Dividing with Unit Fractions and Whole Numbers

In Grade 5 math, you will learn how to divide using unit fractions. A unit fraction is any fraction with a numerator of $1$, such as $\frac{1}{2}$, $\frac{1}{3}$, or $\frac{1}{6}$.

There are two main types of problems you will encounter: dividing a unit fraction by a whole number, and dividing a whole number by a unit fraction. Both can be solved easily using the "Keep, Change, Flip" strategy!

Dividing a Unit Fraction by a Whole Number

When you divide a fraction by a whole number, you are taking a part of something and splitting it into even smaller pieces. This means your answer will be a smaller fraction.

Example: $\frac{1}{3} \div 4$

Imagine you have $\frac{1}{3}$ of a cake left over. If you want to share that remaining piece equally among $4$ friends, how much of the original whole cake does each person get?

Using the Keep, Change, Flip method:

1. Keep the first fraction: $\frac{1}{3}$
2. Change the division sign to multiplication: $\times$
3. Flip the whole number into a fraction (remember that $4$ is the same as $\frac{4}{1}$, so flipping it makes it $\frac{1}{4}$)

$\frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$

Each friend gets $\frac{1}{12}$ of the cake.

Dividing a Whole Number by a Unit Fraction

When you divide a whole number by a fraction, you are asking, "How many of these fraction pieces fit into my whole number?" Because you are counting smaller pieces, your answer will be a larger whole number.

Example: $5 \div \frac{1}{2}$

Imagine you have $5$ whole pizzas. If you cut every pizza into halves ($\frac{1}{2}$), how many slices of pizza will you have in total?

Using Keep, Change, Flip:

1. Keep the whole number: $5$
2. Change the division sign to multiplication: $\times$
3. Flip the fraction: $\frac{1}{2}$ becomes $\frac{2}{1}$ (which is just $2$)

$5 \times 2 = 10$

You will have $10$ slices of pizza!

Summary of the Steps

Whenever you divide with fractions and whole numbers, just remember:

• Keep the first number exactly the same.
• Change $\div$ to $\times$.
• Flip the second number upside down.
• Multiply straight across!

Practice Example: $\frac{1}{6} \div 3 = \frac{1}{6} \times \frac{1}{3} = \frac{1}{18}$