This MCQ module is based on: Fractions Chapter Exercises
TOPIC 28 OF 41
Fractions Chapter Exercises
🎓 Class 6
Mathematics
CBSE
Theory
Ch 7 — Fractions
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Fractions Chapter Exercises
Targeting Class 6 level in Fractions, with Basic difficulty.
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Chapter 7 — Exercises & Summary
Time to practise the full chapter! Solve each exercise? and click "Show Answer" to check. Then read the Summary at the end.
Section 7.6 Exercises — Equivalent Fractions
Q1. Find equivalent fractions for each pair so that the fractional units are the same:
(a) \(\frac{7}{2}, \frac{3}{5}\) (b) \(\frac{8}{3}, \frac{5}{6}\) (c) \(\frac{3}{4}, \frac{3}{5}\) (d) \(\frac{6}{7}, \frac{8}{5}\) (e) \(\frac{9}{4}, \frac{5}{2}\) (f) \(\frac{1}{10}, \frac{2}{9}\) (g) \(\frac{8}{3}, \frac{11}{4}\) (h) \(\frac{13}{6}, \frac{1}{9}\)
(a) \(\frac{7}{2}, \frac{3}{5}\) (b) \(\frac{8}{3}, \frac{5}{6}\) (c) \(\frac{3}{4}, \frac{3}{5}\) (d) \(\frac{6}{7}, \frac{8}{5}\) (e) \(\frac{9}{4}, \frac{5}{2}\) (f) \(\frac{1}{10}, \frac{2}{9}\) (g) \(\frac{8}{3}, \frac{11}{4}\) (h) \(\frac{13}{6}, \frac{1}{9}\)
(a) \(\tfrac{35}{10}, \tfrac{6}{10}\) (b) \(\tfrac{16}{6}, \tfrac{5}{6}\) (c) \(\tfrac{15}{20}, \tfrac{12}{20}\) (d) \(\tfrac{30}{35}, \tfrac{56}{35}\) (e) \(\tfrac{9}{4}, \tfrac{10}{4}\) (f) \(\tfrac{9}{90}, \tfrac{20}{90}\) (g) \(\tfrac{32}{12}, \tfrac{33}{12}\) (h) \(\tfrac{39}{18}, \tfrac{2}{18}\).
Q2. Rahim mixes \(\frac{2}{3}\) litre of yellow paint with \(\frac{3}{4}\) litre of blue paint. What is the volume of green paint?
\(\frac{2}{3}+\frac{3}{4}=\frac{8+9}{12}=\frac{17}{12}=1\tfrac{5}{12}\) litres.
Q3. Geeta bought \(\frac{2}{5}\) m lace, Shamim bought \(\frac{3}{4}\) m of the same lace. Perimeter = 1 m. Find total length and say if it's enough.
Total = \(1\tfrac{3}{20}\) m. Yes, this covers the 1 m perimeter with 15 cm extra.
Section 7.7 Exercises — Mixed Addition
Q1. Compute:
(a) \(\frac{6}{7}+\frac{7}{7}\) (b) \(\frac{6}{7}+\frac{1}{12}\) (c) \(\frac{9}{6}\) (simplify) (d) \(\frac{3}{7}+\frac{11}{21}\) (e) \(\frac{7}{10}+\frac{11}{12}\) (f) \(\frac{2}{3}+\frac{4}{5}\) (g) \(\frac{5}{8}+\frac{7}{12}\) (h) \(\frac{7}{10}+\frac{7}{8}\) (i) \(5\tfrac{3}{4}\) (j) \(2\tfrac{20}{21}\) (k) \(\frac{7}{10}+\frac{11}{12}\) again (l) \(1\tfrac{94}{105}\) (m) \(6\tfrac{11}{12}\).
(a) \(\frac{6}{7}+\frac{7}{7}\) (b) \(\frac{6}{7}+\frac{1}{12}\) (c) \(\frac{9}{6}\) (simplify) (d) \(\frac{3}{7}+\frac{11}{21}\) (e) \(\frac{7}{10}+\frac{11}{12}\) (f) \(\frac{2}{3}+\frac{4}{5}\) (g) \(\frac{5}{8}+\frac{7}{12}\) (h) \(\frac{7}{10}+\frac{7}{8}\) (i) \(5\tfrac{3}{4}\) (j) \(2\tfrac{20}{21}\) (k) \(\frac{7}{10}+\frac{11}{12}\) again (l) \(1\tfrac{94}{105}\) (m) \(6\tfrac{11}{12}\).
