Grade 5 Mathematics
Dividing fractions comes in TWO types that mean very different things!
Type 1: Unit fraction / whole number = Making something SMALLER
Type 2: Whole number / unit fraction = Finding HOW MANY fit inside
"I have a piece and I'm sharing it" - The answer is always smaller than what you started with.
Story: You have 1/2 of a pizza. You share it equally among 4 friends. How much does each friend get?
Start with 1/2, then divide it into 4 equal parts
The Rule: 1a / b = 1a x b So 12 / 4 = 12 x 4 = 18
"How many pieces fit inside?" - The answer is always bigger than what you started with.
Story: You have 3 whole pizzas. Each serving is 1/4 of a pizza. How many servings can you make?
How many fourths (1/4) are in 3 wholes?
Total: 12 servings!
The Rule: a / 1b = a x b So 3 / 14 = 3 x 4 = 12
Common Mistake: Students confuse 1/4 / 3 with 3 / 1/4. These are VERY different!
Remember:
- 1/4 / 3 = 1/12 (splitting a small piece into 3 parts = even smaller)
- 3 / 1/4 = 12 (finding how many fourths in 3 wholes = many pieces)
"How many jumps of 1/3 does it take to go from 0 to 2?"
6 jumps of 1/3 to reach 2, so 2 / 1/3 = 6
1. Type 1: 1/3 / 2 = ?
Think: "I have 1/3 and I'm splitting it between 2 people..."
2. Type 2: 4 / 1/2 = ?
Think: "How many halves fit in 4 wholes?"
3. Word Problem: A ribbon is 1/4 meter long. It needs to be cut into 5 equal pieces. How long is each piece?
Which type? ____ Expression: _____________ = _____________ meter
4. Word Problem: You have 6 yards of fabric. Each pillowcase needs 1/3 yard. How many pillowcases can you make?
Which type? ____ Expression: _____________ = _____________ pillowcases