Illustration

Selected solved question of integers

question 1. Find value of ‘m’ in the equation 6m – 14 = 4

Solution: 6m – 14 = 4

6m = 18

m= 3.

question 2. Write down the integral solution of the equation 2x – 31 = 1.

Solution: 2x – 31 = 1

2x = 32

x= 16.

question 3. The sum of three times a number & 11 is 32. Find the number?

Solution: Let the number is x.

Three times the number is 3x.

3x + 11 = 32

3x = 32 – 11

3x = 21

x = ²¹/₃ = 7

question 4.The sum of the ages of three persons is 30 years. What will be the sum their

Ages after 5 years?

Solution: Let sum of ages is 30.

After 5 years .Each will increases by 5.

Total age will increases by 3× 5 = 15.

Total age will be 30 + 15 = 45.

question 5.One – fifth of a number minus 2 gives 6. Find which of the following is the number?

Solution: Let the number is n.

Thus one fifth of the number is ⁿ/₅

And the number is ( ⁿ/₅ -2 )

n = 40.

question 6.Shaurya and Akhil each have marbles. Shaurya has five more than twice the number that Akhil has. If Akhil has 8 marbles, how many does Shaurya have?

Solution: This question is looking for the total number of marbles Shaurya has. The number that Akhil has is given in the problem.

Start with the fact that Akhil has 8 marbles and use key words and basic operations to solve. Calculate what number is equal to five more than twice eight marbles.

Five more than twice eight marbles is equal to 8 times 2, plus 5.

X = 8 × 2 + 5 = 16 + 5 = 21

question 7.Harshit scores 27 points in a basketball game. If he made one 3-point basket and every other basket he made scored 2 points, what is the total number of baskets he made?

Solution: Harshit scores 27 points

One basket is of 3 points.

Total number of 2 pointers are 27- 3 =24

Total number of two pointers are ²⁴/₂ = 12

Total number of baskets are 12+1 = 13

question 8.Mrs. Lalkamal has a bank balance of -12 dollars at the start of the month. After she deposits 10 dollars, what is the new balance?

Solution: The starting balance is -12.

Depositing money means adding money to the account.

Total balance is

-12 + 10 = – 2.

question 9.A hike starts at an elevation 1000 meters below sea level and ends at a point 8500 meters higher than the starting point. How high would you be at the end of the hike?

Solution: The starting point is 1000 meters below sea level, or -1000. The ending point is 8500 meters higher than the starting point. ‘Higher’ implies addition.

Equation: – 1000 + 8500 = 7500

question 10.At sunrise, the outside temperature was 1° below zero. By lunch time, the temperature rose by 17° and then fell by 4° by night. What was the temperature at the end of the day?

Solution: The starting temperature is 1° below zero, or -1°.

Later, the temperature rose, or went up, by 17°.

Then, the temperature fell, or went down, by 4°.

Temperature -1° + 17° – 4° = 12⁰

question 11.A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 meters, what is its new position?

Solution:The starting elevation is 240 meters below sea level, or -240.

Descending, or going down, by 160 meters means -160.

Ascending, or going up, by 390 meters means 390.

Equation: – 240 + (- 160) + 390 = -10 metres.

question  12.The sum of two consecutive integers is 15. Find the numbers.

Solution: I know that I am adding two numbers, and their sum is fifteen and I know that the numbers are integer.

Represent the first number by “n“.

Then the second number has to be “n + 1″.

Their sum is then:

n + (n + 1) = 15

2n + 1 = 15

2n = 14

n = 7

The exercise did not ask me for the value of the variable n; it asked for the identity of two numbers. So my answer is not “n = 7″; the actual answer is:

“The numbers are 7 and 8.”

question 13.The sum of two consecutive even integers is 26. Find the numbers.

Solution: Let the first number be “2n” and the second number be “2n + 2″

I have: (2n)+(2n + 2) = 26

4n+2 = 26

4n = 24

n = 6

The number is 6 .

question 14.Find Factor of 4 into prime numbers.

Solution: We know that

4 = 2 . 2 = 2²

thus two factors are 2,2.

question 15.Divide Factor 20 into prime numbers.

Solution:We know that

20 = 2 .10

20 = 2 .2 . 5

thus

20 = 2 .2 . 5 = 2² . 5

question 16.Show that the sum of two even numbers is even.

Solution: Let 2n and 2k be the two even numbers. The sum of the two numbers is written in factored form as follows

2n + 2k = 2(n + k)

Let N = n + k and write the sum as2n + 2k = 2N

The sum is an even number.

question 17.Show that the sum of an even number and an odd number is an odd number.

Solution: Let 2n be the even number and 2k + 1 be the odd number. The sum of the two numbers is given by: (2n) + (2k + 1) = 2n + 2k + 1 = 2(n + k) + 1

Let N = n + k and write the sum as (2n) + (2k + 1) = 2N + 1

The sum is an odd number.

question 18.Show that the sum of two odd numbers is an even number.

Solution: Let 2n + 1 and 2k + 1 be the odd numbers to add. The sum of the two numbers is given by

(2n + 1) + (2k + 1) = 2n + 2k + 2 = 2(n + k + 1)

Let N = n + k + 1 and write the sum as (2n + 1) + (2k + 1) = 2N

The sum is an even number.

question 19.Show that the square of an odd number is an odd number.

