Page 46 - ICSE Math 6

9. Write the following integers in increasing order.
(a) 0, –9, –5, –11 (b) 121, –98, –76, –123 (c) –287, –827, –728, –278

10. Write the following integers in decreasing order.
(a) –99, –990, –777, –567 (b) +876, –706, –901, 0 (c) –167, –237, –953, 1

11. Evaluate: (a) |–13| (b) |+27| (c) |13 – 15| (d) |–11 – 7|
12. Using a number line, answer the following.
(a) Which number is 4 units to the left of 0?
(b) Which number is 7 units to the right of –11?

(c) In which direction should one move to reach –67 from –80?
(d) In which direction should one move to reach 0 from –23?
13. For the following statements, write True or False. Write the false statement correctly.

(a) –270 is greater than –170.
(b) 0 is a positive integer.
(c) On the number line, –5 is to the right of –1.

(d) All negative integers are smaller than a natural number.
(e) The absolute value of an integer is always smaller than the integer.

Operations on Integers

Addition of integers
For addition of integers, we have two cases:
(a) When the integers to be added have the same sign, i.e., either all of them are positive integers or
all of them are negative integers, then add their absolute values and assign the same sign to the
sum.

(b) When the integers to be added do not have the same sign, then add all the positive integers together
and all the negative integers together. Then find the absolute values of both the sums. Finally, find the
difference between the two absolute values and assign the sign of the greater sum to this difference.

Example 13: Add the following.
(a) +121 and +55 (b) –99 and –38 (c) (–16), (+5), (–80) and (+25)
Solution: (a) Both the integers are positive. So, add their absolute values.

Sum of absolute values = 121 + 55 = 176
\ (+121) + (+55) = +176
(b) Both the integers are negative. So, add their absolute values.
Sum of absolute values = 99 + 38 = 137

\ (–99) + (–38) = –137
(c) Two integers are positive and two are negative.
Add the positive integers together to get (+5) + (+25) = +30.
Add the negative integers together to get (–16) + (–80) = –96.
Difference of the absolute values of the sums is 96 – 30 = 66.

\ (–19) + (+5) + (–80) + (+25) = –66

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