Divide a whole number by a unit fraction

Dividing a whole number by a unit fraction means determining how many equal parts of size $1/b$ are contained in the whole number, so $n \div \frac{1}{b}=n\times b$ ; for example, $3\div\frac14=12$ . Number lines and bar models show this as counting fourths within three wholes, while multiplication verifies the inverse relationship. The focus is on whole-number dividends and positive unit fractions, not division by non-unit fractions or more general rational-number cases.

Detailed Explanation: Divide a whole number by a unit fraction

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

How many pieces of size $\frac{1}{b}$ fit inside the whole number?

A unit fraction has $1$ in the numerator, such as $\frac14$ or $\frac13$ . Dividing by $\frac{1}{b}$ is the same as multiplying by $b$ :

n\div\frac{1}{b}=n\times b

Example: $4\div\frac13$

Step 1: Understand the divisor.
The fraction $\frac13$ means one piece out of three equal pieces. So we are counting how many thirds are in $4$ wholes.

Step 2: Count the thirds in one whole.
Each whole contains $3$ thirds:

1=\frac13+\frac13+\frac13

Step 3: Count the thirds in four wholes.

4\times 3=12

So,

4\div\frac13=12

Step 4: Check with multiplication.
Division and multiplication are inverse operations:

12\times\frac13=\frac{12}{3}=4

Therefore, $\boxed{4\div\frac13=12}$ .

Learn by doing: Divide a whole number by a unit fraction

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Fraction Division - Whole by Simple - Don't Simplify

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