Multiplicative comparison
Year 4 introduces a new way of comparing two quantities — not "how many more", but "how many times as many". This is called multiplicative comparison, and you solve it with multiplication or division.
Two ways to compare
| Phrase | Operation | Example |
|---|---|---|
| "how many more apples" | subtract | 12 apples − 8 apples = 4 more |
| "how many times as many apples" | divide (or multiply) | 12 apples ÷ 4 apples = 3 times as many |
The first compares using difference. The second compares using ratio — how many of the smaller quantity fit into the bigger one.
Three classic question shapes
Shape 1 — How many times as many?
Both quantities are given. Divide the bigger by the smaller.
Sam has 6 marbles. Lily has 24 marbles. How many times as many marbles does Lily have?
24 ÷ 6 = 4 times as many.
Shape 2 — Find the bigger quantity
You're told the smaller quantity and "how many times as many" the bigger one has.
The cat weighs 3 kg. The dog weighs 5 times as much as the cat. How much does the dog weigh?
3 × 5 = 15 kg.
Shape 3 — Find the smaller quantity
You're told the bigger quantity and "how many times as many" the smaller fits into the bigger.
An adult elephant weighs 4 000 kg. That is 8 times as much as the baby elephant weighs. How much does the baby weigh?
4 000 ÷ 8 = 500 kg.
Spotting the words
Watch out for these phrases — they signal multiplicative comparison:
- "X times as many"
- "X times as much"
- "X times bigger" (older textbooks; literally it means X+1 times as big, but in Year 4 it is treated like "X times as much")
- "twice as many" = 2 ×
- "three times as many" = 3 ×
- "half as many" = ÷ 2
Phrases like "more than" or "less than" without "times" are additive, not multiplicative — they use addition or subtraction.
Comparing with a difference and a ratio
A single story can mix both.
A bag of red marbles has 30. A bag of blue marbles has 6. How many more red marbles? How many times as many?
- More: 30 − 6 = 24 more red marbles.
- Times as many: 30 ÷ 6 = 5 times as many.
Both are correct answers to different questions. The Year-4 trick is reading the question carefully and choosing the right operation.
A worked example with sentences
Anna has 7 stickers. Mark has 4 times as many stickers as Anna. How many stickers does Mark have?
- Operation: 4 × 7 = 28 stickers.
- Sentence answer: Mark has 28 stickers.
Anna has 7 stickers. Mark has 21 stickers. How many times as many stickers does Mark have?
- Operation: 21 ÷ 7 = 3 times as many.
- Sentence answer: Mark has 3 times as many stickers as Anna.
Anna has 7 stickers. Mark has 21 stickers. How many more stickers does Mark have?
- Operation: 21 − 7 = 14 more.
- Sentence answer: Mark has 14 more stickers than Anna.
⚠️ All three questions use the same numbers but ask different things. Read the question word by word before computing.
Common mistakes
- Adding when you should multiply. "5 times as many" is not "5 more". 5 times 7 is 35, not 12.
- Using the wrong direction for division. When asked "how many times as many?", divide the bigger by the smaller — not the other way around.
- Mixing "as many" and "more" in the same sentence. They mean different things; pause and re-read.