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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