Questions: Multiply. Write your answer as a mixed number in simplest form. 5 × 3 2/3

Multiply. Write your answer as a mixed number in simplest form.
5 × 3 2/3
Transcript text: Multiply. Write your answer as a mixed number in simplest form. \[ 5 \times 3 \frac{2}{3} \]
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Solution

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Solution Steps

Step 1: Convert the mixed number to an improper fraction

To convert \(a \frac{b}{c}\) to an improper fraction, calculate \(a \times c + b\). Thus, \(a \frac{b}{c} = \frac{11}{3}\).

Step 2: Multiply the whole number by the improper fraction

Multiplying the whole number \(n\) by the improper fraction gives \(n \times \frac{11}{3} = \frac{55}{3}\).

Step 3: Simplify the fraction

The GCD of the numerator and the denominator is 1, so we divide both by this number. This simplifies to \(\frac{55}{3}\).

Step 4: Convert the improper fraction back to a mixed number

The improper fraction \(\frac{55}{3}\) can be expressed as a mixed number. This gives us \( 18 \frac{1}{3} \).

Final Answer

The product of the whole number and the mixed number, expressed as a mixed number in simplest form, is 18 1/3.

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