What are the different types of numbers in the Cambridge Lower Secondary Mathematics curriculum?

In the Cambridge Lower Secondary Mathematics curriculum, students learn about various types of numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Natural numbers are counting numbers starting from 1, whole numbers include all natural numbers and zero, integers extend whole numbers to include negative numbers, rational numbers are fractions or ratios of integers, and irrational numbers cannot be expressed as simple fractions.

How do you perform operations with integers in Mathematics?

Performing operations with integers involves understanding the rules for addition, subtraction, multiplication, and division. For addition and subtraction, remember that adding a negative number is the same as subtracting its positive counterpart, and subtracting a negative number is like adding its positive counterpart. For multiplication and division, the product or quotient of two integers with the same sign is positive, while with different signs, it is negative.

What is the importance of understanding place value in numbers?

Understanding place value is crucial as it helps students comprehend the value of each digit in a number based on its position. This understanding is fundamental for performing arithmetic operations, comparing numbers, and understanding the base-ten number system. It also aids in developing skills for estimating and rounding numbers, which are essential for problem-solving in Mathematics.

How can students effectively compare and order numbers?

Students can effectively compare and order numbers by first understanding the number line and the concept of greater than, less than, and equal to. They should practice arranging numbers in ascending or descending order by looking at the highest place value first. Using visual aids like number lines or charts can also help in visualizing the relative size of numbers, making it easier to compare and order them.

What strategies can be used to solve problems involving fractions and decimals?

To solve problems involving fractions and decimals, students should first ensure they understand the concepts of equivalent fractions and decimal place value. Strategies include converting fractions to decimals or vice versa for easier comparison, using common denominators for adding or subtracting fractions, and applying multiplication and division rules for fractions and decimals. Practice with real-world problems can also enhance understanding and application of these concepts.

Why is "Treating 'subtract a negative' as a subtraction, e.g. writing $7 - (-2) = 5$." a common mistake in Integers and Order of Operations?

Why it happens: The two minus signs sitting next to each other are read as one big subtraction. How to avoid it: Two negative signs together make a plus. Rewrite first: 7 - (-2) = 7 + 2 = 9.

Why is "Thinking $-8$ is bigger than $-2$ because 8 is bigger than 2." a common mistake in Integers and Order of Operations?

Why it happens: Only the digits are compared, ignoring the minus sign and the number line. How to avoid it: The further left a number sits, the smaller it is. -8 is left of -2, so -8 is smaller.

Why is "Doing all multiplication before all division (or all addition before subtraction)." a common mistake in Integers and Order of Operations?

Why it happens: BIDMAS is read as a strict top-to-bottom list, so D looks like it always beats M. How to avoid it: Division and multiplication rank equally — work them left to right. Same for addition and subtraction.

Why is "Working a calculation strictly left to right, e.g. $2 + 3 \times 4 = 20$." a common mistake in Integers and Order of Operations?

Why it happens: Reading left to right is the natural habit from everyday language. How to avoid it: Scan for brackets, indices and ×/÷ first. Here 3 × 4 = 12, then 2 + 12 = 14.

Why is "Getting the sign wrong when multiplying, e.g. writing $-4 \times -3 = -12$." a common mistake in Integers and Order of Operations?

Why it happens: It feels like two negatives should keep the answer negative. How to avoid it: Same signs give a positive: -4 × -3 = 12. Different signs give a negative.

Number line showing −3 + 5 = 2

Learning Portal

Learning Platform

Launching your learning experience…

Report issue

Integers and Order of Operations — Cambridge Lower Secondary Maths, Grade 6

Negative numbers turn up everywhere — in temperatures, game scores and money you owe. This guide walks you through the number line, calculating with positive and negative integers, and BIDMAS, the running order that makes sure everyone gets the same answer.

At a glance

An integer is a whole number — it can be positive, negative or zero, but never a fraction.
Negative numbers sit to the LEFT of zero on the number line; positives sit to the right.
Adding a positive moves you right; adding a negative moves you left.
Subtracting a negative is the same as adding — $7 - (-2) = 9$ .
When you multiply or divide: same signs give a positive, different signs give a negative.
BIDMAS sets the order: Brackets, Indices, Division/Multiplication, Addition/Subtraction.
Division and multiplication rank equally — work them left to right.
Picture the number line whenever a sign question feels tricky.

What you’ll learn

Mapped to the Cambridge Lower Secondary Mathematics curriculum framework.

Stage 7 — Add, subtract, multiply and divide positive and negative integers, picturing the number line where helpful.
Stage 7 — Recognise that two signs next to each other combine, so subtracting a negative is the same as adding.
Stage 7 — Use the correct order of operations (BIDMAS), including brackets and indices, to work out multi-step calculations.
Stage 7 — Use brackets to change the order of a calculation on purpose.

Integers and the number line

Integers are whole numbers. The number line shows where each one lives.

An integer is a whole number. It can be positive ( $3$ , $58$ ), negative ( $-3$ , $-58$ ) or zero — but it is never a fraction or a decimal.

You already meet negative integers all the time. A game score can drop to $-20$ . A cold morning might be . If you owe a friend $5, your "money" is .

Adding and subtracting integers

Adding moves you right, subtracting moves you left — and two signs together combine.

The number line makes adding and subtracting easy to picture.

Adding a positive number moves you RIGHT.
Subtracting a positive number moves you LEFT.

Starting at −3 and rising 5 steps lands you on +2, so −3 + 5 = 2.

So if the temperature is $- 3 °$ and it rises by , you start at and move 5 steps right: the answer is .

