Multlipication and Division of Directed Number – JSS2 Mathematics Lesson Note (First Term)

To multiply or divide directed numbers, look at the signs. If the signs are the same, the answer is positive. If the signs are different, the answer is negative. For example, (-3) × (-8) = +24 and (+80) ÷ (-10) = -8.

Behavioural objectives

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

• revise the addition and subtraction of directed numbers;
• state the sign rules for multiplying directed numbers;
• multiply two or more directed numbers;
• state the sign rules for dividing directed numbers;
• divide directed numbers correctly.

How do we add and subtract directed numbers?

When two signs appear together, replace them with one sign:

• (a) + + = + or – – = + (the same signs together are replaced by a positive sign).
• (b) + – = – or – + = – (two different signs together are replaced by a negative sign).

Example 1

Find the values of the following: (a) +7 + (+8) (b) +13 – (+6)

Solution

(a) +7 + (+8) = 7 + 8 = 15
(b) +13 – (+6) = 13 – 6 = 7

Example 2

Calculate the following: (a) 25 – (+3) (b) 12 – (-9)

Solution

(a) 25 – (+3) = 25 – 3 = 22
(b) 12 – (-9) = 12 + 9 = 21

How do we multiply directed numbers?

Rules

1. + × – = – or – × + = -. If different signs are multiplied, the answer is negative.
2. + × + = + or – × – = +. If the same signs are multiplied, the answer is positive.

Example 1

Simplify the following: (a) (+12) × (+5) (b) (-3) × (-8)

Solution

(a) 12 × 5 = 60
(b) -3 × -8 = +24

Example 2

Find the values of the following: (a) -4 × -2 × -2 × -2 × -2 (b) 7 × (-3) × (-1) × (-1) × 20

Solution

(a) Using the rules, equal signs give a positive answer and different signs give a negative answer. Multiplying step by step: -4 × -2 = 8, 8 × -2 = -16, -16 × -2 = 32, 32 × -2 = -64.
So -4 × -2 × -2 × -2 × -2 = -64.

(b) 7 × (-3) = -21
-21 × (-1) = 21
21 × (-1) = -21
-21 × 20 = -420

How do we divide directed numbers?

Rules

1. + ÷ + = + or – ÷ – = +. If the signs are the same, the answer is positive.
2. + ÷ – = – or – ÷ + = -. If the signs are different, the answer is negative.

Example

Work out the following: (a) (+80) ÷ (-10) (b) (-25) ÷ (-5)

Solution

(a) (+80) ÷ (-10) = -8 (because the signs are different)
(b) (-25) ÷ (-5) = +5 (because the signs are the same)

Evaluation

1. State the sign of the answer when two numbers with different signs are multiplied.
2. State the sign of the answer when two numbers with the same sign are divided.
3. Simplify (+12) × (+5) and (-3) × (-8).
4. Work out (+80) ÷ (-10) and (-25) ÷ (-5).
5. Find the value of 7 × (-3) × (-1) × (-1) × 20.

Assignment

Simplify the following:

1. 3 × 5 × 2 × 15 (-9)
2. -5 × 25 × 3
3. -8 × (-11) × 9 × (-5)
4. 2 × (-33) × (-3)