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### Transcript of Directed Number

DIRECTED NUMBERS

Subtopic 1 Perform computations involving multiplication and division of integers to solve problems. At the end of this subtopic, you will be able to:I ) multiply integers II ) solve problems involving multiplication of integers III) divide integers IV) solve problems involving division of integers

Do you still remember ???

+How many items are there ?

= ?

14 + 12 = 26

Smart TIP+ + X X X X

+ + -

= = = =

+ +

HORIZONTAL NUMBER LINE

NEGATIVE INTEGERS

POSITIVE INTEGERS

-5 -4 -3 -2 -1 0 1 2 3 4 5NEGATIVE DIRECTION DIRECTION POSITIVE

VERTICAL NUMBER LINEP O S I T I V E I N T E G E R S P O S I T I V E D I R E C T I O N

N E G A T I V E

I N T E G E R S

N E G A T I V E

D I R E C T I O N

To multiply integers: 1. face the number to be multiplied 2. move forward if the sign of the other number is +. 3. move backward if the sign of the other number is . -2 X 4 sign Other number Number to be multiplied

Solve the following:-2 X 4 = (-2) + (-2) + (-2) + (-2) = -8Face negative direction and move 2 steps backward 4 times

-8

-7

-6

-5

-4

-3

-2

-1

0

Solve the following: 4X2 = (2) + (2) + (2) + (2) = Face positive direction and move 2 steps forward 4 times 8

0 1

2

3

4

5

6

7

8

Solve the following: (a) 6 X (-5) = - 30 ((b) -4 X (-9) = 36 ((c) -4 X (-2) X (-3) = -24 (((d) -7 X 6 X (-2) = 84 (-

HOT TIPS +X+ =+ -X+ =+X-=-X-= +

Smart TIP + + -

+=+ -=+=-=+

If there are like signs, the answer is positive. If there are unlike signs, the answer is negative.

To divide integers EXAMPLE: + + + + + + -division is the process of equal 12 sharing or equal + + + grouping + + ++ + + + + + + + + + + +

3= 4

-12 3 = -4Example:-

-

-

-

-

-

-

Division is the inverse of multiplication 12 3 = 4 , then, 3 X 4 = 12 -12 3 = - 4, then, 3 X ( -4) = -12 Since 3 X 4 = - 12, then, - 12 ( - 3 ) = 4. Since - 3 X ( - 4 ) = 12, then, 12 ( - 3 ) = - 4

EXERCISE 1. 8 (-2 ) 2. -63 ( -7) 3. -40 4 5 4. 48 ( - 8) (-2)

Subtopic 2 Perform computation involving combined operation of addition, subtraction, multiplication and division of integers to solve problems At the end of this subtopic, you will be able to:I ) perform computations involving combined operations of addition, subtraction, multiplication and division of integers II ) solve problems involving combined operations of addition, subtraction, multiplication and division of integers including the use of brackets

Combined Operations on IntegersTo perform addition , subtraction, multiplication and division on integers Examples:

Evaluate : a) -2 + 5 7 =37 = -4 Do the operations from left to right

b) 6 X (- 4) ( - 3 ) = 24 ( - 3 ) = -8

EXERCISE

Calculate: a) 7 + 3 15 b) -2 11 + 3 c) -3 ( -2 ) 8 d) - 8 13 (- 6) e) - 9 + ( - 6) 12 f) - 15 + (-7) (-12)

EXERCISEa) 4 X (- 3) 2 b) - 5 X ( - 8) 10 c) - 12 X (- 2) (-8) d) - 40 8 X (- 11) e) - 128 4 X ( - 3 ) f) - 9 X (- 8) (- 12)

Subtopic 3 Extend the concept of integers to fractions to solve problems At the end of this subtopic, you will be able to:I ) compare and order fractions II ) perform addition, subtraction, multiplication or division on fractions

How much is left, in fraction ?

+

?

Positive and Negative Fractions*A positive fraction has a + sign before it or has no sign. Example: + 1 , 3 4 7 A negative fraction has a sign before it. Example: - 1 , - 5 4 9

Complete the fractional number linedivide the number line to equal parts according to the LCM of the denominators

-1

-5 6

-4 -2 6 3

-3 -1 6 2

-2 -1 6 3

-1 6

0

1 6

1 2 3 6

3 1 6 2

2 4 6 3

5 6

1

7 6

8 11 1 1 3 6 2

Arrange the following fractions in ascending order.

4 , 5

5 7 and,

7 10

v 7 v 10 v 7 v 10

5 v 5 v 10 7 v 5 v 10

7v 5v 7 10 v 5 v 7

280 350

250 350

245 350

7 10