Basic operations on directed numbers

ADDITION AND SUBTRACTION OF DIRECTED NUMBER LINE (REVISION)

Addition: to add using the number line, we move to the right (forward) of the number line counting each step till the addition is complete. The number at the end is the result of the addition.

Subtraction: to subtract using the number line, we move to the left (backwards) of the number line counting each step till the subtraction is complete. The number at the end is the result of the subtraction.

Try out the exercises on this worksheet using the first representation as an example

1

2.

3

MULTIPLICATION OF DIRECTED NUMBERS

Multiplication is a short way of writing repeated additions. For example,

3 x 4     = 3 lots of 4

= 4 + 4 + 4

= 12

With directed numbers,

(+4) + (+4) + (+4) = 3 lots of (+4)

= 3 X (+4)

The multiplier is 3. It is positive. Thus,

(+3) X (+4) = (+4) + (+4) + (+4) = +12

START

The illustration above shows 1 x (+4) and (+3) x (+4) as movement on the number line. The movements are in the same direction from 0.

Similarly,

(-2)+ (-2) + (-2) + (-2) + (-2)

= 5 lots of (-2)

= 5 X (-2)

The multiplier is 5. It is positive.

Thus, (+5) x (-2)

= (-2)+ (-2) + (-2) + (-2) + (-2)

= -10

This is illustrated below:

START

In general, (+a) x (+b) = + (a x b)

(+a) x (-b) = – (a x b)

(+a) (-b) = – (a

(-a) (-b) = + (a

ADDITIVE INVERSE

Additive identity is the value obtained when a number is added to its inverse. Thus additive identity is 0.

MULTIPLICATIVE INVERSE

Multiplicative identity is 1.

CLASS ACTIVITY

1. State the additive identity of:
2. a) +14; b) -23 c) – ½
3. State the multiplicative inverse of:
4. a) +5; b) – ¼; c) + 2/7

ASSIGNMENT

1. Copy and complete the multiplication table in the figure below.

Second number