Master dividing fractions by fractions using the reciprocal method and measurement division!
Scenario: You have a watering can with 5/6 liters of water. Each plant needs 1/3 liters of water. How many plants can you water with the water in your can?
To divide fractions, we multiply by the reciprocal (flip) of the divisor:
a/b ÷ c/d = a/b × d/c
5/6 ÷ 1/3 = 5/2 = 2 1/2
You can water 2 complete plants and half of another
Answer: You can water 2 1/2 plants with 5/6 liters of water!
We can also think of this as "How many groups of 1/3 are in 5/6?" This is measurement division.
5/6 liters divided into groups of 1/3 liters each:
Each group = 1/3 liter
We can fit 2 complete groups of 1/3, plus 1/2 of another group
2 × 1/3 + 1/2 × 1/3 = 2/3 + 1/6 = 5/6 ✓
Let's verify that 2 1/2 plants makes sense by working backwards:
2 plants × 1/3 L = 2/3 L
Water for 2 complete plants
1/2 plant × 1/3 L = 1/6 L
Water for half a plant
2/3 + 1/6 = 4/6 + 1/6 = 5/6 L ✓
Total water used
Perfect! Our answer checks out. We used exactly 5/6 liters of water.
A recipe calls for 3/4 cup of flour, but you only have 1/2 cup. What fraction of the recipe can you make?
1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3
Answer: You can make 2/3 of the recipe.
Calculate: 3/5 ÷ 2/7
3/5 ÷ 2/7 = 3/5 × 7/2 = 21/10 = 2 1/10
Calculate: 4/9 ÷ 5/3
4/9 ÷ 5/3 = 4/9 × 3/5 = 12/45 = 4/15
❌ 5/6 ÷ 1/3 = 5/6 × 1/3 = 5/18 (WRONG!)
You must flip the second fraction!
Correct: 5/6 ÷ 1/3 = 5/6 × 3/1 = 15/6 = 5/2
❌ 5/6 ÷ 1/3 = 6/5 × 3/1 = 18/5 (WRONG!)
Only flip the second fraction!
Correct: Keep the first fraction, flip only the second: 5/6 × 3/1