# Long Multiplication and Long Division

> Multiply by 2-digit numbers, divide by 2-digit numbers, cross off zeros, handle zeros in short division and decide what to do with a remainder.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/long-multiplication-and-division/. Updated 4 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The school camp buses
The school is taking 250 students to camp. Each bus holds 45 students. Mr Park works out $250 \div 45$ and gets 5 remainder 25. "Five buses," he says.

"Then 25 students stay home!" says Ella. "We need 6 buses."

Mr Park laughs. The division was right, but the answer has to make sense for the story. A remainder sometimes means one more, and sometimes means it is left over.

**In short:** Long multiplication multiplies by the tens and the ones separately, then adds. Long division repeats four steps: divide, multiply, subtract, bring down. When there is a remainder, read the question to decide whether to round up, round down or keep it.

## Before you start

- Times tables up to $12 \times 12$.
- Multiplying and dividing by 10, 100 and 1000 (see Multiplying and Dividing by 10, 100 and 1000).
- Short division by a 1-digit number.

## Long multiplication

To multiply by a 2-digit number, split it into tens and ones.

### Worked example: $347 \times 26$
$26 = 20 + 6$.

- $347 \times 6 = 2082$
- $347 \times 20 = 6940$ (work out $347 \times 2$, then put a 0 on the end)
- Add: $2082 + 6940 = 9022$

### Exam tip: Make 10s and 100s
Look for pairs that make 100 before you start: $25 \times 4 = 100$ and $50 \times 2 = 100$.

$25 \times 36 = 25 \times 4 \times 9 = 100 \times 9 = 900$.

## Cross off zeros

When both numbers end in zeros, cross off the **same number** of zeros from each. The answer does not change.

### Worked example: Crossing off
$4800 \div 60$: cross off one zero from each to get $480 \div 6 = 80$.

$35\,000 \div 700$: cross off two zeros from each to get $350 \div 7 = 50$.

### Watch out: Only cross off zeros at the end
In $4080 \div 40$ you can cross off one zero from each: $408 \div 4 = 102$. You cannot cross off the 0 in the middle of 4080.

## Zeros in short division

If a step does not go, write a 0 in the answer and carry on.

### Worked example: $4824 \div 8$
- 8 does not go into 4, so look at 48: $48 \div 8 = 6$.
- 8 does not go into 2: write 0, and the 2 joins the next digit to make 24.
- $24 \div 8 = 3$.

So $4824 \div 8 = 603$. Check: $8 \times 603 = 4824$.

## Long division by a 2-digit number

### Key idea: Four steps, again and again
1. **Divide**: how many times does the divisor go in?
2. **Multiply**: that number times the divisor.
3. **Subtract**: find what is left.
4. **Bring down** the next digit, then start again.

### Worked example: $936 \div 24$
- 24 does not go into 9. Try 93: $24 \times 3 = 72$, so it goes 3 times.
- $93 - 72 = 21$. Bring down the 6 to make 216.
- $24 \times 9 = 216$, so it goes 9 times, with nothing left.

So $936 \div 24 = 39$.

### Exam tip: Estimate first
Round the divisor to guess each step: 24 is about 25, and $25 \times 4 = 100$. So $216 \div 24$ is a bit less than 10. Try 9.

## What to do with a remainder

| The question asks | Example | Answer to $250 \div 45 = 5$ r 25 |
|---|---|---|
| How many are needed? Round **up** | Buses for 250 students | 6 buses |
| How many full ones? Round **down** | 45 cm pieces from 250 cm of rope | 5 pieces |
| How many are left? Keep the remainder | Sweets left after sharing | 25 left |

### Challenge: Selective level: working backwards from a remainder
A number divided by 23 gives 17 with a remainder of 9. Work backwards: number $= 23 \times 17 + 9 = 391 + 9 = 400$.

What is the biggest 3-digit number that divides exactly by 24? $999 \div 24 = 41$ remainder 15. So the answer is $999 - 15 = 984$, which is $24 \times 41$.

A club pays 2856 dollars for 34 tickets. One ticket costs $2856 \div 34$. 34 is about 35, and $35 \times 80 = 2800$, so try 84: $34 \times 84 = 2856$. Each ticket costs 84 dollars.

**Mind map**

```text
Long multiplication and division
  Multiplying
    Split into tens and ones
    Add the two parts
    Look for 25 x 4
  Dividing
    Cross off equal zeros
    Write 0 when a step does not go
    Divide, multiply, subtract, bring down
  Remainders
    Round up for how many needed
    Round down for full ones
    Keep for left over
```

## Quick summary

- Long multiplication: multiply by the ones, then by the tens (add a 0), then add.
- Cross off the same number of end zeros from both numbers before dividing.
- In short division, write 0 in the answer when a step does not go.
- Long division: divide, multiply, subtract, bring down, and repeat.
- A remainder can mean round up, round down or something left over. Read the question.
- Check a division by multiplying back.

## Quiz

Try these questions from the chapter quiz.

1. What is $4800 \div 60$?
   - A. 8
   - B. 80
   - C. 800
   - D. 48
   - Answer: B. 80. Cross off one zero from each: $480 \div 6 = 80$.

2. What is $4824 \div 8$?
   - A. 63
   - B. 630
   - C. 603
   - D. 6003
   - Answer: C. 603. $48 \div 8 = 6$, 8 does not go into 2 so write 0, then $24 \div 8 = 3$.

3. What is $35\,000 \div 700$?
   - A. 5
   - B. 50
   - C. 500
   - D. 5000
   - Answer: B. 50. Cross off two zeros from each: $350 \div 7 = 50$.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/long-multiplication-and-division/#quiz