Using a Common Denominator to Order Fraction Online Quiz

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Questions and Answers
Q 1 - First, rewrite $\frac{2}{5}$ and $\frac{10}{11}$ so that they have a common denominator. Then use <, = or > to order $\frac{2}{5}$ and $\frac{10}{11}$.

Answer : B

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{2}{5}$ and $\frac{10}{11}$ is 55.

Step 2:

Rewriting the fractions with this denominator.

$\frac{2}{5}$ = 2×11 ÷ 5×11 = $\frac{22}{55}$

$\frac{10}{11}$ = 10×5 ÷ 11×5 = $\frac{50}{55}$

Step 3:

Ordering them using their numerators.

Because 22 < 50, we have

$\frac{22}{55}$ < $\frac{50}{55}$

Step 4:

Writing these fractions in original form $\frac{2}{5}$ < $\frac{10}{11}$

Q 2 - First, rewrite $\frac{3}{4}$ and $\frac{7}{9}$ so that they have a common denominator. Then use <, = or > to order $\frac{3}{4}$ and $\frac{7}{9}$.

Answer : D

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{3}{4}$ and $\frac{7}{9}$ is 36.

Step 2:

Rewriting the fractions with this denominator.

$\frac{3}{4}$ = 3×9 ÷ 4×9 = $\frac{27}{36}$

$\frac{7}{9}$ = 7×4 ÷ 9×4 = $\frac{28}{36}$

Step 3:

Because 27 < 28, we have

$\frac{27}{36}$ < $\frac{28}{36}$

Step 4:

Writing these fractions in original form $\frac{3}{4}$ < $\frac{7}{9}$

Q 3 - First, rewrite $\frac{2}{5}$ and $\frac{4}{10}$ so that they have a common denominator. Then use <, = or > to order 2/5 and $\frac{4}{10}$.

 

Answer : A

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{2}{5}$ and $\frac{4}{10}$ is 10.

Step 2:

Rewriting the fractions with this denominator.

$\frac{2}{5}$ = 2×2 ÷ 5×2 = $\frac{4}{10}$

$\frac{4}{10}$ = 4×1 ÷ 10×1 = $\frac{4}{10}$

Step 3:

Because 4 = 4, we have $\frac{4}{10}$ = $\frac{4}{10}$

Step 4:

Writing these fractions in original form $\frac{2}{5}$ = $\frac{4}{10}$

Q 4 - First, rewrite $\frac{2}{6}$ and $\frac{3}{10}$ so that they have a common denominator. Then use <, = or > to order $\frac{2}{6}$ and $\frac{3}{10}$.

Answer : C

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{2}{6}$ and $\frac{3}{10}$ is 30.

Step 2:

Rewriting the fractions with this denominator.

$\frac{2}{6}$ = 2×5 ÷ 6×5 = $\frac{10}{30}$

$\frac{3}{10}$ = 3×3 ÷ 10×3 = $\frac{9}{30}$

Step 3:

Because 9 < 10, we have $\frac{9}{30}$ < $\frac{10}{30}$

Step 4:

Writing these fractions in original form $\frac{3}{10}$ < $\frac{2}{6}$ or $\frac{2}{6}$ > $\frac{3}{10}$

Q 5 - First, rewrite $\frac{9}{11}$ and $\frac{5}{7}$ so that they have a common denominator. Then use <, = or > to order $\frac{9}{11}$ and $\frac{5}{7}$.

Answer : B

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{9}{11}$ and $\frac{5}{7}$ is 77.

Step 2:

Rewriting the fractions with this denominator.

$\frac{9}{11}$ = 9×7 ÷ 11×7 = $\frac{63}{77}$

$\frac{5}{7}$ = 5×11 ÷ 7×11 = $\frac{55}{77}$

Step 3:

Because 55 < 63, we have $\frac{55}{77}$ < $\frac{63}{77}$

Step 4:

Writing these fractions in original form $\frac{5}{7}$ < $\frac{9}{11}$ or $\frac{9}{11}$ > $\frac{5}{7}$

Q 6 - First, rewrite $\frac{2}{3}$ and $\frac{4}{9}$ so that they have a common denominator. Then use >, = or > to order $\frac{2}{3}$ and $\frac{4}{9}$.