Solution: Let 2n + 1 be the odd number to square and expand the square.

(2n + 1)² = 4n² + 4n + 1 = 2 (2n² + 2n) + 1

Let N = 2n² + 2n and write the square of the odd number as(2n + 1)² = 2 N + 1

The square of an odd number is an odd number.

question 20.Show that the product of an odd number and an even number is an even number.

Solution: Let 2 m + 1 be the odd number and 2n be the even number. The product is given by

(2 m + 1)(2 n) = 4mn + 2n = 2(2m n + n)

Let N = 2m n + n and write the product as (2 m + 1)(2 n) = 2 N

The product of an odd number and an even number is an even number.

question 21. 2 In addition and subtraction of two integers, sign of the answer depends upon

(a)Smaller number (b) Their difference (c) Their sum (d) Greater numerical value

Solution: Suppose that we can subtract +4 – 5 \= -1

So, from this is clear that addition and subtraction of two integers, sign of the answer depends upon the greater numerical value.

question 22.Sum of two negative numbers is always

Positive (b) Negative (c) 0 (d) 1

Solution: Negative

question 23.Sum of two Positive numbers is always

Negative (b) Positive (c) 1 (d) 0

Solution: Positive

question 24.Sum of – 36 and 29 is

65 (b) 65 (c) – 7 (d) 7

Solution: – 36 + 29 = – 7

question 25.Sum of – 19 and – 21 is

– 40 (b) 40 (c) 2 (d) – 2

Solution: – 19 + – 21 = – 40

question 26.The pair of integers whose sum is – 5

1, – 4 (b) -1 , 6 (c) -3 ,- 2 (d) 5, 0

Solution:-3 + -2 = -5

question 27.What integers or number should be added to – 5 to get 4

1 (b) – 1 (c) – 9 (d) 9

Solution: 9 integer should be added to -5 to get 4

9 + -5 = 4

question 28.What will be the additive inverse of – 5

– 6 (b) – 4 (c) 3 (d) 5

Solution: 5

question 29.Predecessor of – 7 is

– 8 (b) 8 (c) – 6 (d) 6

Solution: Predecessor of – 7 is -8

question 30.Successor of 1 is

– 2 (b) 0 (c) 1 (d) 2

Solution:Successor of 1 is 2

question 31.The value of 6 – ( – 3 ) is

3 (b) – 9 (c) – 3 (d) 9

Solution:6 – (-3) = 6 + 3 = 9

question 32.The value of 26 – 30 is equal to

(a) 4 (b) – 4 (c) – 56 (d) 56

Solution: 26 – 30 = -4

question 33.Multiplication of 3 and – 4

(a) 7 (b) – 12 (c) 12 (d) 7

Solution: 3 × (-4) = -12

question 34.Multiplication of -2,-7 and -10 gives

(a) – 34 (b) 19 (c) -140 (d) 90

Solution: -2 × -7 × (-10) = -14 × -10 = -140

question 35.Multiplication of 2, – 5 and 0 gives

(a) 10 (b) 0 (c) -10 (d) 7

Solution: 2 × (-5) × 0 = 0

We know that if the any number is multiplied by zero. So, its result will also be zero.

question 36.Identify the property used in the following: 2 13 + 8 13 = ( 2+8 ) 13

(a) Commutative (b) Closure (c) Associative (d) Distributive

Solution: a × b + c × b = (a + c) × b

It is a distributive property

question 37.Which number is multiplicative identity for the whole numbers?

(a) 0 (b) 1 ( c) 2 (d) 3

Solution: 1 is multiplicative identity for the whole numbers.

question 38.Which property is reflected in the following: 7 ×5 = 5 ×7

(a) Closure (b) Commutative (c) Associative (d) Distributive

Solution: a × b = b × a

It is Commutative property

question 39.– 18 ÷2 gives

(a) 36 (b) 9 (c) – 9 (d) – 16

Solution: – 18 ÷ 2 = -9

question 40.15 divided by – 3 is equal to

(a) 12 (b) – 12 (c) – 5 (d) 5

Solution: 15 ÷ -3 = -5

question 41.Which of the following is not true

0 ÷ 2 = 0 (b) – 25 ÷ 5 = – 5 (c) 12 ÷ 0 = 12 (d) 4 ÷ 1 = 4

Solution: 12 ÷ 0 = 12 is not true because any number is divided by 0. So, its result is not defined.

question 42 . Which of the following does not represent pair of integer (a, b) such that a ÷ b = 2

(a) ( – 6 , – 3 ) (b) ( – 2 , 1) (c) ( – 10 ,- 5 ) (d) (8 , 4 )

Solution: ( – 2 , 1) does not represent pair of integer (a, b) such that a ÷ b = 2 because -2 ÷ 1 = -2

question 43.On dividing a negative integers by other negative integer the quotient will be

(a) Always negative (b) Always positive (c) Either positive or negative (d) 1

Solution: On dividing a negative integers by other negative integer the quotient will be always positive.

question 44.Which of the following statement is true

(a) 7 ÷ 0 = 7 (b) 7 ÷ 0 = 0 (c) 7 ÷ 0 = 0 ÷ 7 (d) 0 ÷ 7 = 0

Solution: 0 ÷ 7 = 0 is true

question 45.Product of two negative integers is always

(a) Always negative (b) Always positive (c) Either positive or negative (d) 0

Solution: Product of two negative integers is always positive

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