FORM 2 • TERM 1 • LESSON 02

In the last lesson you sorted numbers into natural numbers, whole numbers and integers, and put integers in order. Now we put integers to work. You will add, subtract, multiply and divide positive and negative integers, spot where integers are used in everyday life, and use them to solve problems about temperature, sea level, money and sport. Much of this builds on the Form 1 lessons on adding and subtracting and multiplying and dividing directed numbers.

Learning outcomes

By the end of this lesson you should be able to:

• 2.1.1.3 – Add, subtract, multiply and divide with positive and negative integers.
• 2.1.1.4 – Spot where integers show up in daily life (temperature, sea level, bank balances).
• 2.1.1.5 – Work out simple real-life problems that use integers.

Integers in everyday life

Whenever a quantity can go above or below a starting point, integers are a natural way to describe it. Zero is the starting point.

Situation	Zero means	Positive	Negative
Temperature	0 °C, the freezing point of water	above freezing	below freezing
Height	sea level	above sea level	below sea level
Bank account	an empty account	money in the account	overdrawn (money owed)
Business	breaking even	a profit	a loss
Golf	level par	over par	under par
Lift buttons	the ground floor	floors above	basement levels
Football	equal goals for and against	positive goal difference	negative goal difference

Adding and subtracting integers

• Same signs: add the sizes and keep the sign. 5 + 3 = 8 and (−5) + (−3) = −8.
• Different signs: subtract the smaller size from the larger, and keep the sign of the one with the larger size. (−9) + 4 = −5 and 9 + (−4) = 5.
• Subtracting is the same as adding the opposite. 6 − 10 = 6 + (−10) = −4 and 3 − (−7) = 3 + 7 = 10.

If you are not sure, picture a number line: adding a positive moves you right, adding a negative moves you left.

Multiplying and dividing integers

Look at this pattern. Each answer is 3 less than the one before it, so the pattern carries on below zero:

3 × (−3) = −9
2 × (−3) = −6
1 × (−3) = −3
0 × (−3) = 0
(−1) × (−3) = 3
(−2) × (−3) = 6

Once the first number becomes negative the answers become positive. This gives the sign rules, which work the same way for division:

Signs	× or ÷ gives	Examples
positive and positive	positive	4 × 5 = 20; 20 ÷ 5 = 4
negative and negative	positive	(−4) × (−5) = 20; (−20) ÷ (−5) = 4
positive and negative	negative	4 × (−5) = −20; 20 ÷ (−5) = −4
negative and positive	negative	(−4) × 5 = −20; (−20) ÷ 5 = −4

In short: same signs give a positive answer, different signs give a negative answer. Work out the size of the answer as usual, then fix the sign.

Solving problems with integers

1. Read the problem and decide where zero is (sea level, freezing point, an empty account…).
2. Write the facts as integers, using negatives for “below”, “owed”, “loss” or “drop”.
3. Calculate, using the rules above.
4. Answer in words, and check that the answer makes sense (for example −25 dollars means overdrawn by $25).

Worked examples

Example 1: Adding with the same sign

Question: Work out (−8) + (−5).

1. Both are negative, so add the sizes: 8 + 5 = 13.
2. Keep the negative sign.

Answer: −13.

Example 2: Adding with different signs

Question: Work out 6 + (−11).

1. The sizes are 6 and 11. Subtract: 11 − 6 = 5.
2. 11 is the larger size and it is negative, so the answer is negative.

Answer: −5.

Example 3: Subtracting a negative

Question: Work out −4 − (−9).

1. Subtracting −9 is the same as adding 9: −4 + 9.
2. Different signs: 9 − 4 = 5, and 9 is positive.

Answer: 5.

Example 4: Multiplying and dividing

Question: Work out
(a) (−7) × 6
(b) (−7) × (−6)
(c) (−48) ÷ (−8)
(d) 36 ÷ (−4).

1. (a) Different signs, so negative: 7 × 6 = 42, giving −42.
2. (b) Same signs, so positive: 42.
3. (c) Same signs, so positive: 48 ÷ 8 = 6.
4. (d) Different signs, so negative: 36 ÷ 4 = 9, giving −9.

Answer:
(a) −42
(b) 42
(c) 6
(d) −9.

Example 5: Temperature rise

Question: At 6 a.m. the temperature on a mountain was −5 °C. At noon it was 9 °C. By how many degrees did the temperature rise?

1. Rise = later temperature − earlier temperature = 9 − (−5).
2. Subtracting a negative is adding: 9 + 5 = 14.

Answer: The temperature rose by 14 degrees.

Example 6: Below sea level

Question: A submarine is at −120 m (120 m below sea level). It rises 45 m, then dives 30 m. Where is it now?

1. Rising is adding and diving is subtracting: −120 + 45 − 30.
2. −120 + 45 = −75, then −75 − 30 = −105.

Answer: At −105 m, which is 105 m below sea level.

Example 7: A bank balance

Question: Keisha has $40 in her account. She withdraws $65, then deposits $100. What is her balance after each step?

1. After the withdrawal: 40 − 65 = −25, so she is overdrawn by $25.
2. After the deposit: −25 + 100 = 75.

Answer: −$25 (overdrawn), then $75.

Example 8: A steady drop

Question: The temperature is 4 °C and it falls by 3 degrees every hour for 5 hours. What is the temperature at the end?

1. A fall of 3 degrees each hour is −3, five times: 5 × (−3) = −15.
2. New temperature: 4 + (−15) = −11.

Answer: −11 °C.

Common mistakes

• Using the multiplication rule for adding. (−6) + (−4) is −10, not +10. “Two negatives make a positive” is for × and ÷ only.
• Forgetting the sign when you pass zero. 7 − 12 is −5, not 5.
• Getting the sign of a product wrong. (−4) × (−5) is 20, and (−4) × 5 is −20.
• Finding a difference by subtracting the sizes. The difference between 9 °C and −5 °C is 9 − (−5) = 14 degrees, not 4.
• Leaving out the meaning. An answer of −25 in a money problem should be written in words: overdrawn by $25 (or $25 owed).

Practice questions

Try these yourself first, then open each answer to check your working.

Quick check

Previous: Integers: Natural Numbers, Whole Numbers and Integers, and Ordering Them on the Number Line

Next: Laws of Numbers: Commutative, Associative and Distributive Laws, Closure, Identity and Inverse

Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 2, Term 1, Strand 2.1 Number Operations and Number Theory, Topic 2.1.1 Integers – Learning Outcomes 2.1.1.3 (the four basic operations on integers), 2.1.1.4 (integers in everyday life) and 2.1.1.5 (solving simple problems with integers).

Attributions to media used in this post:

Elevation Sea Level Sign Death Valley 2013.jpg – Tuxyso – CC BY-SA 3.0 (via Wikimedia Commons)

Updates

2026/10/23

– First version of this lesson.

2026/10/24

– Next lesson link now points to Lesson 3.

2026/10/25

– Put each lettered part of the questions and answers on its own line.

© 2026 Vedesh Kungebeharry. All rights reserved.