Question

Which of the following is/are incorrect

• A. $\frac{4}{6}>\frac{3}{5}$
• B. $\frac{1}{4}>\frac{2}{5}$
• C. $\frac{22}{11}>\frac{11}{22}$
• D. $\frac{100}{10}>\frac{200}{10}$

Answer 1

Answer: (A), (C)

$\frac{22}{11}>\frac{11}{22}$

To comapre the fractions we have to convert the fractions into the like fractions.

To convert into like fractions, we multiply the denominator of one fraction with the numerator and denominator of the other fraction.

Option A:
$\frac{4}{6}=\frac{4\times 5}{6\times 5}=\frac{20}{30}$

$\frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30}$

The order of numerators: 20 > 18
On comparing $\frac{20}{30}$ and $\frac{18}{30}$ , we see that $\frac{20}{30}=\frac{4}{6}$ is the larger fraction.
$\therefore$ Option A is the correct answer

Option B:
$\frac{1}{4}=\frac{1\times 5}{4\times 5}=\frac{5}{20}$

$\frac{2}{5}=\frac{2\times 4}{5\times 4}=\frac{8}{20}$

The order of numerators: 8 > 5
On comparing $\frac{5}{20}$ and $\frac{8}{20}$ , we see that $\frac{8}{20}=\frac{2}{5}$ is the larger fraction.
$\therefore$ Option B is the incorrect answer

Option C:
Simplify the fractions
$\frac{22}{11}=\frac{2\times 11}{1\times 11}=2$

$\frac{11}{22}=\frac{1\times 11}{2\times 11}=\frac{1}{2}$

$\frac{1}{2}$ is a proper fraction are always less than 1.
Hence, 2 > $\frac{1}{2}$
$\therefore$ Option C is the correct answer

Option D:
Simplify the fractions
$\frac{100}{10}=\frac{10\times 10}{1\times 10}=10$

$\frac{200}{10}=\frac{20\times 10}{1\times 10}=20$

Hence, $20>10$
$\therefore \frac{100}{10}<\frac{200}{10}$
$\therefore$ Option D is the incorrect answer