DIRECTED NUMBERS

Directed numbers

  • Directed numbers are numbers that have a sign (positive or negative) associated with them. 
  • They help us represent quantities that can have opposing directions or values.
  •  Positive-directed numbers indicate a gain or movement in the positive direction, while negative-directed numbers represent a loss or movement in the negative direction.

Directed numbers can be positive or negative numbers. These numbers are characterized by size (2 and 4.8) and direction (– or +).

Positive numbers: +3, +1.5, +0.2, +2, …

Negative numbers: – 3, – 1.5, -0.2, -21, …

Remember:

+3 is read as “positive three.”

+1.5 is read as “positive one point five.”

-3 is read as “negative three.”

-0.2 is read as “negative zero point two.”

Operations Involving Directed Numbers

The following are the rules for dealing with addition, subtraction, multiplication, and division of directed numbers.

Addition

There are two rules:

1. SAK (Same sign – Add – Keep the sign)

Examples:

(-2) + (-3) = -5                  

(-3) + (-4) + (-1) = -8     

2. DSB (Different sign – Subtract – copy the sign of the bigger number)

Examples: 

(-4) + (7) = 3

    (2) + (-8) = -6

Subtraction

Change the sign of the subtrahend to its opposite, then change the operation to addition. 

Examples: 

(-3) – (5) = (-3) + (-5) = -8

Notice that the subtrahend, 5, was changed into -5, and then the operation was changed to addition.

Multiplication and Division 

To multiply or divide integers, perform the operation as in whole numbers and then follow the rule for signs. 

Same Signs: the answer is positive.

Different Signs: the answer is negative. 

Examples:

       (-2) (-3) = 6                          (24) ÷ (-3) = – 8

      (8) (-2) = -16                       (-54) ÷ (-9) = 6

Examples with Solutions

Example 1

Use the number line to solve -2+6.

Solution

Example 2

Find the sum of -7 and 5.

Solution

Since the numbers have different signs, we find the difference between their magnitudes: 7 – 5 = 2. The result will have the sign of the number with the larger magnitude, which is -7. So, the sum is -2.

Example 3

Subtract -4 from 3.

Subtracting -4 is the same as adding its opposite. The opposite of -4 is 4. So, we need to find the sum of 3 and 4, which is 7.

Example 4

Find the absolute value of -9.

Solution

The absolute value of -9 is the distance from -9 to 0 on the number line, which is 9.

Example 5

Add -3 and -6.

Solution

We add their magnitudes: 3 + 6= 9 since both numbers have the same sign

. The sum will have the same sign as the original numbers, which is negative. So, the sum is -9.

Example 6

Perform the indicated operations: (2 + -3) x (-8).

Solution

Let us simplify the parentheses first, then multiply.

(2 + -3) x (-8) =                                

(2 + -3) = -1

(-1) x (-8) = 8

%%%%%%%%ALL THE BEST%%%%%%%%


Comments

  1. Pauldasantus20 August 2024 at 23:38

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    ReplyDelete
  2. Ndinnah21 August 2024 at 00:14

    Who ever missed this lesson in class can come here for further explanation,this is incredible work

    ReplyDelete

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