Evaluate the expression. $\newline$ $\frac{2}{5} \div \frac{2}{3} - \frac{1}{2}$ $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ ______

Full solution

Q. Evaluate the expression.

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\frac{2}{5} \div \frac{2}{3} - \frac{1}{2}

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Write your answer as a fraction or as a whole or mixed number.

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______

Convert to multiplication: Step $1$ : Convert the division of fractions to multiplication by using the reciprocal of the divisor. $\newline$ Calculation: $\frac{2}{5} \div \frac{2}{3} = \frac{2}{5} \times \frac{3}{2}$
Multiply numerators and denominators: Step $2$ : Multiply the numerators and the denominators. $\newline$ Calculation: $\frac{2 \times 3}{5 \times 2} = \frac{6}{10}$
Simplify the fraction: Step $3$ : Simplify the fraction obtained from the multiplication. $\newline$ Calculation: $\frac{6}{10} = \frac{3}{5}$
Subtract from $1$ / $2$ : Step $4$ : Subtract the result from Step $3$ by $\frac{1}{2}$ . $\newline$ Calculation: $\frac{3}{5} - \frac{1}{2}$
Find common denominator: Step $5$ : Find a common denominator for the fractions to subtract. $\newline$ Calculation: Common denominator of $5$ and $2$ is $10$ . $\newline$ $\frac{3}{5} = \frac{6}{10}$ and $\frac{1}{2} = \frac{5}{10}$
Perform subtraction: Step $6$ : Perform the subtraction with the common denominator. $\newline$ Calculation: $\frac{6}{10} - \frac{5}{10} = \frac{1}{10}$