Second: \(5\div\tfrac12 = 10\) loaves.
Q5. If \(4\tfrac12\) kg of flour is used to make 12 rotis, how much flour is used for 6 rotis?
Per roti: \(\tfrac{9}{2}\div 12 = \tfrac{3}{8}\) kg. For 6: \(6\times\tfrac{3}{8}=\tfrac{18}{8}=2\tfrac14\) kg.
Q6. A colony of ants moves along a tree that splits in half at each point (an equal split). After 5 such branch-points, what fraction of the original group reaches the rightmost branch?
\(\tfrac12\times\tfrac12\times\tfrac12\times\tfrac12\times\tfrac12 = \tfrac{1}{32}\).
Q7. Evaluate the telescoping product: \((1-\tfrac12)\times(1-\tfrac13)\times(1-\tfrac14)\times(1-\tfrac15)\).
\(\tfrac12\times\tfrac23\times\tfrac34\times\tfrac45 = \tfrac{1\cdot 2\cdot 3\cdot 4}{2\cdot 3\cdot 4\cdot 5} = \tfrac{1}{5}\). In general, the product \((1-\tfrac12)(1-\tfrac13)\cdots(1-\tfrac1n) = \tfrac{1}{n}\).
Q8. Find: \(7\tfrac{3}{4}\) as a fraction.
\(7\tfrac34 = \tfrac{7\times 4+3}{4} = \tfrac{31}{4}\).

Summary

  • Brahmagupta's multiplication formula: \(\tfrac{a}{b}\times\tfrac{c}{d}=\tfrac{ac}{bd}\).
  • When multiplying fractions, we can cancel common factors between any numerator and any denominator before multiplying.
  • In multiplication, when both numbers being multiplied lie strictly between 0 and 1, the product is smaller than each factor.
  • In multiplication, if exactly one of the numbers is > 1, the product is larger than the smaller factor.
  • The reciprocal of \(\tfrac{a}{b}\) is \(\tfrac{b}{a}\). A fraction multiplied by its reciprocal equals 1.
  • Brahmagupta's division formula: \(\tfrac{a}{b}\div\tfrac{c}{d}=\tfrac{a}{b}\times\tfrac{d}{c}=\tfrac{ad}{bc}\).
  • In division, when the divisor is < 1, the quotient is larger than the dividend. When the divisor is > 1, the quotient is smaller than the dividend.
Activity: Fractional Relations Puzzle
Materials: Square grid paper, ruler, pencil.
  1. Draw a large square and divide it into a 4 × 4 grid (16 small squares).
  2. Shade one row completely — what fraction of the square is that? \(\tfrac14\)
  3. Shade one of the 16 small squares in red — what fraction? \(\tfrac{1}{16}\)
  4. Verify with multiplication: \(\tfrac14\times\tfrac14=\tfrac{1}{16}\).
  5. Now divide the big square into a 3 × 3 grid and shade 2 rows + 2 columns; find the overlap area as a fraction.
Overlap = \(\tfrac23\times\tfrac23 = \tfrac49\) of the big square (4 of the 9 small squares).

Competency-Based Questions

Scenario: A small library has \(\tfrac{3}{4}\) of its shelves filled. Of the filled shelves, \(\tfrac{2}{5}\) are fiction. A new shipment arrives that will fill the remaining shelves.
Q1. What fraction of the total shelf space is fiction?
L3 Apply
\(\tfrac{3}{4}\times\tfrac{2}{5} = \tfrac{6}{20}=\tfrac{3}{10}\).
Q2. What fraction of shelf space is empty before the shipment?
L4 Analyse
\(1-\tfrac34=\tfrac14\) is empty.
Q3. Evaluate: if each shelf holds \(\tfrac12\) m of books and the library has 80 shelves in total, how many metres of books are currently shelved?
L5 Evaluate
Filled shelves = \(\tfrac34\times 80 = 60\). Total book length = \(60\times\tfrac12 = 30\) m.
Q4. Design a new shelving plan: if the library wants fiction to occupy exactly \(\tfrac{1}{4}\) of total space and non-fiction \(\tfrac{1}{2}\), what fraction remains for reference and journals?
L6 Create
\(1-\tfrac14-\tfrac12 = \tfrac14\) — a quarter of the space is reserved for reference and journals.

Assertion–Reason Questions

A: \(\tfrac{4}{9}\times\tfrac{3}{8}=\tfrac{1}{6}\).
R: We may cancel a common factor between a numerator and a denominator before multiplying.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
(a) — cancel 4 with 8 and 3 with 9: \(\tfrac{1}{3}\times\tfrac{1}{2}=\tfrac{1}{6}\). R explains A.
A: \(\tfrac35\div\tfrac14 = \tfrac{3}{20}\).
R: Dividing by a fraction means multiplying by its reciprocal.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
(d) — A is false: \(\tfrac35\div\tfrac14 = \tfrac35\times 4 = \tfrac{12}{5}\). R is true.
A: \((1-\tfrac12)(1-\tfrac13)\cdots(1-\tfrac1{100}) = \tfrac{1}{100}\).
R: In the telescoping product, every factor cancels except the first numerator and the last denominator.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
(a) — the product simplifies to \(\tfrac{1}{2}\cdot\tfrac{2}{3}\cdots\tfrac{99}{100}=\tfrac{1}{100}\). R explains A.

Frequently Asked Questions

What is the summary of Chapter 8 Working with Fractions?
Chapter 8 covers all four arithmetic operations on fractions with a focus on multiplication and division, including the reciprocal rule and real-life applications such as area, sharing and scaling quantities.
How do word problems on fractions use multiplication?
Typical problems ask for the cost of 2/3 kg of an item or 3/4 of a quantity. Multiplying the fraction with the given price or total gives the answer.
Why convert mixed fractions before multiplying or dividing?
Converting to improper fractions makes the rules clean and uniform: multiply numerators, multiply denominators, or take the reciprocal for division.
How do exercises test division of fractions?
They include dividing a fraction by a whole number, a whole number by a fraction, and one fraction by another, often framed as sharing or rate questions.
What is a common mistake in fraction division?
Forgetting to invert the second fraction before multiplying, or inverting both fractions. Only the divisor (second fraction) is inverted.
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Mathematics Class 7 — Ganita Prakash
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