Question

evaluate the expression.
\\(\frac{3}{4} \times \frac{1}{2} div left( \frac{2}{5} - \frac{1}{4}
ight)\\)
write your answer as a fraction or as a whole or mixed numbe

Explanation:

Step1: Calculate the denominator (subtract the fractions)

First, we need to find the value of the parentheses: $\frac{2}{5} - \frac{1}{4}$. To subtract these fractions, we find a common denominator, which is 20. So we rewrite the fractions: $\frac{2}{5} = \frac{8}{20}$ and $\frac{1}{4} = \frac{5}{20}$. Then we subtract: $\frac{8}{20} - \frac{5}{20} = \frac{3}{20}$.

Step2: Calculate the numerator (multiply the fractions)

Next, we calculate the product of $\frac{3}{4}$ and $\frac{1}{2}$. Multiplying the numerators and denominators: $\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}$.

Step3: Divide the numerator by the denominator

Now we have to divide $\frac{3}{8}$ by $\frac{3}{20}$. Dividing by a fraction is the same as multiplying by its reciprocal, so $\frac{3}{8} \div \frac{3}{20} = \frac{3}{8} \times \frac{20}{3}$. The 3s cancel out, and we have $\frac{20}{8}$. Simplifying this fraction by dividing numerator and denominator by 4, we get $\frac{5}{2}$.

Answer:

$\frac{5}{2}$ (or $2\frac{1}{2}$)