Last reviewed: 11 November 2026
Updated November 2026. These Grade 8 integers notes show how to identify integers, represent them on a number line, and add or subtract them by moving right or left along that line. Integers are the whole numbers and their negatives, including zero: …, −3, −2, −1, 0, 1, 2, 3, … A storey above the ground can stand for a positive integer, a basement for a negative integer, and the ground floor for zero.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 8 Mathematics numbers sub-strand on integers in the KICD Grade Eight curriculum designs. Multiplication and deeper combined work come later, including in the Grade 9 integers notes. For Grade 8 topics overall, use the Grade 8 mathematics revision guide and the Grade 8 notes hub.
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Identifying Integers and Placing Them on a Number Line
An integer has no fractional or decimal part. 7, −4 and 0 are integers. 2.5, 3/4 and 0.01 are not. On a number line, positive integers lie to the right of zero and negative integers to the left. Equal spaces must be used so that the step from 0 to 1 matches the step from 0 to −1. OpenStax Prealgebra’s introduction to integers uses the same number-line picture.
Worked example: which of these are integers?
From the list −8, 0, 4.2, 15, 1/2 and −3, the integers are −8, 0, 15 and −3. 4.2 has a decimal part and 1/2 is a fraction, so they are not integers.
To represent −5, 0 and 3 on a line, mark zero, then three equal steps right for 3 and five equal steps left for −5. A common mistake is to squeeze the negative side into smaller gaps; the size of one unit must stay the same.
Adding and Subtracting Integers on the Number Line
Addition of a positive integer is a move to the right. Addition of a negative integer is a move to the left. Subtraction of a positive integer is a move to the left; subtraction of a negative integer is a move to the right. In short: adding a negative, or subtracting a positive, takes you left; adding a positive, or subtracting a negative, takes you right. The same moves are practised in OpenStax Prealgebra’s section on adding integers.
Worked example: addition
Find −3 + 5. Start at −3 and move 5 steps right: −2, −1, 0, 1, 2. The landing point is 2.
Find 4 + (−7). Start at 4 and move 7 steps left: 3, 2, 1, 0, −1, −2, −3. The landing point is −3.
Worked example: subtraction and combined operations
Find 4 − 7. Start at 4 and move 7 steps left, which is the same journey as 4 + (−7), so the answer is again −3.
Find −2 − (−6). Subtracting −6 is a move of 6 steps right from −2: −1, 0, 1, 2, 3, 4. The answer is 4.
Combined operations stay on the same line. For −2 + 6 − 5, start at −2, move 6 right to 4, then 5 left to −1.
A real-life reading
A morning temperature in the highlands is 3 °C. It falls by 8 °C at night. On the number line that is 3 + (−8) or 3 − 8, which lands at −5 °C.
Original Practice Questions With Worked Answers
- Which of −11, 0.6, 9 and 3/5 are integers? −11 and 9. 0.6 is a decimal and 3/5 is a fraction.
- Represent −4 and 2 on a number line, then find −4 + 2 by moving. Start at −4 and move 2 right to −2.
- Work out 8 + (−3) on a number line. Start at 8, move 3 left, and land on 5.
- Work out −1 − 6. Start at −1 and move 6 left to −7.
- Work out 5 − (−4). Subtracting −4 is a move of 4 right from 5, so the answer is 9.
- A lift starts at floor 2, goes down 5 floors, then up 3 floors. Where does it stop if ground level is 0? 2 − 5 + 3 = 0, the ground floor.
Cover the answers and walk each jump on a sketched number line before checking. For more Grade 8 number practice see the Grade 8 decimals notes. Timed quizzes are in the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What are integers in Grade 8 maths?
Integers are whole numbers and their negatives, including zero. They have no fractional or decimal part, so −7, 0 and 12 are integers while 1/2 and 3.4 are not.
How do you add integers on a number line?
Start at the first number. Move right to add a positive integer and left to add a negative integer. −3 + 5 starts at −3 and moves five steps right to 2.
Why is subtracting a negative the same as adding?
Subtracting is the opposite of adding, so subtracting a leftward move becomes a rightward move. 5 − (−4) is a jump of 4 to the right from 5, which lands on 9.
Does Grade 8 integers include multiplication?
This Grade 8 sub-strand focuses on identifying integers, placing them on a number line, and adding or subtracting them there. Multiplication and extra operations are built in later grades.
Get the marked answers for the Grade 8 Mathematics paper, KSh 20.
Open the paper