Addition & Subtraction of Directed Numbers JSS1 Mathematics Lesson Note

Addition & Subtraction of Directed Numbers

In a horizontal number line:

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

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

Example: Use a number line to find the value of the (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

EXERCISE:

1. Draw a suitable horizontal number line to answer the following
2. 5–8
3. 6 – 2
4. (-5) – (-8)
5. 7 + 2
6. 5 + 8

2. Use the rules to answer the following
3. +5 – (+6)
4. 25 + (-55)
5. +24 + (+28)
6. 18–68
7. -7 + 5 – 2 + 7 – 10 – 3 

RULES FOR ADDITION AND SUBTRACTION

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

(a) Replace the same signs that appear together with a positive sign. [+ +  = +],[ – – = -].

Examples: +7 + (+5) = 7+5 = 12 (same sign gives +)

+6 – (-8) = 6 + 8 = 14 (same sign gives +)

(b) Replace two signs that appear together with a negative sign. [+ – = -],[- + = -].

Examples +8 + (-5) = 8 – 5 = 3 [Different signs give negative.]

+9 – (+4) = 9 – 4 = 5 [different sign gives negative sign].

Note: To subtract two numbers with different signs, subtract the smaller number from the larger number and then place the sign before 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 sign gives negative sign]
3. (+12) + (-5) = 12 – 5 = 7 [different sign gives negative sign]
4. (+29) + (+13) = 29 + 13 = 42 (same sign gives +)