EVALUATE THE GIVEN EXPRESSION USING NUMBER LINE

Definition of number line :

A line on which equally spaced points are marked is called a number line. 

definition-of-number-line.png

The number line allows the order and relative positions of numbers to be shown.

definition-of-number-linep1.png

The arrow head shows that the line can continue indefinitely.

We sometime use number lines to help us measuring things. For example, ruler and tape measures are number lines which start from zero.

Draw a number line and show the following operations. Give a final answer.

Problem 1 :

9 + 8 - 6

Solution :

number-line-s1

Each arrow represents 1. From 0, we should move forward 9 units.

From 9 again, we have to move forward 8 units.

(9 + 8) = 17

From 17, we have to perform -6.

We have to move backward 6 units.

(17 - 6) = 11

Problem 2 :

2 + 4 + 8 - 2

Solution :

number-line-s2

Each arrow represents 1. From 0, we should move forward 2 units. From 2, we have to move forward 4 units.

Now we are in 4, from 4, we have to move forward 8 units.

(2 + 4 + 8) = 14

From 14, we have to perform -2.

We have to move backward -2 units.

(14 - 2) = 12

Problem 3 :

40 + 70 + 90 - 50

Solution :

number-line-s3

Each arrow represents 10. From 0, we should move forward 4 units. Now we are in 40,  we have to move forward 7 units.

From 70, we have to move forward 9 units.

(40 + 70 + 90) = 200

From 200, since we have to perform -50.

We have to move backward -50 units.

(200 - 50) = 150

Problem 4 :

55 + 60 + 75 - 40

Solution :

number-line-s4

Each arrow represents 10. From 0, we should move forward 5.5 units. Now we are is 55. 

(55 + 60 + 75) = 190

From 190, we have to perform -40.

We have to move backward -40 units.

190 - 40 = 150

Problem 5 :

3 × 9 - 8

Solution :

number-line-s5

From 0, we should move forward 9 units. From 9 again, we have to move forward 9 units.

(3 × 9) = 27

From 27 since we have to perform -8.

We have to move backward -8 units.

27 - 8 = 19

Problem 6 :

4 × 6 ÷ 5

Solution :

number-line-s6

From 0, we should move forward 4 equal jumps. So, we will be at 24.

From 24, we have to move back 5 equal jumps. The 5 th jump is not sufficient, because we have 24. So, the remainder is 4.

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