Skill: Divide whole numbers by fractions

To divide a whole number by a positive fraction, ask:

“How many groups of this fractional size fit in the whole number?”

A fraction less than $1$ can make the quotient larger than the starting whole number because each group is small.

Example: $6 \div \frac{3}{4}$

Step 1: Interpret the division.

We are finding how many groups of $\frac{3}{4}$ fit into $6$:

$$6 \div \frac{3}{4}$$

Step 2: Think in equal parts.

Each whole has $4$ fourths. Therefore, $6$ wholes have:

$$6 \times 4 = 24 \text{ fourths}$$

Each group uses $3$ fourths, so the number of groups is:

$$24 \div 3 = 8$$

Thus,

$$6 \div \frac{3}{4}=8$$

Step 3: Use the reciprocal to calculate.

To divide by a fraction, multiply by its reciprocal. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$:

$$6 \div \frac{3}{4} =6\times\frac{4}{3} =\frac{24}{3} =8$$

So, eight groups of $\frac{3}{4}$ fit into $6$. The answer is greater than $6$ because each group is less than $1$.