Question

Which of the following groups of fractions have been arranged in descending order? (Note: There can be more than one correct answer.)

• A. $\frac{8}{9}>\frac{8}{10}>\frac{4}{6}>\frac{4}{16}$
• B. $\frac{2}{3}>\frac{1}{4}>\frac{4}{5}>\frac{4}{3}$
• C. $\frac{4}{3}>\frac{4}{5}>\frac{2}{3}>\frac{1}{4}$
• D. $\frac{4}{3}>\frac{4}{5}>\frac{8}{12}>\frac{2}{8}$

Answer 1

Answer: (A), (C), (D)

$\frac{4}{3}>\frac{4}{5}>\frac{8}{12}>\frac{2}{8}$

To compare the fractions, we need to make their numerators or denominators the same.
Let’s check each of the given options.
Let’s compare the fractions in option a by making their numerators the same.
$\frac{4}{3},\frac{4}{5},\frac{2}{3}$, $\frac{1}{4}$
Make all numerators 4 to compare the fractions.
$\frac{2}{3}$ = $\frac{2\times 2}{3\times 2}$ = $\frac{4}{6}$
$\frac{1}{4}$ = $\frac{1\times 4}{4\times 4}$ = $\frac{4}{16}$
When the numerators are the same, the fraction with the smaller denominator has the higher value.
Therefore.
$\frac{4}{3}>\frac{4}{5}>\frac{2}{3}$ > $\frac{1}{4}$
Let’s compare the fractions in option b by making their numerators the same.
$\frac{4}{3},\frac{4}{5},\frac{8}{12}$, $\frac{2}{8}$
Make all numerators 8 to compare the fractions.
$\frac{4}{3}$ = $\frac{4\times 2}{3\times 2}$ = $\frac{8}{6}$
$\frac{4}{5}$ = $\frac{4\times 2}{5\times 2}$ = $\frac{8}{10}$
$\frac{2}{8}$ = $\frac{2\times 4}{8\times 4}$ = $\frac{8}{32}$
When the numerators are the same, the fraction with the smaller denominator has the higher value.
Therefore,
$\frac{4}{3}>\frac{4}{5}>\frac{8}{12}$ > $\frac{2}{8}$

Let’s compare the fractions in option c by making their numerators the same.
$\frac{2}{3},\frac{1}{4},\frac{4}{5}$, $\frac{4}{3}$
Make all numerators 4 to compare the fractions
$\frac{2}{3}$ = $\frac{2\times 2}{3\times 2}$ = $\frac{4}{6}$
$\frac{1}{4}$ = $\frac{1\times 4}{4\times 4}$ = $\frac{4}{16}$
When the numerators are the same, the fraction with the smaller denominator has the higher value.
Therefore,
$\frac{4}{3}>\frac{4}{5}>\frac{2}{3}$ > $\frac{1}{4}$
Let’s compare the fractions in option d by making their numerators the same.
$\frac{8}{9},\frac{8}{10},\frac{4}{6}$, $\frac{4}{16}$
Make all numerators 8 to compare the fractions.
$\frac{4}{6}$ = $\frac{4\times 2}{6\times 2}$ = $\frac{8}{12}$
$\frac{4}{16}$ = $\frac{4\times 2}{16\times 2}$ = $\frac{8}{32}$
When the numerators are the same, the fraction with the smaller denominator has the higher value.
Therefore,
$\frac{8}{9}>\frac{8}{10}>\frac{4}{6}$ > $\frac{4}{16}$
Hence, options a, b, and d are correct.