Math / Numbers & Operations

Question(3) Evaluate the expression $\frac{4}{5} \div \frac{2}{3} \times \frac{1}{2}$
Write your answer as a fracti $\square$

Studdy Solution

STEP 1

1. The expression involves division and multiplication of fractions.
2. We need to evaluate the expression and provide the answer as a fraction.

STEP 2

1. Rewrite the division as multiplication.
2. Perform the multiplication of fractions.
3. Simplify the resulting fraction.

STEP 3

Rewrite the division as multiplication by the reciprocal.
The expression is:
$\frac{4}{5} \div \frac{2}{3} \times \frac{1}{2}$
Rewrite the division:
$\frac{4}{5} \times \frac{3}{2} \times \frac{1}{2}$

STEP 4

Multiply the fractions.
First, multiply the first two fractions:
$\left(\frac{4}{5} \times \frac{3}{2}\right) = \frac{4 \times 3}{5 \times 2} = \frac{12}{10}$
Now, multiply the result by the third fraction:
$\frac{12}{10} \times \frac{1}{2} = \frac{12 \times 1}{10 \times 2} = \frac{12}{20}$

STEP 5

Simplify the resulting fraction.
Find the greatest common divisor (GCD) of $12$ and $20$ , which is $4$ .
Divide the numerator and the denominator by $4$ :
$\frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5}$
The simplified result of the expression is:
$\boxed{\frac{3}{5}}$

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