Addition and subtraction of whole numbers
🎯 In this topic you will
- Compose whole numbers by putting smaller parts together.
- Decompose whole numbers into meaningful parts.
- Regroup numbers as part of addition and subtraction calculations.
- Select appropriate mental or written methods to add and subtract whole numbers.
- Estimate the size of an answer before carrying out a calculation.
🧠 Key Words
- compose
- decompose
- difference
- regroup
Show Definitions
- compose: To form a whole number by putting together two or more smaller numbers.
- decompose: To break a whole number into smaller parts that add up to the original number.
- difference: The result of a subtraction, showing how much one number is greater or smaller than another.
- regroup: To rearrange numbers into different groups to make addition or subtraction easier.
Using Maths When You Shop
When you go shopping you spend money. You use addition to work out how much to pay, and you use subtraction to work out how much change you should get.
Mental and Written Calculations
In this section, you will estimate and then add and subtract pairs of two-digit numbers mentally. You will also learn about different written methods for addition and subtraction.
💡 Quick Math Tip
Use estimation as a check: Before doing written addition or subtraction, round the numbers to nearby hundreds to estimate the answer. This helps you quickly judge whether your final result is sensible.
🧠 Think like a Mathematician
Addition patterns
You can use any calendar for this investigation.
Method:
- Choose a $3 \times 3$ square of numbers from a calendar.
- Add the numbers in the opposite corners of the square.
- Investigate several different $3 \times 3$ squares from the calendar.
- Record your results clearly.
Example:
$\begin{matrix} 8 & 9 & 10 \\ 15 & 16 & 17 \\ 22 & 23 & 24 \end{matrix}$
Opposite corners:
$8 + 24 = 32$
$10 + 22 = 32$
Reflection prompts:
- You will show you are generalising when you recognise patterns in your results.
- If you explain your results clearly, you will show you are convincing.
Show Answers
- Pattern: In every $3 \times 3$ calendar square, the sums of the opposite corners are always equal.
- Reason: Calendar numbers increase by $1$ across rows and by $7$ down columns, so opposite corners are always the same total distance apart.
- Generalisation: For any $3 \times 3$ calendar square, both pairs of opposite corners will always add to the same number.
❓ EXERCISES
🧠 Reasoning Tip
Remember to estimate before you calculate.
1.
a. Calculate $607 - 391$.
b. Find the sum of $376$ and $219$.
c. What is the difference between $345$ and $67$?
d. Subtract $385$ from $721$.
👀 Show answer
b. $376 + 219 = 595$
c. $345 - 67 = 278$
d. $721 - 385 = 336$
2. Rajiv says, ‘If you add $6$ to a number ending in $7$ you will always get a number ending in $3$.’ Is Rajiv correct? Discuss your answer with a partner and write an explanation.
👀 Show answer
3. Asif needs $355$ chairs for a school concert. He has $269$ chairs already. How many more chairs does he need?
👀 Show answer
4. The table shows the mass of some fruit and vegetables. How much do the apple and banana weigh altogether?
| Fruit or vegetable | Mass |
|---|---|
| Apple | $130\,\text{g}$ |
| Banana | $210\,\text{g}$ |
| Carrot | $90\,\text{g}$ |
| Potato | $240\,\text{g}$ |
👀 Show answer
5. Pierre had $469$ stamps at the beginning of the year. During the year he collected $137$ more stamps. How many stamps does he have at the end of the year?
👀 Show answer
6. Bashir is thinking of a number. He says, ‘If I subtract $16$ from my number, the answer is $95$.’ What number is Bashir thinking of? Discuss your answer with a partner.
👀 Show answer
7. Aiko says, ‘When you add two $2$-digit whole numbers together the answer cannot be a $4$-digit number.’ Is Aiko correct? Explain your reasoning.