P3 Multiplication and Division

Multiplication describes equal groups. Division can share a total into equal groups or count how many groups fit. Keep every object in the picture, and let the written algorithm show each partial product or quotient digit.

Parents: ask your child to predict the product or remainder first. In the table lab, choose a fact by its product; a fact can belong to two familiar table families.

By the end you will be able to recall tables 6 to 9, use inverse facts, interpret remainders, calculate up to 3 digits by 1 digit, and work mentally within multiplication tables.

Recall tables 6, 7, 8 and 9

The P3 focus is the 6, 7, 8 and 9 table families. Equal groups give each fact a meaning: seven groups of eight objects make 56. A fact such as 6 × 8 can be recalled from either the 6 or the 8 family, so the useful question is “What is the product?” rather than forcing one exclusive label.

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Equal groups: tables 6–9

🤔 Predict first: What is 7 × 8?

485664

Use inverse facts

The same three numbers can make one multiplication fact and two division facts. From 8 × 7 = 56, we know 56 ÷ 8 = 7 and 56 ÷ 7 = 8. The groups in the lab make both inverse facts visible.

Keep the fact family together

$$8\times7=56$$

$$56\div8=7$$

$$56\div7=8$$

Division with a remainder

When a total cannot be split into complete groups, the ungrouped part is the remainder. For 26 ÷ 4, make six complete groups of four, then keep two objects loose. The remainder is smaller than the group size.

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Equal groups: a remainder

🤔 Predict first: When 26 objects are put into groups of 4, how many stay loose?

123

Conserve the objects

$$26\div4=6\text{ remainder }2$$

$$4\times6+2=26$$

$$\text{remainder }2<4$$

The equation 4 × 6 + 2 = 26 checks that the complete groups and the loose objects account for the whole dividend.

Written multiplication: show each carry

For 236 × 4, start with the ones. The 24 ones become 4 ones and 2 tens; that carry joins the tens calculation. Exchange ten tens for one hundred when the tens calculation makes 14.

Multiply 236 by 4

$$\begin{array}{r r r r}\text{carry}&1&2&\\&2&3&6\\\times& & &4\\\hline&9&4&4\\\end{array}$$

$$\text{ones: }6\times4=24\Rightarrow\text{ write 4, carry 2}$$

$$\text{tens: }3\times4+2=14\Rightarrow\text{ write 4, carry 1}$$

$$\text{hundreds: }2\times4+1=9$$

$$236\times4=944$$

Written division: record every quotient digit

For 857 ÷ 4, divide from the hundreds place, subtract the product, bring the next digit down, and repeat. The first remainder becomes part of the next place value.

quotient214

4857

8

bring down05

4

bring down17

16

remainder1

857 ÷ 4 = 214 remainder 1

Check: 4 × 214 + 1 = 857

Mental table calculation

Mental multiplication and division use a known table fact. For 8 × 7, recall 56. For 56 ÷ 8, ask which 8 fact makes 56. This is different from the written algorithms for 3-digit numbers.

Use a known table fact

$$8\times7=56$$

$$56\div8=7$$

Practise with worked steps

Practice 1. Calculate 236 × 4 in aligned columns and show each carry.

Show the multiplication algorithm

Carry from each place

$$\begin{array}{r r r r}\text{carry}&1&2&\\&2&3&6\\\times& & &4\\\hline&9&4&4\\\end{array}$$

$$6\times4=24\Rightarrow4\text{, carry }2$$

$$3\times4+2=14\Rightarrow4\text{, carry }1$$

$$2\times4+1=9$$

$$236\times4=944$$

Practice 2. Calculate 857 ÷ 4, recording each quotient digit and the final remainder.

Show the division algorithm

quotient214

4857

8

bring down05

4

bring down17

16

remainder1

857 ÷ 4 = 214 remainder 1

Check: 4 × 214 + 1 = 857

Practice 3. Share 26 objects into groups of 4 and state the complete groups and loose objects.

Show the grouping solution

Keep the loose remainder

$$26\div4=6\text{ remainder }2$$

$$4\times6+2=26$$

Watch out — easily mixed up

Follow the operation path

Review P3 addition and subtraction for place-aligned written work. Return to P3 whole numbers when a question asks you to read, compare or order the numbers in a multiplication or division story.

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. What is 7 × 8?

   42485456

2. What is 9 × 6?

   45546356

3. Which division fact is an inverse of 8 × 7 = 56?

   56 ÷ 8 = 756 ÷ 7 = 68 ÷ 56 = 756 ÷ 8 = 8

4. A bakery packs 75 biscuits into boxes of 8. How many full boxes and biscuits are left over?

   8 remainder 119 remainder 210 remainder 59 remainder 3

5. What is 123 × 3?

   326363369396

6. A class packs 857 stickers into packets of 4, making 214 full packets and 1 sticker left. Which equation proves this?

   214 × 4 = 856215 × 4 = 860214 × 4 + 1 = 857857 − 4 = 853

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