Answer : C

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{2}{3}$ and $\frac{4}{9}$ is 9.

Step 2:

Rewriting the fractions with this denominator.

$\frac{2}{3}$ = 2×3 ÷ 3×3 = $\frac{6}{9}$

$\frac{4}{9}$ = 4×1 ÷ 9×1 = $\frac{4}{9}$

Step 3:

Because 4 < 6, we have $\frac{4}{9}$ < $\frac{6}{9}$

Step 4:

Writing these fractions in original form $\frac{4}{9}$ < $\frac{2}{3}$ or $\frac{2}{3}$ > $\frac{4}{9}$

Q 7 - First, rewrite $\frac{2}{7}$ and $\frac{9}{10}$ so that they have a common denominator. Then use <, = or > to order $\frac{2}{3}$ and $\frac{9}{10}$.

Answer : D

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{2}{7}$ and $\frac{9}{10}$ is 70.

Step 2:

Rewriting the fractions with this denominator.

$\frac{2}{7}$ = 2×10 ÷ 7×10 = $\frac{20}{70}$

$\frac{9}{10}$ = 9×7 ÷ 10×7 = $\frac{63}{70}$

Step 3:

Because 20 < 63, we have $\frac{20}{70}$ < $\frac{63}{70}$

Step 4:

Writing these fractions in original form $\frac{2}{7}$ < $\frac{9}{10}$

Q 8 - First, rewrite $\frac{8}{9}$ and $\frac{5}{6}$ so that they have a common denominator. Then use <, = or > to order $\frac{8}{9}$ and $\frac{5}{6}$.

Answer : A

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{8}{9}$ and $\frac{5}{6}$ is 18.

Step 2:

Rewriting the fractions with this denominator.

$\frac{8}{9}$ = 8×2 ÷9×2 = $\frac{16}{18}$

$\frac{5}{6}$ = 5×3 ÷ 6×3 = $\frac{15}{18}$

Step 3:

Because 15 < 16, we have $\frac{15}{18}$ < $\frac{16}{18}$

Step 4:

Writing these fractions in original form $\frac{5}{6}$ < $\frac{8}{9}$ or $\frac{8}{9}$ > $\frac{5}{6}$

Q 9 - First, rewrite $\frac{7}{9}$ and $\frac{10}{12}$ so that they have a common denominator. Then use <, = or > to order $\frac{7}{9}$ and $\frac{10}{12}$.

Answer : C

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{7}{9}$ and $\frac{10}{12}$ is 36.

Step 2:

Rewriting the fractions with this denominator.

$\frac{7}{9}$ = 7×4 ÷ 9×4 = $\frac{28}{36}$

$\frac{12}{10}$ = 10×3 ÷ 12×3 = $\frac{30}{36}$

Step 3:

Because 28 < 30, we have $\frac{28}{36}$ < $\frac{30}{36}$

Step 4:

Writing these fractions in original form $\frac{7}{9}$ < $\frac{10}{12}$

Q 10 - First, rewrite $\frac{3}{8}$ and $\frac{2}{7}$ so that they have a common denominator. Then use <, = or > to order $\frac{3}{8}$ and $\frac{2}{7}$.

Answer : B

Explanation

Step 1:

We rewrite the fractions so that they have a common denominator. The LCD of $\frac{3}{8}$ and $\frac{2}{7}$ is 56.

Step 2:

Rewriting the fractions with this denominator.

$\frac{3}{8}$ = 3×7 ÷ 8×7 = $\frac{21}{56}$

$\frac{2}{7}$ = 2×8 ÷ 7×8 = $\frac{16}{56}$

Step 3:

Because 16 < 21, we have $\frac{16}{56}$ < $\frac{21}{56}$

Step 4:

Writing these fractions in original form $\frac{2}{7}$ < $\frac{3}{8}$ or $\frac{3}{8}$ > $\frac{2}{7}$

using_common_denominator_to_order_fraction.htm
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