Questions: 5/8 · 2/3 = □ (Type a simplified fraction.)

$5/8 · 2/3 = □ (Type a simplified fraction.)$

Transcript text: $\frac{5}{8} \cdot \frac{2}{3}=$ $\square$ (Type a simplified fraction.)

Solution

Solution Steps

To solve the problem of multiplying two fractions, we need to multiply the numerators together and the denominators together. Then, we simplify the resulting fraction if possible.

Step 1: Multiply the Numerators

To multiply the fractions $\frac{5}{8}$ and $\frac{2}{3}$, we first multiply the numerators: \[ 5 \times 2 = 10 \]

Step 2: Multiply the Denominators

Next, we multiply the denominators: \[ 8 \times 3 = 24 \]

Step 3: Form the New Fraction

We form the new fraction using the results from the previous steps: \[ \frac{10}{24} \]

Step 4: Simplify the Fraction

To simplify $\frac{10}{24}$, we find the greatest common divisor (GCD) of 10 and 24, which is 2. We then divide both the numerator and the denominator by their GCD: \[ \frac{10 \div 2}{24 \div 2} = \frac{5}{12} \]

Final Answer

\[ \boxed{\frac{5}{12}} \]

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