(a) \(\frac{13}{7}\) (b) \(\frac{13}{12}\) (c) \(\frac{9}{6}=\frac{3}{2}\) (d) \(\frac{20}{21}\) (e) \(\frac{77}{60}\) (f) \(\frac{22}{15}\) (g) \(\frac{22}{15}\) (h) \(\frac{49}{40}\) (i) \(\frac{23}{4}\) (j) \(\frac{62}{21}\) (k) \(\frac{77}{60}\) (l) \(\frac{199}{105}\) (m) \(\frac{83}{12}\).
Section 7.8 Exercises — Subtraction (Brahmagupta's Method)
Q1. Subtract using Brahmagupta's method:
(a) \(\frac{8}{15}-\frac{3}{15}\) (b) \(\frac{2}{5}-\frac{4}{15}\) (c) \(\frac{5}{6}-\frac{4}{9}\) (d) \(\frac{2}{3}-\frac{1}{2}\)
(a) \(\frac{8}{15}-\frac{3}{15}\) (b) \(\frac{2}{5}-\frac{4}{15}\) (c) \(\frac{5}{6}-\frac{4}{9}\) (d) \(\frac{2}{3}-\frac{1}{2}\)
(a) \(\frac{5}{15}=\frac{1}{3}\) (b) \(\frac{6-4}{15}=\frac{2}{15}\) (c) \(\frac{15-8}{18}=\frac{7}{18}\) (d) \(\frac{4-3}{6}=\frac{1}{6}\).
Q2. Subtract as indicated:
(a) \(\frac{13}{4}\) from \(\frac{10}{3}\) (b) \(\frac{18}{5}\) from \(\frac{23}{3}\) (c) \(\frac{29}{7}\) from \(\frac{45}{7}\)
(a) \(\frac{13}{4}\) from \(\frac{10}{3}\) (b) \(\frac{18}{5}\) from \(\frac{23}{3}\) (c) \(\frac{29}{7}\) from \(\frac{45}{7}\)
(a) \(\frac{40-39}{12}=\frac{1}{12}\) (b) \(\frac{115-54}{15}=\frac{61}{15}\) (c) \(\frac{45-29}{7}=\frac{16}{7}\).
Q3. Word problems:
(a) Jaya's school is \(\frac{7}{10}\) km from her home. She takes an auto for \(\frac{1}{2}\) km and walks the rest. How far does she walk?
(b) Jeevika takes \(\frac{10}{3}\) min for a round; Namit takes \(\frac{13}{4}\) min. Who is faster, and by how much?
(a) Jaya's school is \(\frac{7}{10}\) km from her home. She takes an auto for \(\frac{1}{2}\) km and walks the rest. How far does she walk?
(b) Jeevika takes \(\frac{10}{3}\) min for a round; Namit takes \(\frac{13}{4}\) min. Who is faster, and by how much?
(a) Walk = \(\frac{7}{10}-\frac{1}{2}=\frac{7-5}{10}=\frac{2}{10}=\frac{1}{5}\) km.
(b) \(\frac{10}{3}=\frac{40}{12}\), \(\frac{13}{4}=\frac{39}{12}\). Namit is faster by \(\frac{1}{12}\) min.
(b) \(\frac{10}{3}=\frac{40}{12}\), \(\frac{13}{4}=\frac{39}{12}\). Namit is faster by \(\frac{1}{12}\) min.
Activity: Egyptian Unit Fractions
L4 AnalyseMaterials: Paper, pencil.
Predict: Ancient Egyptians wrote every fraction as a sum of different unit fractions. Can you express \(\frac{2}{5}\) this way?
- Try \(\frac{2}{5}=\frac{1}{3}+\frac{?}{?}\). What's left? \(\frac{2}{5}-\frac{1}{3}=\frac{6-5}{15}=\frac{1}{15}\).
- So \(\frac{2}{5}=\frac{1}{3}+\frac{1}{15}\). Two different unit fractions!
- Try writing \(\frac{3}{7}\) the same way.
\(\frac{3}{7}=\frac{1}{3}+\frac{1}{11}+\frac{1}{231}\). (There are many valid Egyptian decompositions — this is one.)
Competency-Based Questions — Chapter Mix
Scenario: A recipe needs \(\frac{3}{4}\) cup of flour, \(\frac{1}{2}\) cup of sugar, and \(\frac{1}{3}\) cup of milk. Roshni is tripling the recipe for a larger batch.
