Write the opposite of each of the following statements :
(i) Gain of ₹ 90
(ii) 70 m above sea-level
(iii) 200 m due west
(iv) 25% increase
(v) 10°C below freezing point
(vi) 30 m to the left
(vii) Below average
(viii) Gaining a weight of 1 kg
(ix) Depositing ₹ 500 in a bank
(x) +45
(xi) -50
Answer
(i) Gain of ₹ 90
The opposite of "gaining" something (an increase) is "losing" it (a decrease).
Hence, opposite of "gain of ₹ 90" is "loss of ₹ 90".
(ii) 70 m above sea-level
"Above" and "below" are opposite directions on a vertical axis.
Hence, opposite of "70 m above sea-level" is "70 m below sea-level".
(iii) 200 m due west
"West" and "east" are opposite directions on a horizontal axis.
Hence, opposite of "200 m due west" is "200 m due east".
(iv) 25% increase
"Increase" means to get larger, while "decrease" means to get smaller.
Hence, opposite of "25% increase" is "25% decrease".
(v) 10°C below freezing point
"Below" and "above" are opposite directions on a temperature scale.
Hence, opposite of “10°C below the freezing point” is “10°C above the freezing point”.
(vi) 30 m to the left
"Left" and "right" are opposite directions.
Hence, opposite of 30 m to the left is 30 m to the right.
(vii) Below average
"Below" and "above" are used to describe values relative to a reference point (the average).
Hence, opposite of below average is above average.
(viii) Gaining 1 kg of weight
"Gaining" weight is the opposite of "losing" weight.
Hence, opposite of gaining 1 kg of weight is losing 1 kg of weight.
(ix) Depositing ₹ 500 in a bank
"Depositing" money increases a bank balance, while "withdrawing" decreases it.
Hence, opposite of depositing ₹ 500 in a bank is withdrawing ₹ 500 from a bank.
(x) +45
The opposite of a positive number is its negative counterpart.
Hence, opposite of +45 is -45.
(xi) -50
The opposite of a negative number is its positive counterpart.
Hence, opposite of -50 is +50.
Indicate the following using negative sign :
(i) An increase of 8
(ii) Loss of ₹ 300
(iii) Spending ₹ 725
(iv) 53 m below sea-level
(v) 20°C below freezing point
(vi) 4 above average
Answer
(i) An increase of 8
"Increase" means to get larger, while "decrease" means to get smaller.
Hence, an increase of 8 can be indicated using a negative sign as a decrease of -8.
(ii) Loss of ₹ 300
A loss is a negative change. This is represented by -₹ 300.
Hence, loss of ₹ 300 is -₹ 300.
(iii) Spending ₹ 725
Spending money decreases a total amount, so it is a negative change. This is represented by -₹ 725.
Hence, spending ₹ 725 is -₹ 725.
(iv) 53 m below sea-level
"Below" is a negative direction. This is represented by -53 m.
Hence, 53 m below sea-level is -53 m.
(v) 20°C below freezing point
"Below" is a negative value on a temperature scale. This is represented by -20°C.
Hence, 20°C below freezing point is -20°C.
(vi) 4 above average
4 above average is a positive change. Its opposite, 4 below average, is represented by -4.
Hence, negative sign of 4 above average is -4.
Write all integers between :
(i) 3 and 10
(ii) -3 and 6
(iii) -7 and 0
(iv) -12 and -8
(v) -20 and -14
(vi) -8 and 4
Answer
(i) Integers between 3 and 10
4, 5, 6, 7, 8, 9.
(ii) Integers between -3 and 6
-2, -1, 0, 1, 2, 3, 4, 5.
(iii) Integers between -7 and 0
-6, -5, -4, -3, -2, -1.
(iv) Integers between -12 and -8
-11, -10, -9.
(v) Integers between -20 and -14
-19, -18, -17, -16, -15.
(vi) Integers between -8 and 4
-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3.
Write seven integers, each greater than -6.
Answer
Seven integers, each greater than -6 are -5, -4, -3, -2, -1, 0, 1.
Fill in the blanks by using > or < or = in each of the following :
(i) -5 ............... 3
(ii) 0 ............... -4
(iii) -8 ............... -14
(iv) -23 ............... -16
(v) 15 ............... -15
(vi) -1 ............... -12
(vii) 9 ............... (-1)
(viii) (-9) ............... 1
(ix) (-9) ............... (-1)
Answer
(i) -5 ............... 3
A negative number is always less than a positive number.
