Lesson Guide
Explanation
Multiplying is counting equal groups. Six groups of five is thirty. Now push the groups together in pairs: you get three groups of ten, and that is also thirty. Fewer groups means bigger groups, and the total never changes. The test asks this the other way round — six groups of five is the same as three groups of what — and the answer is ten, because you halved the number of groups so each group has to double.
Your Turn
4 groups of 6 is the same as 2 groups of how many? Check: 12, and both make 24.
Watch Out
Halve the number of groups and each group DOUBLES. It does not halve too.
Explanation
Twelve pizzas, four to a tray. To find how many trays, you divide: twelve divided by four is three. Dividing and multiplying undo each other, so check it — three times four is twelve. Some test questions ask which number sentence finds the answer rather than asking for the answer itself, so read carefully, because twelve divided by four and twelve times four look alike on the page and mean very different things.
Your Turn
20 pencils shared into boxes of 5. How many boxes? Check: 20 ÷ 5 = 4.
Watch Out
A division sign and a multiplication sign are easy to misread. Look twice.
Explanation
Twenty-seven classmates, and biscuits come in packets of ten. Twenty-seven divided by ten is two with seven left over — but two packets is not enough, because seven children would get nothing. You need a third packet, so the answer is three. When something is left over, you almost always need one more. Ask yourself whether the leftover people would miss out, and if they would, round up.
Your Turn
35 children, and each car holds 4. How many cars? Check: 8 cars carry 32, so 9 cars.
Watch Out
Do not throw the remainder away. It is usually the whole point of the question.
Explanation
A quarter means one of four equal parts, so one orange cut into quarters gives four pieces, and five oranges give twenty. To find a fraction of an amount, divide by the bottom number and then multiply by the top. Three quarters of twelve dollars: twelve divided by four is three, and three times three is nine. So three quarters of twelve dollars is nine dollars. Divide by the bottom, multiply by the top — that order, every time.
Your Turn
What is three quarters of $20? Check: 20 ÷ 4 = 5, and 5 × 3 = 15.
Watch Out
Three quarters of $12 is $9, not $3. The $3 is only ONE quarter — do not stop there.
Explanation
Fifteen dollars buys three model cars. How many will forty-five dollars buy? Always find the cost of one first: fifteen divided by three is five dollars a car. Then forty-five divided by five is nine, so forty-five dollars buys nine cars. Check it — nine cars at five dollars each is forty-five. That is the whole strand: groups of, sharing, rounding up when there is a remainder, a fraction of an amount, and the cost of one. Quiz and exercises now.
Your Turn
$18 buys 6 pencils. How much for 10 pencils? Check: one is $3, so 10 cost $30.
Watch Out
Find the cost of ONE before doing anything else. Guessing from the two big numbers rarely works.
📌 Key Points — this lesson in a nutshell
- Groups of. 6 groups of 5 is 30 — and so is 3 groups of 10. Same total, different grouping.
- Multiplying and dividing undo each other: 12 ÷ 4 = 3 because 3 × 4 = 12.
- If something is left over, you usually need one MORE — round up, not down.
- A fraction of an amount: divide by the bottom number, then multiply by the top.
Step 1: Introduction
Step 1 of 5
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