Question

A recipe needs $2\frac{5}{22}$ teaspoon black pepper and $1\frac{4}{33}$ teaspoon red pepper. How much more black pepper than the red pepper does the recipe need?

• A. $2\frac{7}{33}$
• B. $1\frac{7}{66}$
• C. $3\frac{7}{22}$
• D. $1\frac{7}{22}$

Answer 1

The correct option is B $1\frac{7}{66}$

Convert each mixed fractions into the improper fractions as follows

$2\frac{5}{22}=\frac{22\times 2+5}{22}=\frac{44+5}{22}=\frac{49}{22}$

$1\frac{4}{33}=\frac{33\times 1+4}{33}=\frac{37}{33}$

Amount of more black pepper needed than the red papper
$=\frac{49}{22}-\frac{37}{33}$

As these are unlike fractions, convert them into the like fraction.
LCM of denominators of 22 and 33 = 66

Rewrite the denominators in each fraction as 66 (LCM of 22 and 33) as follows

$\frac{49}{22}=\frac{49\times 3}{22\times 3}=\frac{147}{66}$

$\frac{37}{33}=\frac{37\times 2}{33\times 2}=\frac{74}{66}$

$\therefore \frac{49}{22}-\frac{37}{33}$

$=\frac{147}{66}-\frac{74}{66}$

$=\frac{147-74}{66}$

$=\frac{73}{66}$

As $\frac{73}{66}$ is an improper fraction, convert it into the mixed number as follows

$\frac{73}{66}=\frac{66+7}{66}$

$=\frac{66}{66}+\frac{7}{66}$

$=1+\frac{7}{66}$

$=1\frac{7}{66}$