What are integers in the context of IB MYP Mathematics?

In the IB MYP Mathematics curriculum, integers are defined as whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. Integers are used to represent quantities in various real-world contexts, such as temperature changes, financial transactions, and elevation levels.

How do you add and subtract integers?

To add integers, if they have the same sign, add their absolute values and keep the sign. If they have different signs, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value. For subtraction, change the operation to addition and switch the sign of the second integer, then follow the rules for addition.

What is the importance of understanding integers in IB MYP Mathematics?

Understanding integers is crucial in IB MYP Mathematics as they form the foundation for more complex mathematical concepts. Integers are used in various mathematical operations and real-life applications, such as calculating profits and losses, measuring temperature differences, and understanding elevation changes. Mastery of integers helps students develop critical thinking and problem-solving skills.

How do you multiply and divide integers?

When multiplying or dividing integers, if the signs of the numbers are the same, the result is positive. If the signs are different, the result is negative. For multiplication, multiply the absolute values of the integers. For division, divide the absolute values. Ensure to apply the correct sign to the final result.

What are some common misconceptions about integers in Mathematics?

A common misconception is that zero is neither positive nor negative, which is correct, but students often mistakenly treat it as a positive number. Another misconception is that negative numbers are always smaller than positive numbers, which is true, but students sometimes struggle with comparing negative numbers themselves. Understanding these concepts is essential for solving problems accurately in IB MYP Mathematics.

Why is "Writing $5 - (-3) = 5 - 3 = 2$." a common mistake in Integers?

Why it happens: Treating the two minus signs as a single subtraction. How to avoid it: -(-3) = +3. Rewrite as 5 + 3 = 8. Always rewrite double signs first.

Why is "Saying $-10$ is bigger than $-2$." a common mistake in Integers?

Why it happens: Confusing 'absolute size' with 'magnitude on the number line'. How to avoid it: On the number line, -10 is far LEFT, so it is SMALLER. Use -10 < -2.

Why is "Writing $-3^2 = 9$." a common mistake in Integers?

Why it happens: Squaring is applied without brackets. How to avoid it: -3^2 means -(3^2) = -9. Only (-3)^2 = 9. Always include brackets when squaring a negative.

NumberIB MYP Maths Extended Level

Integers

Q: Why is "Writing $-3^2 = 9$." a common mistake in Integers?

Why it happens: Squaring is applied without brackets. How to avoid it: -3^2 means -(3^2) = -9. Only (-3)^2 = 9. Always include brackets when squaring a negative.

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Integers — IB MYP Mathematics (Extended): operations with positive and negative whole numbers

Integers are the foundation of arithmetic. This MYP Mathematics Extended note covers the sign rules, the number line, and how to add, subtract, multiply and divide negatives confidently.

What you’ll learn

Mapped to the IB MYP Mathematics subject guide (2026 onwards).

MYP Mathematics A — Identify integers and order them on the number line.
MYP Mathematics A — Apply the four operations to integers.
MYP Mathematics C — Write working clearly using correct signs.
MYP Mathematics D — Use signed numbers in real contexts (temperatures, sea level, balances).

The integer number line

A visual model for ordering and operating on integers.

An integer is any whole number, including zero and its negatives: $\ldots,-3,-2,-1,0,1,2,3,\ldots$

On a horizontal number line, positives go RIGHT of 0 and negatives go LEFT. Two integers can always be compared by their position on the line: the further right, the larger.

The number line is the standard tool for ordering and operating on integers. 0 is the boundary between negatives and positives.

For example, $-3 < -1$ because $-3$ sits to the LEFT of $-1$ . Be careful — although $3 > 1$ for positives, the order REVERSES for the negatives: $-3 < -1$ .

The absolute value of an integer is its distance from 0 (always positive): $|-3| = 3, \quad |5| = 5, \quad |0| = 0.$

Larger negatives sit further LEFT (e.g. $-7 < -2$ ).
Absolute value $|x|$ is always positive.
Zero is the only integer that is neither positive nor negative.

