Now that you can multiply fractions, here is a way to predict the size of a product before you work it out. Think of multiplying as stretching or shrinking.
Key idea
Multiplying a number by a fraction less than 1 makes it smaller. Multiplying by a number greater than 1 makes it bigger. Multiplying by 1 (like $\frac{4}{4}$) leaves it the same.
Why it works
$\frac{3}{4} \times 8$ means $\frac{3}{4}$ of 8: only part of the 8, so less than 8. $\frac{5}{4} \times 8$ means all of 8 and another $\frac{1}{4}$ of it, so more than 8. The factor tells you what share of the number you take.
Worked examples
Worked example: Smaller or bigger?
Without multiplying, is $\frac{7}{8} \times 25$ more or less than 25?
- $\frac{7}{8}$ is less than 1.
- So the product is only part of 25.
Answer: less than 25
Worked example: Compare two products
Which is greater: $\frac{2}{3} \times 9$ or $1\frac{1}{3} \times 9$?
- $\frac{2}{3}$ is less than 1, so the first product is less than 9.
- $1\frac{1}{3}$ is more than 1, so the second product is more than 9.
Answer: $1\frac{1}{3} \times 9$
Common mistake
Believing that multiplying always makes a number bigger. That is true for whole numbers greater than 1, but not for fractions less than 1: $\frac{1}{2} \times 10 = 5$. Check by asking: is the factor more or less than 1?