Integers — Exercise 1(D)

The sum of two integers is -15. If one of them is 9, find the other.

Answer

Let the other integer be x.

9 + x = -15

x = -15 - 9

x = -24

∴ The other integer is -24.

The difference between integers x and -6 is -5. Find the values of x.

x - (-6) = -5 or -6 - x = -5

Answer

The difference between x and -6 is -5.

x - (-6) = -5 or -6 - x = -5

x + 6 = -5 or -x = -5 + 6

x = -5 - 6 or -x = 1

x = -11 or x = -1

∴ x = -11 or -1

The sum of two integers is 28. If one integer is -45, find the other.

Answer

Let the other integer be x.

(-45) + x = 28

x = 28 - (-45)

x = 28 + 45

x = 73

∴ The other integer is 73.

The sum of two integers is -56. If one integer is -42, find the other.

Answer

Let the other integer be x.

(-42) + x = -56

x = -56 - (-42)

x = -56 + 42

x = -14

∴ The other integer is -14.

The difference between an integer x and (-9) is 6. Find all possible values of x.

Answer

The difference between x and -9 is 6.

x - (-9) = 6 or -9 - x = 6

x + 9 = 6 or -x = 6 + 9

x = 6 - 9 or -x = 15

x = -3 or x = -15

∴ x = -3 or -15

Write all the integers between -15 and 15, which are divisible by 2 and 3.

Answer

An integer divisible by both 2 and 3 is divisible by 6.

The multiples of 6 lying between -15 and 15 are :

-12, -6, 0, 6, 12

Write all the integers between -5 and 5, which are divisible by 2 or 3.

Answer

The integers between -5 and 5 are -4, -3, -2, -1, 0, 1, 2, 3, 4.

Integers divisible by 2 : -4, -2, 0, 2, 4

Integers divisible by 3 : -3, 0, 3

Combining (taking each integer once), the integers divisible by 2 or 3 are :

-4, -3, -2, 0, 2, 3, 4

Find the result of subtracting the sum of all integers between 20 and 30 from the sum of all integers from 20 to 30.

Answer

Sum of all integers from 20 to 30 (both included) :

= 20 + 21 + 22 + ... + 30

= 275

Sum of all integers between 20 and 30 (both excluded) :

= 21 + 22 + ... + 29

= 225

Required result = 275 - 225 = 50

Hence, the required result is 50.

Add the product of (-13) and (-17) to the quotient of (-187) and 11.

Answer

Product of (-13) and (-17) = (-13) × (-17) = 221

Quotient of (-187) and 11 = $(-187) \div 11 = \dfrac{-187}{11} = \dfrac{-17 \times 11}{11} = -17$

Required sum = 221 + (-17) = 221 - 17 = 204

Hence, the required result is 204.

The product of two integers is -180. If one of them is 12, find the other.

Answer

Let the other integer be x.

12 × x = -180

x = $\dfrac{-180}{12}$

x = $\dfrac{-15 \times 12}{12}$

x = -15

∴ The other integer is -15.

(i) A number changes from -20 to 30. What is the increase or decrease in the number ?

(ii) A number changes from 40 to -30. What is the increase or decrease in the number ?

Answer

(i) Change = 30 - (-20)

= 30 + 20

= 50

Since the change is positive,

∴ There is an increase of 50.

(ii) Change = -30 - 40

= -70

Since the change is negative,

∴ There is a decrease of 70.