Use of Integers as Directed Numbers

Here we will learn the use of integers as directed numbers. We know, when numbers represent direction, the numbers are called directed numbers.

1. What do the following expressions mean?

(i) Profit of - $27.

(ii) -14 km to the East.

(iii) Ascending -30 meters.

Solution:

(i) Profit of -27 dollars = Loss of 27 dollars.

(ii) -14 km to the East = 14 km towards West.

(iii) Ascending -30 meters or -30 meters upward movement = 30 meters downward movement.

2. A boy moves 32 m due East and then 27 m due West. Find his position with respect to his starting point.

Solution:

Let 32 m due East is represented by +32, then -27 represents 27 m due West.

On adding +32 and -27, we get;

(+32) + (-27)

= +32 – 27

= +5; which is positive.

Therefore, the position of the boy with respect to his starting point is 5 m due East.

3. A person walks 37 m due South and then 45 m due North. Find his position with respect to his starting point.

Solution:

Let 37 m due South is represented by +37, then -45 represents 45 m due North.

On adding +37 and -45, we get;

(+37) + (-45)

= +37 – 45

= -8; which is negative.

Therefore, the position of the person with respect to his starting point is -8 m due South.

4. The temperature of a body first rises by 25° C and then falls by 32° C. Find the final temperature of the body, if its initial temperature is:

(i) 0° C

(ii) 18° C

(iii) -20° C

(iv) 1° C

Solution:

(i) Final temperature = 0° C + (+ 25° C) + (- 32° C)

                               = 0° C + 25° C - 32° C

                               = 25° C - 32° C

                               = -7° C

(ii) Final temperature = 18° C + (+ 25° C) + (- 32° C)

                                = 18° C + 25° C - 32° C

                                = 43° C - 32° C

                                = 11° C

(iii) Final temperature = -20° C + (+ 25° C) + (- 32° C)

                                = -20° C + 25° C - 32° C

                                = 25° C - 52° C

                                = -27° C

(iv) Final temperature = 1° C + (+ 25° C) + (- 32° C)

                                = 1° C + 25° C - 32° C

                                = 26° C - 32° C

                                = -6° C

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