Word Problems: Multiplication and Division

What is a word problem?

A word problem is a little story that hides a maths question inside it. Instead of just seeing "6 × 4," you read about boxes of apples or children sharing sweets, and you have to work out what the maths is. The hardest part is usually not the calculation — it is deciding which operation to use.

This lesson is all about multiplication and division word problems. If you want a quick refresher on the operations themselves first, look at Introduction to Multiplication and Division Made Simple. Then come back here and we will turn stories into number sentences.

The two big ideas

Almost every multiplication or division word problem is built on one simple picture: equal groups.

• Multiplication joins equal groups together to find a total.

3 bags, 5 marbles in each bag → 3 × 5 = 15 marbles.

• Division does the opposite. It either shares a total into equal groups, or finds how many groups fit.

15 marbles shared between 3 bags → 15 ÷ 3 = 5 marbles in each bag.

Multiplication and division are opposites (we say they are inverse operations). That is why you can always check a division with a multiplication, and the other way around.

A four-step plan

Use the same plan every time and word problems stop feeling scary.

1. Read the problem twice. The first read is for the story; the second is for the numbers.
2. Underline the numbers and circle the question — what is it actually asking?
3. Choose the operation by picturing equal groups. Draw it if you can.
4. Solve and check — does your answer make sense for the story?

Keyword clues (use with care)

Some words act like signposts. They are helpful, but they are clues, not strict rules — always picture the story too.

Operation	Common clue words	Example phrase
Multiplication	each, per, groups of, times, in total	"5 rows of 6 chairs"
Division (sharing)	shared equally, split, each gets	"shared between 4 friends"
Division (grouping)	how many groups, fit into, packs of	"put into bags of 8"

Worked example 1 — multiplication

A classroom has 8 tables. Each table seats 4 children. How many children can sit down?

Step 1–2: The numbers are 8 tables and 4 children per table. The question is the total number of children.

Step 3: This is equal groups joined into a total — 8 groups of 4 — so we multiply.

Step 4: 8 × 4 = 32 children.

Check: 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32. ✓ A class of about 32 is sensible.

Worked example 2 — division (sharing)

A teacher has 35 stickers to share equally between 5 children. How many stickers does each child get?

Step 3: We are sharing one total into equal groups, so we divide.

$$ 35 \div 5 = 7 $$

Each child gets 7 stickers.

Check with the inverse: 5 × 7 = 35. ✓ It matches the total we started with.

Worked example 3 — division (grouping)

A shop has 48 eggs. They go into cartons that hold 6 eggs each. How many cartons are needed?

Here we are not sharing between people — we are asking how many groups of 6 fit into 48. That is still division.

$$ 48 \div 6 = 8 \text{ cartons} $$

Check: 8 cartons × 6 eggs = 48 eggs. ✓

Worked example 4 — a two-step problem

Some problems hide two operations. Take your time and do one step at a time.

A baker makes 4 trays of buns with 6 buns on each tray. She sells 9 buns. How many buns are left?

Step A (multiply): total buns made = 4 × 6 = 24. Step B (subtract): buns left = 24 − 9 = 15 buns.

Notice how the picture changes between steps. First we joined equal groups, then we took some away.

A picture beats a guess

When you are stuck, draw a bar model. For "30 sweets shared between 5 children," draw one long bar of 30, split it into 5 equal parts, and the size of one part is your answer. Seeing the equal parts makes the operation obvious, even before you do the arithmetic.

Practice activity

Try these on paper. Use the four-step plan and draw a picture for each one.

1. There are 7 boxes of crayons with 8 crayons in each box. How many crayons altogether?
2. 56 books are placed equally onto 8 shelves. How many books per shelf?
3. A bag holds 9 marbles. How many bags do you need for 63 marbles?
4. Two-step: 5 friends each pick 4 flowers, then give 3 flowers away in total. How many flowers do they keep?

Answers: 1) 7 × 8 = 56 2) 56 ÷ 8 = 7 3) 63 ÷ 9 = 7 4) 5 × 4 = 20, then 20 − 3 = 17.

Why this matters

Word problems are how maths shows up in real life — sharing snacks, packing boxes, planning seats, working out costs. Nobody hands you a bare sum; you have to find the maths yourself. Once you can spot equal groups and decide between multiplying and dividing, you have a tool you will use for the rest of your life. Read carefully, draw the story, solve, and check — every single time.