Homeschool Math

Fractions Guide

How to Divide Fractions

Keep Change Flip — Explained Simply

Dividing fractions confuses most kids because the method feels like a trick with no reason behind it. This guide shows both the method AND why it works — so it actually sticks.

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The Method:

KEEP → CHANGE → FLIP

Keep the first fraction. Change ÷ to ×. Flip the second fraction. Then multiply as normal.

Keep Change Flip — Step by Step

Let's use ¾ ÷ ½ as our example

¾ ÷ ½ = ?
Start with the problem
¾ ÷ ½

We need to divide ¾ by ½. The Keep Change Flip method makes this straightforward.

KEEP the first fraction
Keep ¾ exactly as it is
¾ ___

The first fraction never changes. Write it down and leave it alone.

CHANGE the division sign
Change ÷ to ×
¾ × ___

Replace the division sign with a multiplication sign. Division becomes multiplication.

FLIP the second fraction
Flip ½ to become 2/1
¾ × 2/1

Swap the numerator and denominator of the second fraction. ½ becomes 2/1 (which is just 2).

Now multiply as normal
3×2 = 6, 4×1 = 4
6/4

Multiply across the top and multiply across the bottom.

Simplify the answer
6/4 = 3/2 = 1½
¾ ÷ ½ = 1½ ✓

Both 6 and 4 divide by 2. So 6/4 = 3/2. As a mixed number that's 1½.

Why Keep Change Flip Works

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal is just the fraction flipped upside down. This is because division and multiplication are inverse operations — they undo each other.

¾ ÷ ½
= ¾ × (1 ÷ ½)
= ¾ × 2/1
= ¾ × 2
= 6/4 = 1½ ✓

Plain English: "How many halves fit into three quarters?" The answer is 1½ — because one half fits once, with a quarter left over which is half of a half.

Try These Examples

Keep Change Flip then multiply — same method every time

½ ÷ ¼
→ ½ × 4/1
= 2 ✓
⅔ ÷ ⅓
→ ⅔ × 3/1
= 2 ✓
¾ ÷ ⅓
→ ¾ × 3/1
= 9/4 = 2¼ ✓
⅗ ÷ ½
→ ⅗ × 2/1
= 6/5 = 1⅕ ✓
⅘ ÷ ⅖
→ ⅘ × 5/2
= 20/10 = 2 ✓
⅔ ÷ ¾
→ ⅔ × 4/3
= 8/9 ✓

Common Mistakes (And How to Fix Them)

❌ Flipping the first fraction instead of the second
✓ Always KEEP the first fraction unchanged. Only the second fraction (the divisor) gets flipped.
❌ Forgetting to change the sign before flipping
✓ The order matters: Keep → Change the sign → Flip. All three steps are needed. Missing the sign change gives a wrong answer.
❌ Not simplifying the final answer
✓ After multiplying, check if your answer can be simplified. Also check if an improper fraction should be written as a mixed number.

Make sure you're confident with multiplying fractions first — dividing fractions uses the exact same multiplication step.

Number Sense Foundations

GRADES K–2

$57

Keep Change Flip is memorable — but children who truly understand fractions as quantities don't need to rely on it. This course builds the conceptual foundation from the ground up: what fractions mean, how they relate to division, and why operations on fractions work the way they do.

Get Number Sense Foundations on Gumroad →

More Math Tricks & Guides

How to Multiply Fractions
The easier operation — start here
How to Simplify Fractions
Reducing to lowest terms
What Is a Denominator?
Understand the bottom number
Fractions Worksheets
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