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Problem 4

# $$12 \div \frac{1}{3}$$

Expert verified
The short answer is: To evaluate $$12 \div \frac{1}{3}$$, first change the division to multiplication by using the reciprocal of $$\frac{1}{3}$$, which is $$\frac{3}{1}$$ or 3. Then, multiply $$12 \times \frac{3}{1}$$ to get $$\frac{36}{1}$$, which simplifies to 36. Therefore, $$12 \div \frac{1}{3} = 36$$.
See the step by step solution

## Step 1: Write down the given expression

Write down the expression that we need to evaluate: $12 \div \frac{1}{3}$

## Step 2: Change the division operation to multiplication

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of a fraction is obtained by flipping the numerator and the denominator. In this case, the reciprocal of $$\frac{1}{3}$$ is $$\frac{3}{1}$$ or simply 3. So we change the given expression to: $12 \times \frac{3}{1}$

## Step 3: Multiply the whole number by the fraction

Now multiply the whole number by the fraction: $12 \times \frac{3}{1} = \frac{12 \times 3}{1}$

## Step 4: Perform the multiplication

Multiply the numerators and denominators: $\frac{12 \times 3}{1} = \frac{36}{1}$

## Step 5: Simplify the result

Since dividing by 1 doesn't change the value of a number, we can express the result as a whole number: $\frac{36}{1} = 36$ So, $$12 \div \frac{1}{3} = 36$$.

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