CHAPTER 2

WORKING WITH INTEGERS

Key Words: positive, negative, BODMAS, LCM, HCF

Introduction:

Jodan was sent to a shop up the hill to buy 1kg of rice, a packet of salt and a packet of tealeaves. He was given UGX. 5,000 note but all items cost her UGX. 6,500. How much money did Jodan owe the shopkeeper?

In your day-to-day life, you use numbers to count items, to keep information, to transact business and many others. Since you use numbers in your day-to-today situations, knowledge of integers will be helpful to you.

2.1 Natural numbers:

Natural numbers can be classified into various groups of numbers. In your primary education, you learnt numbers such as even, odd, prime and composite.

1. Natural Numbers: These are numbers used in counting. e.g N= {1,2,3,4, . . . }

2. Whole Numbers: These are counting numbers including zero .e.g W= {0,1,2,3, . . }

Activity: Writing and reading numbers:

EXAMPLES:

Exercise:

2.2 Use Directed Numbers (Limited to Integers) in Real-life Situations.

Numbers which have a direction and a size are called directed numbers. Once a direction is chosen as positive (+), the opposite direction is taken as negative (-)

Activity: Integers in real-life situations

Read the story below and answer the questions.

Once upon a time, there lived an old woman. She had hot and cold stones and a big pot of water. If she put one hot stone in the water, the temperature of the water would rise by 1 degree. If she took the hot stone out of the water again, the temperature would go down by 1 degree. i.e if the temperature of the water was 28 degrees and the old woman removes 2 hot stones, the temperature would drop to 26 degrees ,and if the temperature of the water was at 85 degrees and the old woman adds 4 hot stones, the temperature would rise to 89 degrees.

Questions:

1. If the temperature of the water is 24 degrees and the old woman adds 5 hot stones, what is the new temperature of the water?

2. Now imagine that the temperature of the water is at 29 degrees. The old woman takes a spoon and takes out 3 of the hot stones from the pot. What is the temperature of the water when the old woman removes 3 hot stones? Explain your answer.

3. The old woman also had cold stones. If she adds 1 cold stone to the water, the temperature goes down by 1 degree. The temperature of the water was 26 degrees. Then the old woman added 4 cold stones. What is the temperature of the water after the old woman added 4 cold stones

4. Give a reason for your answer.

5. Imagine that the temperature of the water was 22 degrees and the old woman removes 3 cold stones. What happens to the temperature of the water?

6. What is the new temperature of the water? Explain your answer.

2.4: Use the Hierarchy of Operations to Carry out the Four Mathematical Operations on Integers

Activity: Operations on integers.

Jimmy moved 5 steps to the right from a fixed point. Then she moved 9 steps to the left.

How far is Sarah from the fixed point?
Peter gave his answer as 4 steps to the left of the fixed point and John as -4 (negative 4). Who is correct? Give reasons for your answer.

2.4 Number line

Integers can be illustrated on a number line (number scale) as shown below