Problem-solving methodsMake a calculated guess
Excess and shortage (gap and difference)
Excess and shortage solves problem sums where one amount is shared out two ways and each way leaves some over, falls short or fits exactly. Tuition centres also call it the gap and difference method. Find the total gap, divide by what each share changes by, and you have the number of shares.
- Taught
- P4 to P6
- Also called
- gap and difference
- Spot it by
- Two plans, one amount
When to use excess and shortage
The words in a question that point at this method. You do not need to solve the question to spot them.
“If he gives each of his cousins 5 marbles, he uses them all up”
A plan that fits exactly. Its gap is 0, and the other plan's gap is the whole story.
“he would need 16 more marbles”
The short side of a plan. Short in one plan and exact or over in the other means the gaps add.
“leaves him with 25 marbles … leaves him with 9”
Both plans leave some over. Same side, so the gaps subtract.
“With 5 stickers for each friend, 18 stickers are left over”
A share-out with some left over, the shape the method is built for.
Words to know
- Left over
- What a plan has spare after every share is given out.
- Short
- How many more a plan would need to give every share in full.
- The total gap
- How far apart the two plans land. Opposite sides add, the same side subtracts.
- Difference per share
- How much more each share gets in one plan than in the other.
How to do excess and shortage, step by step
A real question, the way Lah works every question in StudyLah: one step at a time, writing as she goes.
Wei Han has 30 to 45 marbles. If he gives each of his cousins 5 marbles, he uses them all up. For 7, he needs 16 more. How many marbles?
- This word problem shares one amount two ways, so use excess and shortage. With 5 each, none are left, a gap of 0. With 7 each, he is 16 short.
- One plan fits and the other is short, so the gaps add. The total gap is 0 + 16 = 16.
- Each cousin gets 7 − 5 = 2 more in the second plan. Divide the total gap by 2: 16 ÷ 2 = 8 cousins.
- Multiply: 8 × 5 = 40 marbles. Check the other plan: 8 × 7 = 56, and 56 − 40 = 16 short.
- 40 is between 30 and 45, so Wei Han has 40 marbles.
Every question in StudyLah comes with a walkthrough like this one.
Try it freeThe one it gets confused with
The assumption method divides a gap by a difference too, which is why the two get mixed up. Some tuition centres also say "gap and difference" for comparing two price lists (5 apples and 3 oranges against 2 apples and 4 oranges). That is a different technique.
Two kinds of thing with two totals, like heads and legs? That is the assumption method. One amount shared out by two plans? That is this one.
Small numbers and no plans to compare? Try values in a table. Two plans with a gap each? The gaps give the answer in one division.
Excess and shortage questions
Real questions from the years it is taught. Try one together, then tap to check.
P4 question
When Siti gives 6 biscuits to each friend, 20 remain. When she gives 9 to each friend, 2 remain. How many biscuits does Siti have?
Show answer
Answer56. Both plans leave some over, so subtract the gaps: 18. Each friend gets 3 more, so there are 6 friends, and 6 × 6 + 20 = 56.
P4 question
Kumar has a box of erasers for his classmates. He finds that 4 each would leave 30, but 7 each would leave only 9. How many erasers are there?
Show answer
Answer58. Both plans leave some over: 30 − 9 = 21. Each classmate gets 3 more, so 7 classmates, and 7 × 4 + 30 = 58.
P4 question
Priya has between 100 and 150 stickers. With 9 on each album page, every sticker is used. With 10 on each page, she is 15 short. How many stickers?
Show answer
Answer135. One plan fits, one is short: a total gap of 15. Each page takes 1 more, so 15 pages, and 15 × 9 = 135.
Helping at home
How to tell it has clicked
Ask which way each plan misses. A child with the method says "over" or "short" for each plan before any sum, because that one word decides whether the gaps add or subtract.
Watch for a table of guesses. It is a fair way to the answer, and some schools teach it first on these questions. The two gaps get there in one division.
Try this tonight
Put out 12 sweets for 3 children and share them two ways. 3 each, how many are left? 5 each, how many more do we need?
Then ask how those two answers could tell you there are 3 children. The child who says "3 left and 3 short is a gap of 6, and it took 2 more each, so 6 ÷ 2 = 3" has the method.
Where your child will meet it
The topics it turns up in
Want the bigger picture on how these methods fit together? Maths heuristics: every method
See which methods your child reaches for
StudyLah names the method in every worked solution, so you can see whether the problem was the method or the arithmetic.