Page 275 - Ganit Kaushal

Ex. Try evaluating the following expressions by similarly drawing or imagining a suitable lift: (NCERT)
(a) –125 + (–30) (b) +105 – (–55)
Sol. (a) This is the addition of two negative integers. Here, the starting floor is −125 and the movement is
–30.
\ The lift will go down by 30 floors, so we will reach the −155th floor.
\ –125 + (– 30) = −155
(b) This is the subtraction of two integers. Here, the starting floor is –55 and the target floor is +105.
\ We need to go up by (105 + 55) = 160 floors. So, the movement needed is +160. (+ve sign shows
upward movement)
Hence, we have +105 – (– 55) = +160.

Absolute Value of an Integer

The absolute value of an integer is its numerical value irrespective of its sign being negative or positive. The
absolute value of an integer is the distance of a number from zero on the number line. The notation for absolute

value involves placing the number between vertical lines. The symbol is ‘| |’.
For example: |5| = 5, |–5| = 5, |8| = 8, |–8| = 8

Exercise 10.1

1. Evaluate these expressions (you may think of them as Starting Floor + Movement by referring to the
Building of Fun).
(a) (–1) + (+1) = __________ (b) 0 + (+2) = __________
(c) 0 + (–2) = __________ (d) (−2) + (+4) = __________
2. Write the additive inverse of the following integers.
(a) 17 (b) –13 (c) –11 (d) 25
3. Complete these expressions. You may think of them as finding the movement needed to reach the
Target Floor from the Starting Floor. (NCERT)
(a) (+1) – (+4) = __________ (b) (0) – (+2) = __________
(c) (+4) – (+1) = __________ (d) (0) – (–2) = __________
(e) (+4) – (–2) = __________ (f) (−1) – (−2) = __________
(g) (–1) – (+2) = __________ (h) (–2) – (–2) = __________
(i) (–1) – (+1) = __________ (j) (+3) – (–2) = __________
4. Assuming that the Building of Fun has more floors, compare the following numbers and fill in the
boxes with < or >:
(a) 0 –20 (b) +9 –9 (c) –25 –7 (d) +15 –17
5. Find the value of the following.
(a) | –17 | (b) –| –13 | (c) –| 11 | (d) | 25 |
6. Evaluate the following expressions by imagining a suitable lift:
(a) +105 + (+55) (b) +80 – (–150) (c) +80 + (+150) (d) –99 – (–200)
(e) –99 + (+200) ( f ) +1500 – (–1500)
7. Evaluate the following, assuming that the Building of Fun has many more floors.
(a) −2 + | –2 | (b) 6 – | –2 | (c) 10 – | 3 | (d) 0 + [– | 5 |]
(e) | 6 | − (−2) (f) | −2 | − (–2)

The Other Side of Zero 273