Addition & Subtraction of Directed Numbers – JSS1 Mathematics Lesson Note (Second Term)

Directed numbers are numbers with a positive or negative sign. To add or subtract them, you can count along a horizontal number line, where numbers to the right of zero are positive and those to the left are negative. You can also use sign rules to work out the answer without drawing the number line.

Behavioural objectives

By the end of the lesson, students should be able to:

• use a horizontal number line to add and subtract directed numbers;
• state the rules for signs that appear together;
• use the rules to add and subtract directed numbers without a number line.

How do you add and subtract directed numbers on a number line?

On a horizontal number line, numbers to the right of zero are positive and those to the left are negative.

1. When adding, start with the first number and count to the right along the number line.
2. When subtracting, start from the first number and count to the left along the number line.

Example

Use a number line to find the value of (a) 3 + 5, (b) -4 – 6, (c) -9 + 12.

Solution

(a)

-2   -1   0   1   2   3   4   5   6   7   8   9   10   11   12

3 + 5 = 8

(b)

-11   -10   -9   -8   -7   -6   -5   -4   -3   -2   -1   0   1   2   3

-4 – 6 = -10

(c)

-10   -9   -8   -7   -6   -5   -4   -3   -2   -1   0   1   2   3

-9 + 12 = 3

What are the rules for adding and subtracting directed numbers?

Using the rules below, you can do addition and subtraction without drawing the number line.

Rule (a): same signs

Replace the same signs that appear together with a positive sign: + + = + and – – = +.

Examples:

• +7 + (+5) = 7 + 5 = 12 (same sign gives +)
• +6 – (-8) = 6 + 8 = 14 (same sign gives +)

Rule (b): different signs

Replace different signs that appear together with a negative sign: + – = – and – + = -.

Examples:

• +8 + (-5) = 8 – 5 = 3 (different signs give negative)
• +9 – (+4) = 9 – 4 = 5 (different signs give negative)

Note: To add two numbers with different signs, subtract the smaller number from the larger number and then place the sign of the larger number in front of your answer.

Example

Find the value of the following:

1. (+6) + (+9)
2. (+21) – (+9)
3. (+12) + (-5)
4. (+29) + (+13)

Solution

Note: You need to follow the rules.

1. (+6) + (+9) = 6 + 9 = 15 (same sign gives +)
2. (+21) – (+9) = 21 – 9 = 12 (different signs give negative)
3. (+12) + (-5) = 12 – 5 = 7 (different signs give negative)
4. (+29) + (+13) = 29 + 13 = 42 (same sign gives +)

Evaluation

Draw a suitable horizontal number line to answer the following:

1. 5 – 8
2. 6 – 2
3. (-5) – (-8)
4. 7 + 2
5. 5 + 8

Assignment

Use the rules to answer the following:

1. +5 – (+6)
2. 25 + (-55)
3. +24 + (+28)
4. 18 – 68
5. -7 + 5 – 2 + 7 – 10 – 3