Adding and subtracting integers

Two-negatives-make-a-plus, in working form.

Adding an integer means moving along the number line:

Adding a POSITIVE $\to$ move RIGHT.
Adding a NEGATIVE $\to$ move LEFT.

So $5 + (-3) = 5 - 3 = 2$ .

Subtracting an integer reverses this:

Subtracting a POSITIVE $\to$ move LEFT.
Subtracting a NEGATIVE $\to$ move RIGHT.

So $4 - (-2) = 4 + 2 = 6$ . Two minus signs next to each other become a plus.

Working	Result
$-7 + 4$	$-3$
$-7 - 4$	$-11$
$7 - (-4)$	$7 + 4 = 11$
$-7 - (-4)$	$-7 + 4 = -3$

Always REWRITE chains of signs before computing — a clean expression with one operation per pair is far less error-prone.

$+(+) = +$ and $+(-) = -$
$-(+) = -$ and $-(-) = +$
Rewrite double signs FIRST, then compute.

Multiplying and dividing integers

Same signs $\to$ positive; different signs $\to$ negative.

For $\times$ and $\div$ the rule is simply about whether the signs of the two numbers MATCH:

First number	Second number	Result sign
$+$	$+$	$+$
$-$	$-$	$+$
$+$	$-$	$-$
$-$	$+$	$-$

So $(-6) \times (-4) = +24$ and $(-6) \div 3 = -2$ .

For a CHAIN of multiplications, count the number of negative signs:

EVEN number of negatives $\to$ result is POSITIVE.
ODD number $\to$ result is NEGATIVE.

For example $(-2) \times (-3) \times (-5) = -30$ (three negatives, odd).

Worked example. Evaluate $-2 - 3 \times (-4)$ .

BIDMAS: multiplication BEFORE subtraction.
$3 \times (-4) = -12$ .
$-2 - (-12) = -2 + 12 = 10$ .

$(-)(-) = (+)$ and $(+)(+) = (+)$
$(-)(+) = (-)$
Chain rule: count negatives. Even $\to +$ , odd $\to -$ .

Real-world integer applications

Temperature, sea level, money, scores — signs everywhere.

Integers naturally appear whenever a quantity can go above OR below a fixed reference:

Temperature. A drop from $5\,°\text{C}$ to $-3\,°\text{C}$ is a change of $-3 - 5 = -8\,°\text{C}$ .
Elevation. The Dead Sea is at $-430\,\text{m}$ (below sea level); Mount Everest is at $+8849\,\text{m}$ . Difference $= 8849 - (-430) = 9279\,\text{m}$ .
Bank balance. $\$ 120 $minus a$ $200 $purchase gives$ -$80$ (overdraft).
Sports. A football team's goal difference is $\text{goals scored} - \text{goals conceded}$ .

MYP criterion D often gives a real context and asks you to model it with signed integers. Always:

Identify the reference point (where is 0?).
Decide which direction is positive.
Apply the operations consistently.

Choose a clear reference (sea level, freezing point, opening balance).
Be explicit about which direction is positive.
Differences between two signed values use subtraction (which can flip to addition).

How it’s examined

Criterion A: rapid sign manipulation. Criterion C: clearly written working. Criterion D: model real contexts (temperature, elevation, money).

Sources: IB MYP Mathematics subject guide (IBO, official). Last reviewed 2026-05-25.

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Step-by-step worked examples — Integers

Step-by-step solutions to past-paper-style questions on integers, written exactly the way a tutor would explain them at the board.

