Dividing Fractions: Keep, Flip, Multiply

M10Dividing Fractions

Keep the first fraction. Flip the second fraction. Then multiply.

To divide fractions, we keep the first fraction the same, flip the second fraction, and then multiply.

Keep the first fraction

Flip → 43

Answer

💡 Dividing by a fraction is the same as multiplying by its reciprocal: ab ÷ cd = ab × dc

Learn the 3-Step Method

1Keep the first fraction.

Write the first fraction as it is.

2Flip the second fraction.

Turn it upside down (its reciprocal).

34 → 43

3Multiply across.

Multiply the numerators. Multiply the denominators.

23 × 43 = 89

💡 RememberKeep, Flip, Multiply! Then simplify if you can.

Worked Example

Calculate 12 ÷ 23.

Step 1 · Keep

→

Step 2 · Flip

23 → 32

→

Step 3 · Multiply

12 × 32 = 34

→

✓ Answer

✓ We kept the first, flipped the second, then multiplied!

Watch Out! Common Mistakes

Not flipping the second fraction.

23 ÷ 34 = 23 × 34 = 612

Wrong! You must flip the second fraction: × 43.

Flipping the wrong fraction.

23 ÷ 34 = 32 × 34

Wrong! Keep the first fraction the same. Flip only the second.

Only multiplying the top numbers.

23 × 43 = 2 × 43 = 83

Wrong! Multiply the numerators AND the denominators: 89.

⬇ Cheat Sheet

DIVIDING FRACTIONS

Keep the first fraction.
Flip the second fraction.
Multiply across.
Simplify if you can.

Example: 23 ÷ 34 = 23 × 43 = 89
Remember: Keep, Flip, Multiply!

📖 Continue Your Journey

✓ M1 What Are Fractions?✓ M2 Equivalent Fractions ✓ M3 Simplifying Fractions ✓ M4 Comparing Fractions ✓ M5 Ordering Fractions ✓ M6 Adding Fractions (Same Denominator)✓ M7 Adding Fractions (Different Denominator)✓ M8 Subtracting Fractions (Same Denominator)✓ M9 Multiplying Fractions M10 Dividing Fractions M11 Mixed Numbers M12 Fraction of an Amount M13 Percentage

→

Next Lesson: M11 Mixed NumbersA whole number and a fraction together.

📄 Free printable: Download the Dividing Fractions cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Keep the first fraction exactly as it is.
Flip the second fraction upside down — this is called the reciprocal.
Multiply straight across: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.
Only the second fraction is flipped — flipping the first is the classic error.

Frequently asked questions

How do you divide fractions?

Use Keep, Flip, Multiply: keep the first fraction, flip the second fraction (swap its top and bottom), then multiply the numerators and denominators. For example 1/2 ÷ 2/3 = 1/2 × 3/2 = 3/4.

What is a reciprocal?

The reciprocal of a fraction is the fraction turned upside down. The reciprocal of 3/4 is 4/3. Dividing by a fraction is the same as multiplying by its reciprocal.

Why does Keep, Flip, Multiply work?

Dividing asks ‘how many of these fit into that?’. Dividing by 1/2 is the same as asking how many halves fit — which doubles the answer, exactly like multiplying by 2/1.

Is dividing fractions on the primary curriculum?

In England, Year 6 covers dividing a fraction by a whole number. Dividing a fraction by a fraction is formally Key Stage 3, but it appears in 11+ preparation as a stretch topic — which is why we include it.

← Previous lesson

M9 Multiplying Fractions