Integers

NCERT Exercise 1.2

Write down a pair of integers whose:

Sum is – 7
Difference is – 10
Sum is 0

Answer: (a) -14 and 7, (b) 55 and 65, (c) 24 and -24

Answer the following:

Write a pair of integers whose difference gives 8.
Write a negative integer and a positive integer whose sum is – 5.
Write a negative integer and a positive integer whose difference is – 3.

Answer: (a) 15 and 7, (b) 1-5 and 10, (c) Such pair is not possible

In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0 – 40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?

Answer: Score of team `A = - 10 + 10 + 0 = - 30`

Score of team `B = 10 + 0 – 40 = - 30`

Both teams have same score. This shows that we can add integers in any order.

Fill in the blanks to make the following statements true:

`( - 6) + ( - 8) = - 8 + □`
`– 53 + □ = - 53`
`17 + □ = 0`
`[13 + ( - 12)] + □ = 13 + [( - 12) + ( - 7)]`
`( - 4) + [15 + ( - 3)] = [ - 4 + 15] + □`

Answer: (a) -6, (b) 0,(c) -17, (d) -7, (e) -3

Exercise 1.3

Question 1: Find each of the following products:

(a) `3 xx ( - 1)`

Answer: `3 xx ( - 1) = - 3`

(b) `( - 1) xx 225`

Answer: `- 225`

Answer: `( - 21) xx ( - 30) = 630`

(d) `( - 316) xx ( - 1)`

Answer: 316

(e) `( - 15) xx 0 xx ( - 18)`

Answer: Zero because when any number is multiplied by zero the result is zero.

(f) `( - 12) xx ( - 11) xx (10)`

Answer: `( - 12) xx ( - 11) xx (10) = 132 xx 10 = 1320`

(g) `9 xx ( - 3) xx ( - 6)`

Answer: `9 xx ( - 3) xx ( - 6) = 9 xx 18 = 162`

(h) `( - 18) xx ( - 5) xx ( - 4)`

Answer: `( - 18) xx ( - 5) xx ( - 4) = 90 xx ( - 4) = - 360`

(i) `( - 1) xx ( -2) xx ( - 3) xx 4`

Answer: `( - 1) xx ( - 2) xx ( - 3) xx 4 = 2 xx ( - 12) = - 24`

(j) `( - 3) xx ( - 6) xx ( - 2) xx ( - 1)`

Answer: `( - 3) xx ( - 6) xx ( - 2) xx ( - 1) = 18 xx 2 = 36`

Question 2: Verify the following:

(a) `18 xx [7 + ( - 3)] ``= [18 xx 7] + [18 xx ( - 3)]`

Answer: LHS `= 18 xx [7 + ( - 3)] ``= 18 xx [ - 4] = - 72`

RHS `= [18 xx 7] + [18 xx ( - 3)] ``= 126 + [ - 54] = - 72`

Here, LHS = RHS

(b) `( - 21) xx [( - 4) + ( - 6)] ``= [( - 21) xx ( -4)] + [( - 21) xx ( - 6)]`

Answer: LHS `= ( - 21) xx [( - 4) + ( - 6)] ``= - 21 xx [- 10] = 210`

RHS `= [( - 21) xx ( - 4) + [( - 21) xx ( - 6)] ``= 84 + 126 = 210`

Here, LHS = RHS

Question 3: For any integer a, what is ( - 1) x a equal to?

Answer: ( - 1) x a = - a

Question 4: Determine the integer whose product with ( - 1) is

– 22

Answer: 22
37

Answer: - 37
0

Answer: 0

Question 5: Starting from `( - 1) xx 5`, write various products showing some pattern to show `( - 1) xx ( - 1) = 1`.

Answer: `( - 1) xx 5 = - 5`

`( - 1) xx ( - 3) = 3`

`( - 1) xx 1 = - 1`

`( - 1) xx ( - 1) = 1`

Question 6: Find the product, using suitable properties:

(a) `26 xx ( - 48) + ( - 48) xx ( - 36)`

Answer: `26 xx ( - 48) + ( - 48) xx ( - 36)`

`= ( - 48) xx[26 + ( - 36)]`

`= ( - 48) xx [ 26 – 36]`

`= - 48 xx [ - 10] = 480`

This is showing distributive property of multiplication.

(b) `8 xx 53 xx ( -125)`

Answer: `8 xx 53 xx ( - 125)` can also be written as `8 xx ( - 125) xx 53`

This is showing associative property of multiplication.

`8 xx 53 xx ( - 125) =8 xx ( - 125) xx 53`

`= ( - 1000) xx 53 = - 53000`

Answer: This will also show associative property of multiplication.

`15 xx ( - 25) xx ( - 4) xx ( - 10)`

`= 15 xx ( - 10) xx ( - 25) xx ( - 4)`

`=( - 150) xx ( - 100) = 15000`

(d) `( - 41) xx 102`

Answer: `( - 41) xx 102`

`= [( - 41) xx 100] + [( - 41) xx 2]`

`= ( - 4100) + ( - 82) = - 4182`