Question

Choose the correct value of x for the below expression.
$5\frac{8}{3}-3\frac{2}{5}=\frac{x}{12}$

• A. 41
• B. 42
• C. 43
• D. 44

Answer 1

The correct option is A 41

As these are mixed fractions, we need to convert the fractions into improper fractions.

$5\frac{8}{3}=\frac{5\times 3+8}{3}=\frac{23}{3}$

$3\frac{2}{5}=\frac{5\times 3+2}{4}=\frac{17}{4}$

$\text{Subtract}:\frac{23}{3}-\frac{17}{4}$
As these are unlike fractions, we need to convert the fractions into like fractions.

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

Multiply $\frac{23}{3}$ with 4 to convert the denominator into 12, we get:

$\frac{23}{3}=\frac{23\times 4}{3\times 4}=\frac{92}{12}$

$(\because \text{multiplying with the denominator 4 of the second fraction})$

Multiply $\frac{17}{4}$ with 3 to convert the denominator into 12, we get:

$\frac{17}{4}=\frac{3\times 17}{3\times 4}=\frac{51}{12}$

$(\because \text{multiplying with the denominator 3 of the first fraction})$

Let's Subtract the like fractions now.
$\therefore$ $\frac{92}{12}-\frac{51}{12}$

As these are like fractions, subtract the numerators only, and the denominators remains the same

$=\frac{92}{12}-\frac{51}{12}$

$=\frac{92-51}{12}$

$=\frac{41}{12}$

Hence, $5\frac{8}{3}-3\frac{2}{5}=\frac{41}{12}=\frac{x}{12}$

The Value of x is 41 (the numerator of $\frac{41}{12}$)