The Magic of Multiplying Fractions
See how fractions shrink when you multiply them. No cross-multiplying needed!
Equation
y = (1/2)*x
Graph
Table
| x | y |
|---|---|
| 0 | 0 |
| 1 | 0.5 |
| 2 | 1 |
| 3 | 1.5 |
| 4 | 2 |
| 5 | 2.5 |
| 6 | 3 |
| 7 | 3.5 |
| 8 | 4 |
What this lesson covers
What you do
You shape the function y = (a/b)*x and watch the graph answer.
Challenges to clear
- Make the multiplier 3/4: slide a to 3 and b to 4. Check that 3/4 of 8 is 6.
- Same multiplier: 3/4 of 4 must be 3.
- A new multiplier, in fifths. Slide the bottom number b to 5.
- Now the top: slide a until 15 becomes 6. Two fifths of 15 is 6 — a fraction of a number is smaller than the number.
Check yourself
To compute (3/4) × 8, you multiply numerators and denominators. Which is right?
Why did 8 SHRINK when multiplied by 3/4?
- (3 × 8) / (4 × 1) = 24/4 = 6 — correct
- (3 + 8) / (4 + 1) = 11/5
- (3 × 1) / (4 × 8) = 3/32
- Cross-multiply to get 32/3
- Because 3/4 is less than 1 — you take only three quarters of the 8. — correct
- Multiplying always shrinks numbers.
- Because the denominator 4 subtracts from the 8.
- It didn't shrink — multiplication always grows numbers.
Think about it
- Multiplying by a fraction smaller than 1 SHRINKS a number. What is 3/4 of 8?