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Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 1 www.embibe.com CBSE NCERT Solutions for Class 7 Mathematics Chapter 1

Back of Chapter Questions

Exercise: 1.1

1.Following number line shows the temperature in degree Celsius ሺιሻ at different

places on a particular day. (a)Observe this number line and write the temperature of the places marked on it. (b)What is the temperature difference between the hottest and the coldest places among the above?

(c)What is the temperature difference between Lahulspiti and Srinagar?(d)Can we say temperature of Srinagar and Shimla taken together is less than

the temperature at Shimla? Is it also less than the temperature at Srinagar?

Solution:

(a)

Place Temperature ሺԨሻ

Lahulspiti െͺ

Srinagar െʹ

Shimla ͷ

Ooty ͳͶ Bengaluru ʹʹ

(b)The temperature at the hottest place ൌʹʹԨ

The temperature at the coldest place ൌെʹԨTherefore, the difference ൌʹʹԨെሺെʹԨሻ

ൌʹͶԨ (c)The temperature at Lahulspiti ൌെͺԨ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 2 www.embibe.com The temperature at Srinagar ൌെʹԨ Therefore, the difference ൌെʹԨെሺെͺԨሻ ൌ͸Ԩ (d)The temperature of Srinagar and Shimla taken together ൌെʹԨ൅ͷԨ ൌ͵Ԩ The temperature at Shimla ൌͷԨ൐͵ԨǤ Therefore the temperature of Srinagar and Shimla taken together is less than that of Shimla. The tempe rature at Srinagar ൌെʹԨ൏͵ԨǤ Therefore, the tempe rature of Srinagar and Shimla taken together is not less than that of Srinagar

2.In a quiz, positive marks are given for correct answers and negative marks are

given sive rounds were ʹͷǡെͷǡെͳͲǡͳͷ and ͳͲǡ what was his total at the end?

Solution:

ʹͷǡെͷǡെͳͲǡͳͷǡ and ͳͲ

His total scores at the endൌʹͷ൅ሺെͷሻ൅ሺെͳͲሻ൅ሺͳͷሻ൅ሺͳͲሻ

ൌ͵ͷ

3.At Srinagar temperature was െͷι on Monday and then it dropped by ʹι on

Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by Ͷι. What was the temperature on this day?

Solution:

Temperature on Monday ൌെͷԨ

It dropped by ʹԨ

Therefore, temperature on Tuesday ൌെͷԨെʹԨ ൌെ͹Ԩ

It rose again on Wednesday by ͶԨ

Therefore, temperature on Wednesday ൌെ͹Ԩ൅ͶԨ ൌെ͵Ԩ

4.A plane is flying at the height of ͷͲͲͲ m above the sea level. At a particular

point, it is exactly above a submarine floating ͳʹͲͲ m below the sea level. What is the vertical distance between them?

Solution:

Plane flying above sea level at height ൌͷͲͲͲ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 3 www.embibe.com Submarine floating below the sea level ൌͳʹͲͲ

Therefore, the vertical distance between them ൌͷͲͲͲ൅ͳʹͲͲ ൌ͸ʹͲͲ

5. Mohan deposits Rs ʹǡͲͲͲ in his bank account and withdraws Rs ͳǡ͸Ͷʹ from it,

the next day. If withdrawal of a mount from the a ccount is represented by a negative integer, then how will you represent the amount deposited? Find the withdrawal.

Solution:

Amount deposited in the bank ൌRs ʹͲͲͲ Amount withdrawn the next day ൌRs ͳ͸Ͷʹ Therefore, the balance amount in the account ൌʹͲͲͲെͳ͸Ͷʹ ൌRs ͵ͷͺ

6. Rita goes ʹͲ km towards east from a point A to the point B. From B, she moves

͵Ͳ km towards west along the same road. I f t he distance towards e ast is represented by a positive inte ger then, how will you represent the dista nce travelled towards west? By which integer will you represent her final position from A?

Solution:

Rita moves towards east from A to B ൌʹͲ km

Let us assume C as the point travelled westwards

She moves towards west along the same road i.e from B to C ൌ͵Ͳ Therefore, distance travelled by her towards west from A to B ൌʹͲെ͵Ͳ ൌെͳͲ ׵

7. In a magic square each row, column and diagonal have the same sum. Check

which of the following is a magic square (i)

ͷ െͳ െͶ

െͷ െʹ ͹

Ͳ ͵ െ͵

(ii)

ͳ െͳͲ Ͳ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 4 www.embibe.com െͶ െ͵ െʹ െ͸ Ͷ െ͹

Solution:

(i) Sum of the rows:

ͷ൅െͳ൅െͶൌͲ

െͷ൅െʹ൅͹ൌͲ

Ͳ൅͵൅െ͵ൌͲ

Sum of the columns:

ͷ൅െͷ൅ͲൌͲ

െͳ൅െʹ൅͵ൌͲ െͶ൅͹൅െ͵ൌͲ

Sum of the diagonals:

ͷ൅െʹ൅െ͵ൌͲ

െͶ൅െʹ൅Ͳൌെ͸ Thus, this is not a magic square because all the sums are not equal (ii) Sum of the rows: ͳ൅െͳͲ൅Ͳൌെͻ െͶ൅െ͵൅െʹൌെͻ െ͸൅Ͷ൅െ͹ൌെͻ

Sum of the columns:

ͳ൅െͶ൅െ͸ൌെͻ െͳͲ൅െ͵൅Ͷൌെͻ Ͳ൅െʹ൅െ͹ൌെͻ

Sum of the diagonals:

