Directed Number
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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
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