Olympiad topic · P1–P6
Sum and difference
A regular in primary maths competitions such as the Hua Xia Cup, from the P1 and P2 first rounds to the P5 finals.
Try one
★★ MediumA classroom has two bookcases, A and B, holding 54 books in all.
After 2 are moved from bookcase A to bookcase B, the two hold the same number.
How many books were in bookcase B at first?
- Hint 1: Does moving them change the total?
- Hint 2: When they're equal, how many are in each? Then think back to before the move.
- 1.Moving them doesn't change the total. Afterwards the two are equal: 54 ÷ 2 = 27 each.
- 2.Before the move, B didn't have those 2 yet: B held 27 − 2 = 25 at first.
- ⚠️Common mistake: thinking they differed by 2. One lost 2 and the other gained 2, so they differed by 4.
Answer: 25 books
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsThe total and difference are given.
- ★★MediumFree2 question types · unlimited questionsThree amounts, or "equal after moving some".
- ★★★HardFree2 question types · unlimited questionsA condition to translate first, e.g. after giving some away, the other has more.
- ★★★★Expert (competition level)VIP2 question types · unlimited questionsSeveral numbers added in pairs, or several relations at once.
Sum and difference: what it is and how to solve it
You know two numbers' total and their difference; find each number.
For example: Two brothers have 30 stickers in all; the elder has 6 more. How many has the younger? (30 − 6) ÷ 2 = 12.
The key idea: Take the extra away and both are equal: smaller = (total − difference) ÷ 2, larger = (total + difference) ÷ 2. A bar model shows it at once. The usual method at school uses an equation: let the younger have x, so x + (x + 6) = 30.
Practise this topic free →Easy to Hard (★ to ★★★) all free, unlimited questions, no download