-5 < 3
(ii) 0 ............... -4
0 is to the right of -4 on the number line.
0 > -4
(iii) -8 ............... -14
On a number line, -8 is to the right of -14, making it the greater number.
-8 > -14
(iv) -23 ............... -16
-16 is closer to zero than -23, so -16 is greater.
-23 < -16
(v) 15 ............... -15
A negative number is always less than a positive number.
15 > -15
(vi) -1 ............... -12
-1 is closer to zero than -12, so -1 is greater.
-1 > -12
(vii) 9 ............... -1
A negative number is always less than a positive number.
9 > -1
(viii) -9 ............... 1
A negative number is always less than a positive number.
(-9) < 1
(ix) -9 ............... -1
-1 is closer to zero than -9, so -1 is greater.
(-9) < (-1)
Evaluate each of the following :
(i) |-17| - |8|
(ii) |-14| + |5|
(iii) |-9| + |-6|
(iv) |-23| - |-12|
(v) |-8| + |-6| - |-10|
(vi) |-6| + |-1| - |-5|
Answer
(i) |-17| - |8|
= 17 - 8
= 9
Hence, |-17| - |8| = 9.
(ii) |-14| + |5|
= 14 + 5
= 19
Hence, |-14| + |5| = 19.
(iii) |-9| + |-6|
= 9 + 6
= 15
Hence, |-9| + |-6| = 15.
(iv) |-23| - |-12|
= 23 - 12
= 11
Hence, |-23| - |-12| = 11.
(v) |-8| + |-6| - |-10|
= 8 + 6 - 10
= 14 - 10
= 4
Hence, |-8| + |-6| - |-10| = 4.
(vi) |-6| + |-1| - |-5|
= 6 + 1 - 5
= 7 - 5
= 2
Hence, |-6| + |-1| - |-5| = 2.
Write the following integers in ascending order :
(i) 14, -7, -13, 0, 6, -2, 30
(ii) -18, 14, -25, 32, -5, 2
(iii) -9, -24, 26, -2, -11, 18, 9
(iv) 37, -28, -15, 7, 23, -19, -6
Answer
(i) 14, -7, -13, 0, 6, -2, 30
Ascending order: -13 < -7 < -2 < 0 < 6 < 14 < 30.
(ii) -18, 14, -25, 32, -5, 2
Ascending order: -25 < -18 < -5 < 2 < 14 < 32.
(iii) -9, -24, 26, -2, -11, 18, 9
Ascending order: -24 < -11 < -9 < -2 < 9 < 18 < 26.
(iv) 37, -28, -15, 7, 23, -19, -6
Ascending order: -28 < -19 < -15 < -6 < 7 < 23 < 37.
Write the following integers in descending order :
(i) -16, -21, 8, 0, -7, 14
(ii) -4, 31, -41, -23, 6, 0, -11
(iii) -60, -9, -36, -8, 5, 15, 0
(iv) -10, -43, -2, 1, -14, 6, 22
(v) -8, -53, 53, -100, 62, 16, -82
Answer
(i) -16, -21, 8, 0, -7, 14
Descending order: 14 > 8 > 0 > -7 > -16 > -21.
(ii) -4, 31, -41, -23, 6, 0, -11
Descending order: 31 > 6 > 0 > -4 > -11 > -23 > -41.
(iii) -60, -9, -36, -8, 5, 15, 0
Descending order: 15 > 5 > 0 > -8 > -9 > -36 > -60.
(iv) -10, -43, -2, 1, -14, 6, 22
Descending order: 22 > 6 > 1 > -2 > -10 > -14 > -43.
(v) -8, -53, 53, -100, 62, 16, -82
Descending order: 62 > 53 > 16 > -8 > -53 > -82 > -100.
Represent each of the following on the number line :
(i) All integers from -5 to 3.
(ii) All negative integers greater than -6.
(iii) All non-negative integers less than 6.
(iv) All even positive integers less than 12.
(v) All odd negative integers greater than -8.
Answer
(i) All integers from -5 to 3.
(ii) All negative integers greater than -6.
(iii) All non-negative integers less than 6.
(iv) All even positive integers less than 12.
(v) All odd negative integers greater than -8.
