How to Divide Fractions in 3 Simple Steps

Dividing fractions can be confusing—why flip the second fraction? What about mixed numbers or simplifying messy answers? In this guide, we’ll break it all down into three simple steps, with clear examples and a downloadable worksheet at the end.

What is Division of Fractions

Division of fractions means figuring out “how many times one fraction fits into another”. It’s like sharing or splitting, but with pieces of a whole.

Real-life example: If you have \(\frac{1}{2}\) of a pizza and want to know how many \(\frac{1}{4}\) slices that makes, you are dividing:

\[\frac{1}{2} \div \frac{1}{4}\]

In other words: “How many quarter-slices are in half a pizza?”

3 Steps to Solve Division of Fractions

We use the “Flip, Multiply, Simplify” method. Let’s use an example to clearly show these three steps:

\[\frac{5}{6} \div \frac{2}{3}\]

Step 1: Find the Reciprocal — Flip the Second Fraction

When dividing fractions, we don’t really “divide” the way we do with whole numbers. Instead, we use a clever trick: flip the second fraction  — this is called finding the reciprocal, and it turns division into multiplication.

Why flip?

Because dividing by a fraction is the same as multiplying by its reciprocal — much easier!

Therefore, the reciprocal of

\[\frac{2}{3}\]

is

\[\frac{3}{2}\]

, and the expression looks like:

\[\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{5 \times 3}{6 \times 2} = \frac{15}{12}\]

Step 2: Multiply the Fractions — Top × Top, Bottom × Bottom

• Multiply the numerators (top numbers) together;
• Multiply the denominators (bottom numbers) together.

Let’s continue with our example:

\[\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{5 \times 3}{6 \times 2} = \frac{15}{12}\]

Step 3: Simplify the Fraction

We always want our final answer to be as simple and neat as possible. Look at the fraction we got:

\[\frac{15}{12}\]

Both 15 and 12 can be divided by 3. Let’s simplify:

\[\frac{15}{12} = \frac{15 \div 3}{12 \div 3} = \frac{5}{4}\]

This is an improper fraction, so we can also write it as a mixed number if needed:

\[\frac{5}{4} = 1 \frac{1}{4}\]

To recap:

\[\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{5 \times 3}{6 \times 2} = \frac{15}{12} = \frac{5}{4}\]

And that’s it — Flip, Multiply, Simplify!

Example Problem: Division of Fractions

Example 1

What is the result of \(\frac{3}{8} \div \frac{2}{5}\)?

Answer:

\[\frac{3}{8} \div \frac{2}{5} = \frac{3}{8} \times \frac{5}{2} = \frac{15}{16}\]

Example 2

What is the result of \(\frac{4}{5} \div \frac{2}{7}\)?

Answer:

\[\frac{4}{5} \div \frac{2}{7} = \frac{4}{5} \times \frac{7}{2} = \frac{28}{10} = \frac{14}{5}\]

Summery — Dividing Fractions Made Easy

Dividing fractions is as easy as:

• Keep the first fraction;
• Flip the second fraction to find the reciprocal;
• Multiply the Fractions — Top × Top, Bottom × Bottom;
• Simplify the Fraction — Make your answer as simple and neat as possible.

Important: If you see a mixed number, always turn it into an improper fraction first — then follow the steps!

Remember the pizza question at the beginning? If you divide \(\frac{1}{2}\) by \(\frac{1}{4}\), the answer is… 2 slices!

Want more practice?

Additional Math Topics for Grade 6 – with Free Worksheets

• Multiplication of Fractions
• Area of Trapezoid
• Area of Triangles
• Area of Parallelograms

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