Last reviewed: 7 November 2026
Updated November 2026. These Grade 9 integers notes cover adding, subtracting, multiplying and dividing positive and negative whole numbers, and doing combined operations in the correct order. The two rules most learners need are: subtracting a negative is the same as adding (7 − (−3) = 10), and when multiplying or dividing, two like signs give a positive answer while unlike signs give a negative answer ((−4) × (−5) = 20, but (−4) × 5 = −20).
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub.
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What the Grade 9 Curriculum Covers
Integers is the first sub-strand under Numbers in the Kenya Institute of Curriculum Development’s Grade 9 Mathematics design. Learners perform basic operations on integers, work out combined operations in the correct order, and apply integers to real life, for example reading temperatures below zero. The design is listed on the KICD Grade Nine curriculum designs page.
What Are Integers?
Integers are the whole numbers and their negatives: …, −3, −2, −1, 0, 1, 2, 3, … On a number line, numbers to the right are bigger. So −2 is bigger than −7, even though 7 looks bigger. This is why −2 °C is warmer than −7 °C.
Adding Integers
OpenStax Prealgebra’s section on adding integers models addition with counters and the number line. In short:
- Same signs: add the sizes and keep the sign. −6 + (−4) = −10.
- Different signs: subtract the smaller size from the bigger and take the sign of the bigger size. −8 + 5 = −3; 9 + (−2) = 7.
Worked example: temperature
In this made-up example the temperature on a mountain at dawn is −5 °C. By noon it has risen by 12 °C. New temperature: −5 + 12 = 7 °C.
Subtracting Integers
Change the subtraction to adding the opposite, then use the addition rules.
- 4 − 9 = 4 + (−9) = −5
- −6 − (−9) = −6 + 9 = 3
- −2 − 7 = −2 + (−7) = −9
Worked example: difference in temperature
A freezer is at −18 °C and a room at 24 °C. The difference is 24 − (−18) = 24 + 18 = 42 °C. Writing 24 − 18 = 6 is the common mistake here.
Multiplying and Dividing Integers
The sign rules below match OpenStax Prealgebra’s section on multiplying and dividing integers.
| Signs | Answer | Examples |
|---|---|---|
| + and + | Positive | 6 × 3 = 18; 20 ÷ 4 = 5 |
| − and − | Positive | (−4) × (−5) = 20; (−30) ÷ (−6) = 5 |
| + and − | Negative | 7 × (−2) = −14; (−24) ÷ 6 = −4 |
For a longer product, count the negative signs. An even number of negatives gives a positive answer; an odd number gives a negative one. (−1) × (−2) × (−3) = −6, because there are three negatives.
Combined Operations: The Correct Order
Work in this order: brackets first, then division and multiplication (left to right), then addition and subtraction (left to right). Many Kenyan textbooks call this BODMAS.
Worked example one
−3 + 4 × (−2)
- Multiply first: 4 × (−2) = −8.
- Then add: −3 + (−8) = −11.
Working left to right instead gives (−3 + 4) × (−2) = −2, which is wrong.
Worked example two
[(−12) ÷ 3 − (−5)] × (−2)
- Inside the bracket, divide: (−12) ÷ 3 = −4.
- Then subtract: −4 − (−5) = −4 + 5 = 1.
- Multiply: 1 × (−2) = −2.
Worked example three: a real-life problem
A small business records a profit of KSh 3,000 on each of 4 days and a loss of KSh 2,500 on each of 3 days (made-up figures). Net result: 4 × 3,000 + 3 × (−2,500) = 12,000 − 7,500 = KSh 4,500 profit.
Original Practice Questions With Worked Answers
- Evaluate −15 + 8. −7.
- Evaluate −3 − (−11). −3 + 11 = 8.
- Evaluate (−6) × (−7). 42.
- Evaluate (−45) ÷ 9 + 2 × (−3). −5 + (−6) = −11.
- A diver is 14 m below sea level and rises 6 m. Where is she now? −14 + 6 = −8, so 8 m below sea level.
- Evaluate (−2)³. (−2) × (−2) × (−2) = −8.
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 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 is the rule for subtracting a negative number?
Subtracting a negative is the same as adding the positive. For example, 5 − (−3) = 5 + 3 = 8.
Why is a negative times a negative positive?
Multiplying by a negative reverses the direction on the number line. Reversing twice brings you back to the positive direction, so (−3) × (−4) = 12.
What order should I use for combined operations on integers?
Brackets first, then division and multiplication from left to right, then addition and subtraction from left to right.
Is −10 bigger than −3?
No. −3 is further right on the number line, so −3 is bigger than −10.