Question

exercise 4
divide: $1\frac{3}{5} \div \frac{2}{3}$
$1\frac{1}{15}$
$2\frac{2}{5}$
$1\frac{9}{10}$
$2\frac{1}{5}$

Explanation:

Step1: Convert mixed number to improper fraction

To divide \( 1\frac{3}{5} \div \frac{2}{3} \), first convert the mixed number \( 1\frac{3}{5} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 1\frac{3}{5} \), we have \( \frac{1\times5 + 3}{5}=\frac{5 + 3}{5}=\frac{8}{5} \).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. So \( \frac{8}{5} \div \frac{2}{3}=\frac{8}{5}\times\frac{3}{2} \).

Step3: Multiply the fractions

Multiply the numerators and denominators: \( \frac{8\times3}{5\times2}=\frac{24}{10} \).

Step4: Simplify the fraction and convert to mixed number

Simplify \( \frac{24}{10} \) by dividing numerator and denominator by 2: \( \frac{12}{5} \). Now convert \( \frac{12}{5} \) to a mixed number. Divide 12 by 5: 5 goes into 12 twice with a remainder of 2. So \( \frac{12}{5}=2\frac{2}{5} \).

Answer:

\( 2\frac{2}{5} \) (corresponding to the option with this value)