Before we evaluate the expression, let's first rewrite the expression so that all of the numbers are fractions.

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

$a \frac{b}{c} = \frac{a \cdot c + b}{c}$

\frac{3 \cdot 3 + 2}{3} \div \frac{1}{3}

Multiply

\frac{9 + 2}{3} \div \frac{1}{3}

AddTerms

Add terms

\frac{1 1}{3} \div \frac{1}{3}

Recall that dividing fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

\frac{1 1}{3} \div \frac{3}{1} = \frac{1 1}{3} \times \frac{3}{1}

When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

\frac{1 1}{3} \div \frac{3}{1} = \frac{1 1}{3} \times \frac{3}{1}

MultFrac

Multiply fractions

\frac{1 1 \cdot 3}{3 \cdot 1}

Multiply

\frac{3 3}{3}

CalcQuot

Calculate quotient

11

Checking Our Answer

We can check our answer by finding the product using a calculator. However, most calculators will give the product as a decimal number. Because our answer is a fraction, we need to compare the product of the original fractions to the decimal that is equivalent to the final product that we found. First, let's find the decimal form of our product.

Now we will find the product of the fractions using the calculator. Remember to use parentheses around each of the fractions so that the order of operations is performed correctly! Calculators cannot read our minds, unfortunately.

Because the calculator found the same decimal for both calculations, we know that our answer was correct!

Exercise

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