Multiplying and dividing integers

Just look at the two signs: same signs give a positive, different signs give a negative.

Multiplying and dividing integers is quick once you know the sign rule. Forget the number line here — just look at the two signs.

Same signs (both positive or both negative) give a positive answer.
Different signs (one of each) give a negative answer.

Same signs land on green (positive); different signs land on red (negative).

So $-4 \times -3 = 12$ (same signs), but (different signs). The exact same rule works for division: , while .

The order of operations (BIDMAS)

When a calculation has several steps, BIDMAS tells you which to do first.

What is $2 + 3 \times 4$ ? If you work left to right you get 20. But the correct answer is 14. Maths has a fixed running order so everyone gets the same answer.

That order is BIDMAS:

Brackets
Indices (powers and roots)
Division and Multiplication — left to right
Addition and Subtraction — left to right

Putting signs and order together

Real calculations mix negative numbers with BIDMAS — take them one step at a time.

Most calculations combine both ideas: negative numbers and an order to follow. The trick is to slow down and do one step at a time, writing the line out again each time.

Try $5 + (-3) \times 4$ . The multiplication comes first, and it has different signs:

$(-3) \times 4 = -12$ .

Where you'll use this next

Integers and BIDMAS sit underneath almost every topic still to come.

Getting confident with integers and the order of operations now makes everything ahead easier:

Algebra uses negative numbers and BIDMAS every single time you substitute a value or simplify an expression.
Coordinates and graphs stretch the number line into two directions, so negative values appear on both axes.
Geometry and measure often produces negative differences — for instance when comparing temperatures or heights above and below sea level.
In everyday life, you will use these skills for bank balances, game scores, temperatures and any calculator question with more than one step.

If a topic later feels hard, it is often a sign rule or a BIDMAS step underneath that needs a quick refresh. Come back to this guide whenever you need it — there is no prize for rushing.

Algebra reuses negative numbers and BIDMAS constantly.
Coordinate grids extend the number line into two directions.
Geometry uses negative differences for comparisons.
Strong integer skills make every later topic smoother.

Quick recap

An integer is a whole number — positive, negative or zero, never a fraction.
On the number line, negatives are left of zero and the further left, the smaller.
Adding moves right, subtracting moves left; two signs together combine.
Subtracting a negative is the same as adding.
Same signs multiply or divide to a positive; different signs to a negative.
BIDMAS fixes the order: brackets and indices first, then ×/÷, then +/−.
Division and multiplication rank equally — always work left to right.

Sources: Cambridge Lower Secondary Mathematics curriculum framework (Stage 7). Last reviewed 2026-05-19.

C

-3\degree\text{C}

3 \times 4 = 12

\times

-

3

=

12

-4 \times -3 = 12

Integers and Order of Operations — Cambridge Lower Secondary Mathematics — Stage 7 Revision Notes & Practice | Tutopiya

Integers and Order of Operations

Detailed Study Notes

Take this whole topic with you

Integers and Order of Operations — frequently asked questions

Integers and Order of Operations — Cambridge Lower Secondary Maths, Grade 6

At a glance

What you’ll learn

Integers and the number line

Adding and subtracting integers

Multiplying and dividing integers

The order of operations (BIDMAS)

Putting signs and order together

Where you'll use this next

Quick recap

Step-by-step worked examples — Integers and Order of Operations

1Working with negative numbers

2Using BIDMAS in a calculation

3Subtracting a negative number

4Multiplying and dividing with signs

5A multi-step integer challenge

Key Definitions and Keywords — Integers and Order of Operations

Integer

Positive number

Negative number

Number line

Zero

Sum

Difference

Product

Order of operations

BIDMAS

Brackets

Operation

Common Mistakes and Misconceptions — Integers and Order of Operations

✕Treating 'subtract a negative' as a subtraction, e.g. writing $7 - (-2) = 5$ .

✕Thinking $-8$ is bigger than $-2$ because 8 is bigger than 2.

✕Doing all multiplication before all division (or all addition before subtraction).

✕Working a calculation strictly left to right, e.g. $2 + 3 \times 4 = 20$ .

✕Getting the sign wrong when multiplying, e.g. writing $-4 \times -3 = -12$ .

Integers and Order of Operations

Detailed Study Notes

Take this whole topic with you

Integers and Order of Operations — frequently asked questions

At a glance

What you’ll learn

Quick recap

1Working with negative numbers

2Using BIDMAS in a calculation

3Subtracting a negative number

4Multiplying and dividing with signs

5A multi-step integer challenge

Integer

Positive number

Negative number

Number line

Zero

Sum

Difference

Product

Order of operations

BIDMAS

Brackets

Operation

✕Treating 'subtract a negative' as a subtraction, e.g. writing 7−(−2)=57 - (-2) = 57−(−2)=5.

✕Thinking −8-8−8 is bigger than −2-2−2 because 8 is bigger than 2.

✕Doing all multiplication before all division (or all addition before subtraction).

✕Working a calculation strictly left to right, e.g. 2+3×4=202 + 3 \times 4 = 202+3×4=20.

✕Getting the sign wrong when multiplying, e.g. writing −4×−3=−12-4 \times -3 = -12−4×−3=−12.

✕Treating 'subtract a negative' as a subtraction, e.g. writing $7 - (-2) = 5$ .

✕Thinking $-8$ is bigger than $-2$ because 8 is bigger than 2.

✕Working a calculation strictly left to right, e.g. $2 + 3 \times 4 = 20$ .

✕Getting the sign wrong when multiplying, e.g. writing $-4 \times -3 = -12$ .