All 8 problems from "Sum & Difference" with complete step-by-step worked solutions: recognising the type, the idea, the working steps and the conclusion. Use this page to review with your child after the animated lesson, or let them check their own working against it.
Two numbers have a sum of 12 and a difference of 4. What is the larger number?
Key idea: Smaller first: (sum − difference) ÷ 2, then add the difference back.
You know the sum (12) and the difference (4) of two numbers — a sum–difference problem.
Remove the difference so the sum splits into two equal parts.
Smaller = (12 − 4) ÷ 2 = 4.
Larger = 4 + 4 = 8.
So: So the larger number is 8.
Two numbers have a sum of 12 and a difference of 4. What is the smaller number?
Key idea: The smaller number is (sum − difference) ÷ 2.
Sum 12 and difference 4 are both given, and the smaller number is asked for.
Subtracting the difference leaves two copies of the smaller number.
Smaller = (12 − 4) ÷ 2 = 8 ÷ 2 = 4.
Check with the larger: 4 + 4 = 8, and 8 + 4 = 12, 8 − 4 = 4.
So: So the smaller number is 4.
Two numbers add up to 20. One is 6 more than the other. Which pair is correct?
Key idea: “One is 6 more” is a difference in disguise — it is still sum–difference.
Two numbers add to 20 and one is 6 more than the other: sum 20, difference 6.
Find the smaller with (sum − difference) ÷ 2, then add the extra 6.
Smaller = (20 − 6) ÷ 2 = 7.
Larger = 7 + 6 = 13.
Check: 13 + 7 = 20.
So: So the pair is 13 and 7.
The sum of two numbers is 36 and their difference is 10. What is the larger number?
Key idea: Larger first works too: (sum + difference) ÷ 2.
Sum 36, difference 10 — and the larger number is asked for directly.
Adding sum and difference gives two copies of the larger number.
Larger = (36 + 10) ÷ 2 = 46 ÷ 2 = 23.
Smaller = 23 − 10 = 13.
So: So the larger number is 23.
Two numbers have a sum of 50 and a difference of 14. The smaller number is ___ and the larger number is ___.
Key idea: Smaller first: (sum − difference) ÷ 2, then add the difference back.
Sum 50 and difference 14, with both numbers to fill in.
Remove the difference to split 50 into two equal parts.
Smaller = (50 − 14) ÷ 2 = 18.
Larger = 18 + 14 = 32.
Check: 18 + 32 = 50.
So: So the smaller number is 18 and the larger number is 32.
Which formula correctly finds the smaller of two numbers given their sum (S) and difference (D)?
Key idea: Taking the difference away leaves two equal smaller parts.
A formula question — it asks why the smaller number comes from (S − D) ÷ 2.
Subtract D from S to remove the extra part, then halve what remains.
S − D leaves smaller + smaller.
Dividing by 2 gives one smaller number.
So: So the formula is (S − D) ÷ 2.
Ali and Ben have 84 stickers altogether. Ali has 18 more stickers than Ben. How many stickers does Ben have?
Key idea: A story can hide a sum and a difference — pull both numbers out first.
84 stickers altogether and Ali has 18 more: sum 84, difference 18.
Ben is the smaller side: (total − difference) ÷ 2.
Ben = (84 − 18) ÷ 2 = 66 ÷ 2 = 33.
Ali = 33 + 18 = 51.
So: So Ben has 33 stickers.
Two ropes together measure 100 cm. One rope is 24 cm longer than the other. How long is the shorter rope?
Key idea: Shorter first: (total − difference) ÷ 2.
Two ropes total 100 cm and one is 24 cm longer: sum and difference again.
Remove the extra 24 cm, then split what is left equally.
Shorter = (100 − 24) ÷ 2 = 76 ÷ 2 = 38 cm.
Longer = 38 + 24 = 62 cm.
So: So the shorter rope is 38 cm.
Two numbers have a total of 10. One number is 4 greater than the other. What are the two numbers?
Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)
The two unknown numbers add to 10, and the larger is 4 greater than the smaller. We need to find both values.
The big question is hanging on the stage — the whole lesson will answer it.
Change the numbers and watch the diagram redraw itself:
