Multiplying and dividing fractions · Usually met around P5
Does multiplying make it bigger or smaller?
Times more than 1: bigger. Less than 1: smaller.
How to do it
Method
Times more than 1: bigger. Less than 1: smaller
36 × 34 < 36; 36 × 54 > 36
Another way
Think of taking a part
× 34 takes three quarters: less than the whole
In full
You can tell how big a product is without working it out: compare the multiplier with 1. Multiplying by more than 1 makes the number bigger (36 × 54 = 45); by 1 leaves it the same; by more than 0 but less than 1 makes it smaller (36 × 34 = 27). For a fraction, look at the top and bottom: a top smaller than the bottom means less than 1, a top bigger than the bottom more than 1. Another way to think: × 34 takes three quarters, only part of it, so less than the whole; × 54 is the whole and a quarter more. Division goes the other way: dividing by less than 1 makes the answer bigger (÷ 12 is × 2).
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
67 × 1110 is smaller than 67.
True or false?
Show the answer and working
Answer: False
1110 is close to 1, but still compare its top and bottom: a smaller top means less than 1 and a smaller product; a bigger top means more than 1 and a bigger product.
Example 2
Without working it out: is 37 × 87 bigger or smaller than 37?
- A. Can't tell without working it out
- B. Bigger than 37
- C. Smaller than 37
- D. Equal to 37
Choose the right answer
Show the answer and working
Answer: B. Bigger than 37
Just compare the multiplier 87 with 1: more than 1 makes it bigger, less than 1 smaller.
Example 3
20 × 54, 20 × 54, 20 × 54, 20 × 24, 20 × 44. Without working them out, how many of these products are bigger than 20?
Show the answer and working
Answer: 3
Look only at the multipliers: 3 have a top bigger than the bottom (more than 1). Top equal to bottom is 1, no change; a smaller top makes it smaller.
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