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calendar_month Last update: 2025-12-22

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Division of 2-digit numbers booklet

calendar_month 2025-12-22

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Unit 1: Numbers
Unit 2: Geometry and measure
Unit 3 : Statistics and probability

🎯 In this topic you will

Estimate the size of an answer when a number up to 100 is divided by a one-digit number.
Divide a number up to 100 by a one-digit number accurately.
Decide whether to round up or round down after division in order to give a sensible answer to a problem.

🧠 Key Words

division
divisor
remainder
round up / round down

Show Definitions

division: A mathematical operation that splits a number into equal parts.
divisor: The number by which another number is divided.
remainder: The amount left over when a number cannot be divided equally.
round up / round down: A decision made after calculation to increase or decrease a number to the nearest sensible whole value.

Division in Everyday Life 🧮

T hink about when you use division in your everyday life. For example, when organising a party for 45 people, you may need one paper plate for each person. If paper plates come in packs of 8, you need to work out how many packs are required.

Making Sense of the Answer 🤔

Y ou need to develop strategies to divide 45 by 8 and then decide what the answer means in real life. This helps you work out whether you should round your answer up or down so that everyone has what they need.

📘 Worked example

Work out $75 \div 4$

Start with an estimate:
$75$ rounds to $80$, and $80 \div 4 = 20$, so the answer will be a little less than $20$.

Method 1. Using a number line

Count back along a number line, first in a group of $10$ fours, then a group of $8$ fours.

$10$ lots of $4 = 40$
$8$ lots of $4 = 32$
Total: $18$ lots of $4$, with $3$ left over.

Method 2. Repeated subtraction

$75 - 40 = 35$ ($10$ lots of $4$)
$35 - 32 = 3$ ($8$ lots of $4$)

This makes $18$ lots of $4$, with $3$ left over.

Answer:

$75 \div 4 = 18\ \text{r}\ 3$

Estimating first helps you check whether your final answer is sensible. Using large groups of fours makes the division easier, and any amount left at the end is the remainder.

💡 Quick Math Tip

Estimate first: Before dividing, round the number to a nearby multiple of the divisor. This gives you a quick idea of the size of the answer and helps you check whether your final result makes sense.

❓ EXERCISES

1. How many weeks are equivalent to $35$ days?

👀 Show answer

There are $7$ days in a week. $35 \div 7 = 5$, so $35$ days is equal to $5$ weeks.

2. A shop sells cards in packs of $6$. Magda buys some of these packs. She buys $30$ cards. How many packs does Magda buy?

👀 Show answer

Each pack contains $6$ cards. $30 \div 6 = 5$, so Magda buys $5$ packs.

3. Complete these calculations.

a. $98 \div 7$

b. $64 \div 4$

c. $96 \div 8$

d. $84 \div 6$

👀 Show answer

a. $98 \div 7 = 14$
b. $64 \div 4 = 16$
c. $96 \div 8 = 12$
d. $84 \div 6 = 14$

4. Two sets of calculations which have different properties are mixed together.

$20 \div 3 \quad 23 \div 3 \quad 25 \div 3 \quad 14 \div 3 \quad 7 \div 3$

a. Sort the calculations into two sets.

b. Write one more example for each set.

👀 Show answer

One set gives whole number answers: $21 \div 3$, $24 \div 3$, such as $21 \div 3 = 7$.
The other set gives answers with remainders: $20 \div 3$, $23 \div 3$, $25 \div 3$, $14 \div 3$, $7 \div 3$. An extra example is $10 \div 3$.

5. $60$ people go for a walk. They need to cross a lake by boat. Each boat can take $9$ people. What is the least number of boats needed to take all of the people across the lake?

👀 Show answer

$60 \div 9 = 6$ remainder $6$. This means $6$ full boats and one more boat are needed. The least number of boats is $7$.

6. $27$ apricots are put in bags. Each bag holds $6$ apricots. How many full bags are there?

👀 Show answer

$27 \div 6 = 4$ remainder $3$. There are $4$ full bags.

7. Zac and Sarah calculated $75 \div 5$. Zac used repeated subtraction and Sarah used a number line. Whose method do you prefer? Explain your reason.

👀 Show answer

Both methods give the correct answer of $15$. A number line can be quicker and clearer because it shows the jumps of $5$ all at once, while repeated subtraction is more step-by-step.

🧠 Think like a Mathematician

Each of these numbers gives a remainder of $1$ when it is divided by $4$.

$17$

$81$

$49$

a. Investigate other numbers that have a remainder of $1$ when divided by $4$. Put the numbers in order and look at the pattern of the ones digits, for example $5, 9, 13$.

What do you notice about the pattern?

b. What about other remainders? You could choose numbers that have a remainder of $2$ or $3$ when divided by $4$, or numbers that have a remainder of $1$ when divided by $5$.

Write about the patterns you find.

You will show you are specialising when you find solutions to the problem.
You will show you are generalising when you recognise patterns in your results.
If you explain your results, you will show you are convincing.

👀 show answer

a. Numbers that give a remainder of $1$ when divided by $4$ follow the form $4n+1$, such as $5, 9, 13, 17, 21$. The ones digits repeat in the pattern $1, 5, 9, 3, 7$.
b. Numbers with remainder $2$ follow $4n+2$ and end in digits like $2, 6, 0, 4, 8$. Numbers with remainder $3$ follow $4n+3$. For division by $5$ with remainder $1$, numbers follow $5n+1$ and the ones digits repeat every five numbers.
In all cases, numbers with the same remainder form a repeating pattern because the divisor stays constant.

📘 What we've learned

How to estimate the size of an answer before carrying out a division calculation.
How to divide numbers up to $100$ by a one-digit number accurately.
How to interpret remainders depending on the context of a problem, such as deciding whether to round up or count only full groups.
That division problems can be solved and represented using different methods, including repeated subtraction and number lines.
That numbers with the same remainder when divided by a fixed number follow a repeating pattern that can be described algebraically, such as $4n + r$.

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