Class 07 Multiplying integers on the number line

Activity - Integers

 Objective: 

Multiplying integers on the number line.

Materials Required: 

Some sheets of paper, pen, sketch pen, pencil, etc.

Procedure:

I. To multiply two positive integers (say + 2 and + 5)

Using a sketch pen, draw a number line as shown below.

| | | | | | | | | | | | | | | |

-2  -1  0    1    2  3    4   5    6    7    8  9  10  11 12  13

2. Start from 0 and move 2 steps towards right. 

Make 5 such moves to reach at 10.

Thus, (+2) X (+ 5) = + 10 = 10

II. To multiply a positive integer and a negative integer (say – 3 and +5)

Draw a number line as shown below.

| | | | | | | | | | | | | | | | | | |

 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7    -6  -5  -4    -3  -2  -1   0    1   2

2. Start from 0 and move 3 steps towards left. Make 5 such moves to reach at-15.

Thus, (-3) x (+ 5) =-15

III. To multiply two negative integers (say -2 and-4)

Draw a number line as shown below:

| | | | | | | | | | | | | | | | | | |

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

2. Start from 0 and move 2 steps towards left. 

Make 4 such moves to reach at-8.

The above number line shows (-2) (+ 4) = -8

But, we know that a (-b) =-(ab)

So,-2 x (-4) =-(-8) = 8-(-8) = 8, 

because we know that negative of negative of a number is the number itself.

Do yourself: 

Using the number line, find the following products:

(+ 3) (+ 5) (ii) (+6) (+2) (iii) (-3) x (+4) (iv) (+2) × (-6) 

(v) (-5) x (-3) (vi) (-4) x (-4)