1Evaluate a signed expression
Getting started• signs
Question
Evaluate $-6 - (-4) + (-2)$ .
Step-by-step solution
1. Step 1
  Rewrite double signs. $-(-4) = +4$ , so the expression becomes $-6 + 4 - 2$ .
2. Step 2
  Compute left to right: $-6 + 4 = -2$ .
3. Step 3
  Then $-2 - 2 = -4$ .
Answer
$-4$
2Multiplication with multiple negatives
Building confidence• multiplication
Question
Evaluate $(-3) \times 2 \times (-4) \times (-1)$ .
Step-by-step solution
1. Step 1
  Count the negatives: three of them. ODD number $\to$ result is NEGATIVE.
2. Step 2
  Multiply absolute values: $3 \times 2 \times 4 \times 1 = 24$ .
3. Step 3
  Apply the negative sign: $-24$ .
Answer
$-24$
3Real context: temperature change
Building confidence• application, criterion D
Question
Overnight in Reykjavík the temperature dropped from $4\,°\text{C}$ to $-9\,°\text{C}$ . Calculate the size of the drop.
Step-by-step solution
1. Step 1
  Change = final - initial $= -9 - 4 = -13\,°\text{C}$ .
2. Step 2
  The negative sign confirms a drop. The SIZE of the drop is $|-13| = 13\,°\text{C}$ .
Answer
A drop of $13\,°\text{C}$ .
4Order of operations with negatives
Stretch• BIDMAS
Question
Evaluate $-2 - 3 \times (4 - 7)^2 \div 9$ .
Step-by-step solution
1. Step 1
  BIDMAS — Brackets first. $(4-7) = -3$ . Expression: $-2 - 3 \times (-3)^2 \div 9$ .
2. Step 2
  Indices: $(-3)^2 = 9$ . Expression: $-2 - 3 \times 9 \div 9$ .
3. Step 3
  Division and multiplication, left to right: $3 \times 9 = 27$ ; $27 \div 9 = 3$ . Expression: $-2 - 3$ .
4. Step 4
  Subtraction: $-2 - 3 = -5$ .
Answer
$-5$

Key Definitions and Keywords — Integers

Definitions to memorise and the exact keywords mark schemes credit for integers answers — sharpened from recent examiner reports for the 2026 IB MYP Mathematics (Extended) sitting.

Integer
Examiner keyword
A whole number, positive, negative or zero. The set is denoted $\mathbb{Z}$ .
Absolute value $|x|$
Examiner keyword
The distance of $x$ from 0 on the number line. Always non-negative.
Additive inverse
For an integer $a$ , the additive inverse is $-a$ , since $a + (-a) = 0$ .

Common Mistakes and Misconceptions — Integers

The traps other students keep falling into on integers questions — taken from recent IB MYP Mathematics (Extended) examiner reports and mark schemes — and how to avoid them.

✕Writing $5 - (-3) = 5 - 3 = 2$ .
Why it happens
Treating the two minus signs as a single subtraction.
How to avoid it
$-(-3) = +3$ . Rewrite as $5 + 3 = 8$ . Always rewrite double signs first.
✕Saying $-10$ is bigger than $-2$ .
Why it happens
Confusing 'absolute size' with 'magnitude on the number line'.
How to avoid it
On the number line, $-10$ is far LEFT, so it is SMALLER. Use $-10 < -2$ .
✕Writing $-3^2 = 9$ .
Why it happens
Squaring is applied without brackets.
How to avoid it
$-3^2$ means $-(3^2) = -9$ . Only $(-3)^2 = 9$ . Always include brackets when squaring a negative.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

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Integers — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Integers

Short Study Notes in the form of Slides

Short Study Notes — Integers

Detailed Notes

What you’ll learn

How it’s examined

1Evaluate a signed expression

2Multiplication with multiple negatives

3Real context: temperature change

4Order of operations with negatives

Integer

Absolute value ∣x∣|x|∣x∣

Additive inverse

✕Writing 5−(−3)=5−3=25 - (-3) = 5 - 3 = 25−(−3)=5−3=2.

✕Saying −10-10−10 is bigger than −2-2−2.

✕Writing −32=9-3^2 = 9−32=9.

Practice questions

Past paper style quiz

Assess your understanding

Integers — frequently asked questions

Absolute value $|x|$

✕Writing $5 - (-3) = 5 - 3 = 2$ .

✕Saying $-10$ is bigger than $-2$ .

✕Writing $-3^2 = 9$ .