Q1. How much total liquid/dry ingredient volume does the original recipe need? (Sum all three)
L3 Apply\(\frac{3}{4}+\frac{1}{2}+\frac{1}{3}=\frac{9+6+4}{12}=\frac{19}{12}=1\tfrac{7}{12}\) cups.
Q2. Analyse how much flour is needed for 3× the recipe. Write the answer as a mixed fraction.
L4 Analyse\(3 \times \frac{3}{4}=\frac{9}{4}=2\tfrac{1}{4}\) cups.
Q3. Roshni has only a \(\frac{1}{4}\) cup measure. Evaluate how many level \(\frac{1}{4}\)-cup scoops she needs to measure the sugar for the tripled recipe.
L5 EvaluateSugar tripled = \(3\times\frac{1}{2}=\frac{3}{2}\) cup = \(\frac{6}{4}\) cup. She needs 6 scoops of the \(\frac{1}{4}\)-cup measure.
Q4. Create a new recipe where the three ingredient fractions (in cups) sum to exactly \(\frac{5}{4}\) and all three are different fractions with denominators ≤ 8.
L6 CreateOne valid plan: \(\frac{1}{2}+\frac{3}{8}+\frac{3}{8}\) has a repeat. Try \(\frac{1}{2}+\frac{5}{8}+\frac{1}{8}=\frac{4+5+1}{8}=\frac{10}{8}=\frac{5}{4}\) ✓. All different, denominators ≤ 8.
Assertion–Reason Questions
A: \(\frac{2}{3}+\frac{3}{4}=\frac{17}{12}\).
R: LCM of 3 and 4 is 12, and \(\frac{8}{12}+\frac{9}{12}=\frac{17}{12}\).
R: LCM of 3 and 4 is 12, and \(\frac{8}{12}+\frac{9}{12}=\frac{17}{12}\).
(a) — Both true, R explains A.
A: \(\frac{10}{3}>\frac{13}{4}\).
R: \(\frac{40}{12}>\frac{39}{12}\), so Jeevika is slower.
R: \(\frac{40}{12}>\frac{39}{12}\), so Jeevika is slower.
(a) — Both true. \(\frac{40}{12}>\frac{39}{12}\) ⇒ Jeevika takes more time, so is slower.
A: \(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}=1\).
R: Sum of any three unit fractions is 1.
R: Sum of any three unit fractions is 1.
(c) — A is true but R is false. Only specific triples (like 1/2+1/3+1/6) sum to 1, not every triple.
Chapter 7 — Summary
- Fractional units: When a whole is split into \(n\) equal parts, each part is \(\frac{1}{n}\) — a unit fraction.
- Fractions: \(\frac{a}{b}\) means \(a\) copies of the unit \(\frac{1}{b}\). Bigger denominator → smaller pieces (for unit fractions).
- Number line: Any fraction can be located by dividing each unit into equal parts based on the denominator.
- Mixed fractions: An improper fraction \(\frac{a}{b}\) (with \(a\ge b\)) can be written as whole + proper fraction.
- Equivalent fractions: \(\frac{a}{b}=\frac{ak}{bk}\). Simplify by dividing by the common factor.
- Comparing: Make denominators equal, then compare numerators.
- Brahmagupta's method: To add/subtract fractions, first convert to a common fractional unit.
- Indian heritage: Words for fractions (e.g., tri-pada, teen paav, mukkaal) reflect thousands of years of Indian mathematical tradition.
Key Terms
Unit fraction • Numerator • Denominator • Proper fraction • Improper fraction • Mixed fraction • Equivalent fractions • Lowest terms • Common denominator • Brahmagupta's method.
Frequently Asked Questions
What topics do the Chapter 7 exercises cover?
They cover unit fractions, number line plotting, equivalent fractions, simplest form, comparison by LCM and cross multiplication, addition and subtraction of like and unlike fractions, and fraction word problems.
How do you approach a fraction word problem?
Read carefully, identify the total quantity, translate each share as a fraction of the whole, set up the arithmetic using a common denominator if needed, and check the units of the final answer.
Are all the exercise answers in the simplest form?
Yes, NCERT expects final answers to be reduced to the simplest form by dividing the numerator and denominator by their HCF.
What is the summary of Chapter 7 Fractions?
A fraction represents equal parts of a whole. Unit fractions are 1/n, equivalent fractions name the same value, comparison uses LCM, and addition or subtraction needs a common denominator.
How do exercises build fraction fluency?
Exercises move from naming and visualising fractions, through equivalence and comparison, to arithmetic operations, so students master every step before facing mixed word problems.
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