Class 6 Comparing Fractions — practice questions with answers

Fractions · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Which symbol makes this true?

\frac{3}{7}

___

\frac{5}{7}

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Answer: A) <

Same denominator (7). Compare numerators: 3 < 5, so

\frac{3}{7}

\frac{5}{7}

2. Using cross-multiplication, compare

\frac{3}{5}

and

\frac{4}{7}

. Which is greater?

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Answer: A)

\frac{3}{5}

Cross-multiply: 3×7 = 21 and 5×4 = 20. The product 21 is paired with

\frac{3}{5}

and is larger, so

\frac{3}{5}

\frac{4}{7}

3. Which of these equals

\frac{2}{3}

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Answer: A)

\frac{6}{9}

Multiply

\frac{2}{3}

top and bottom by 3 to get

\frac{6}{9}

. So

\frac{6}{9}

\frac{2}{3}

. (

\frac{4}{9}

\frac{3}{6}

\frac{1}{2}

\frac{6}{8}

\frac{3}{4}

are not equal.)

4. A jug holds juice. On Monday it was

\frac{7}{10}

full and on Tuesday it was

\frac{11}{15}

full.
The gardener wants to know on which day the jug had more juice.
Which day had more, and what is the comparison?

\frac{7}{10}

___

\frac{11}{15}

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Answer: B)

\frac{7}{10}

\frac{11}{15}

, Tuesday more

LCM of 10 and 15 is 30.

\frac{7}{10}

\frac{21}{30}

and

\frac{11}{15}

\frac{22}{30}

. Since 21 < 22,

\frac{7}{10}

\frac{11}{15}

, so the jug had more juice on Tuesday.

5. Four banners cover

\frac{5}{6}

\frac{7}{9}

\frac{11}{12}

and

\frac{13}{18}

of a wall each (on identical walls).
The decorator wants the banner that covers the greatest fraction of its wall.
Which banner is it?

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Answer: C)

\frac{11}{12}

LCM of 6, 9, 12, 18 is 36.

\frac{5}{6}

\frac{30}{36}

\frac{7}{9}

\frac{28}{36}

\frac{11}{12}

\frac{33}{36}

\frac{13}{18}

\frac{26}{36}

. Greatest is

\frac{33}{36}

, so

\frac{11}{12}

covers the most.

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