Write down a pair of integers whose:

- Sum is – 7
**Answer:**- 14 and 7 - Difference is – 10
**Answer:**55 and 65 - Sum is 0
**Answer:**24 and – 24

Answer the following:

- Write a pair of integers whose difference gives 8.
**Answer:**15 and 7 - Write a negative integer and a positive integer whose sum is – 5.
**Answer:**- 15 and 10 - Write a negative integer and a positive integer whose difference is – 3.
**Answer:**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 + (………..)`
**Answer:**- 6 - `– 53 + ……….. = - 53`
**Answer:**0 - `17 + …………… = 0`
**Answer:**- 17 - `[13 + ( - 12)] + (…………) = 13 + [( - 12) + ( - 7)]`
**Answer:**- 7 - `( - 4) + [15 + ( - 3)] = [ - 4 + 15] + …………….`
**Answer:**- 3

Find each of the following products:

- `3 xx ( - 1)`
**Answer:**`3 xx ( - 1) = - 3` - `( - 1) xx 225`
**Answer:**`- 225` - `( - 21) xx ( - 30)`
**Answer:**`( - 21) xx ( - 30) = 630` - `( - 316) xx ( - 1)`
**Answer:**316 - `( - 15) xx 0 xx ( - 18)`
**Answer:**Zero because when any number is multiplied by zero the result is zero. - `( - 12) xx ( - 11) xx (10)`
**Answer:**`( - 12) xx ( - 11) xx (10) = 132 xx 10 = 1320` - `9 xx ( - 3) xx ( - 6)`
**Answer:**`9 xx ( - 3) xx ( - 6) = 9 xx 18 = 162` - `( - 18) xx ( - 5) xx ( - 4)`
**Answer:**`( - 18) xx ( - 5) xx ( - 4) = 90 xx ( - 4) = - 360` - `( - 1) xx ( -2) xx ( - 3) xx 4`
**Answer:**`( - 1) xx ( - 2) xx ( - 3) xx 4 = 2 xx ( - 12) = - 24` - `( - 3) xx ( - 6) xx ( - 2) xx ( - 1)`
**Answer:**`( - 3) xx ( - 6) xx ( - 2) xx ( - 1) = 18 xx 2 = 36`

Verify the following:

- `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 - `( - 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

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

**Answer:** ( - 1) x a = - a

Determine the integer whose product with ( - 1) is

- – 22
**Answer:**22 - 37
**Answer:**- 37 - 0
**Answer:**0

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`

Find the product, using suitable properties:

- `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. - `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` - `15 xx ( -25) xx( – 4) xx ( - 10)`
**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` - `( - 41) xx 102`
**Answer:**`( - 41) xx 102`

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

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

This has been solved using distributive property of multiplication. - `625 xx ( - 35) + (- 625) xx 65`
**Answer:**`625 xx ( - 35) + ( - 625) xx 65`

`= ( - 625) xx (35 + 65) ``= ( - 625) xx 100 = - 62500`

This has been solved using distributive property of multiplication. - `7 xx ( 50 – 2)`
**Answer:**`7 xx ( 50 – 2)`

`= 7 xx 50 + 7 xx ( - 2) = 350 – 14 = 336`

This has been solved using distributive property of multiplication. - `( - 17) xx ( - 29)`
**Answer:**`( - 17) xx ( - 29)`

`= 17 xx 29 = 17 (30 – 1)`

`= (17 xx 30) – (17 xx 1)`

`= 510 – 17 = 493`

This has been solved using distributive property of multiplication. - `( - 57) xx ( - 19) + 57`
**Answer:**`( - 57) xx ( -19) + 57`

`= 57 xx 19 + 57`

`= 57 xx (19 + 1)`

`= 57 xx 20 = 1140`

This has been solved using distributive property of multiplication.

A certain freezing process required that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?

**Answer:** Change in room temperature in 1 hour = - 5° C

So, change in room temperature in 10 hours = ( - 5) x 10 = - 50°C

Room temperature after 10 hours = 40°C - 50°C = - 10°C

In a class test containing 10 questions, 5 marks are awarded for every correct answer and ( - 2) marks are awarded for every incorrect answer and 0 for questions not attempted.

- Mohan gets four correct and six incorrect answers. What is his score?
**Answer:**Mohan’s score

`= (4 xx 5) + 6 xx ( - 2) = 20 – 12 = 8` - Reshma gets two correct answers and five incorrect answers, what is her score?
**Answer:**Reshma’s score

`= 2 xx 5 + 5 xx ( - 2) = 10 – 10 = 0` - Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?
**Answer:**Heena’s score

`= 2 xx 5 + 5 xx ( - 2) = 10 – 10 = 0`

A cement company earns a profit of Rs. 8 per bag of white cement sold and a loss of Rs. 5 per bag of grey cement sold.

- The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?
**Answer:**Company’s profit or loss

`= 3000 xx 8 + 5000 xx ( - 5)`

`= 24000 – 25000 = - 1000`

It is a loss of Rs. 1000 - What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.
**Answer:**Loss in selling grey bags

`= 6400 xx ( - 5) = - 32000`

Number of white cement bags required to be sold

`= 32000 ÷ 8 = 4000`

Replace the blank with an integer to make it a true statement

- `( - 3) xx ………… = 27`
**Answer:**9 - `5 xx ………… = - 35`
**Answer:**- 7 - `……… xx ( - 8) = - 56`
**Answer:**7 - `……… xx ( - 12) = 132`
**Answer:**- 11

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