ͳ൅െ͵൅െ͹ൌͲ

Ͳ൅െ͵൅െ͸ൌെͻ Thus, this is a magic square because all the sums are equal

8. Verify െሺെሻൌ൅ for the following values of a and b.

(i) ൌʹͳǡൌͳͺ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 5 www.embibe.com (ii) ൌͳͳͺǡൌͳʹͷ (iii) ൌ͹ͷǡൌͺͶ (iv) ൌʹͺǡൌͳͳ

Solution:

LHS െሺെሻൌʹͳെሺെͳͺሻൌ͵ͻ RHS൅ൌʹͳ൅ͳͺൌ͵ͻ ൌ

Thus verified

LHS െሺെሻൌͳͳͺെሺെͳʹͷሻൌʹͶ͵

RHS ൅ൌͳͳͺ൅ͳʹͷൌʹͶ͵

LHS ൌ RHS

Thus verified

LHS െሺെሻൌ͹ͷെሺെͺͶሻൌͳͷͻ RHS ൅ൌ͹ͷ൅ͺͶൌͳͷͻ

LHS ൌ RHS

Thus verified

LHS െሺെሻൌʹͺെሺെͳͳሻൌ͵ͻ RHS ൅ൌʹͺ൅ͳͳൌ͵ͻ

LHSൌ RHS

Thus verified

9. Use the sign of ൐ǡ൏ or ൌ in the box to make the statements true.

(a) ሺെͺሻ൅ሺെͶሻሺെͺሻെሺെͶሻ

(b) ሺെ͵ሻ൅͹െሺͳͻሻͳͷെͺ൅ሺെͻሻ

(c) ʹ͵െͶͳ൅ͳͳʹ͵െͶͳെͳͳ

(d) ͵ͻ൅ሺെʹͶሻെሺͳͷሻ͵͸൅ሺെͷʹሻെሺെ͵͸ሻ

(e) െʹ͵ͳ൅͹ͻ൅ͷͳെ͵ͻͻ൅ͳͷͻ൅ͺͳ

Solution:

(a) െͳʹ൏െͶ (b) െͳͷ൏െʹ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 6 www.embibe.com (c) െ͹൐െʹͻ (d) Ͳ൏ʹͲ (e) െͳͲͳ൐െͳͷͻ

10. A water tank has steps inside it. A monkey is sitting on the topmost step (i.e. the

first step). The water level is at the ninth step. (i) He jumps ͵ steps down and then jumps back ʹ steps up. In how many jumps will he reach the water level? (ii) After drinking water, he wants to go back. For this, he jumps Ͷ steps up and then jumps back ʹ steps down in every move. In how many jumps will he reach back the top step? (iii) If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following; ሺሻെ͵൅ʹെڮ ሺሻͶെʹ൅ǤǤǤൌͺǤ In (a) the sum ሺെͺሻ represents going down by eight steps. So, what will the sum ͺ in (b) represent?

Solution:

Monkey is on the first step; water level is at the 9th step

1st jump ൌͳ൅͵െʹൌʹ

2nd jumൌʹ൅͵െʹൌ͵

3rd jump ൌ͵൅͵െʹൌͶ

4th jump ൌͶ൅͵െʹൌͷ

5th jump ൌͷ൅͵െʹൌ͸

6th jump ൌ͸൅͵െʹൌ͹

7th jump ൌ͹൅͵െʹൌͺ

8th jump ൌͺ൅͵െʹൌͻ

Therefore in 8 jumps the monkey will reach the water level

1st jump ൌͻെͶ൅ʹൌ͹

2nd jumpൌ͹െͶ൅ʹൌͷ

3rd jumpൌͷെͶ൅ʹൌ͵

4th jump ൌ͵െͶ൅ʹൌͳ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 7 www.embibe.com Therefore in 4 jumps he will reach back the top

(a) െ͵൅ʹെ͵൅ʹെ͵൅ʹെ͵൅ʹെ͵൅ʹെ͵൅ʹെ͵൅ʹെ͵൅ʹൌ

െͺ (b) Ͷെʹ൅Ͷെʹ൅Ͷെʹ൅Ͷെʹൌͺ So, the sum ͺ in B represents climbing up the top

Exercise: 1.2

1. Write down a pair of integers whose:

sum is െ͹ (b) difference is െͳͲ (c) sum is Ͳ

Solution:

A pair of integers whose sum is െ͹

െͷ൅ሺെʹሻൌെ͹ A pair of integers whose difference isെͳͲ െͳ͹െሺെ͹ሻൌെͳͲ

A pair of integers whose sum is Ͳ

െͺ൅ͺൌͲ

2. (a) Write a pair of negative integers whose difference gives ͺ.

(b) Write a negative integer and a positive integer whose sum is െͷǤ (c) Write a negative integer and a positive integer whose difference is െ͵Ǥ

Solution:

A pair of negative integers whose difference is ͺ െ͸െሺെͳͶሻൌͺ A negative integer and a positive integer whose sum is െͷ െͳʹ൅ሺ͹ሻൌെͷ A negative integer and a positive integer whose difference is െ͵ െͳെሺʹሻ

3. In a quiz, tea m A sco red െͶͲǡͳͲǡͲ and tea m B sc ored ͳͲǡͲǡെͶͲ in three

successive rounds. Which team scored more? Can we say that we can add integers in any order?

Solution:

Total of Team A scores ൌെͶͲ൅ͳͲ൅Ͳ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 8 www.embibe.com ൌെ͵Ͳ Total of Team B scores ൌͳͲ൅Ͳ൅ሺെͶͲሻ ൌെ͵Ͳ Both the teams have same scores. Therefore, yes, we can say that integers can be added in any order.

4. Fill in the blanks to make the following statements true:

(i) ሺെͷሻ൅ሺെͺሻൌሺെͺሻ൅ሺǤǤǤǤǤǤǤǤǤǤǤǤሻ

(ii) െͷ͵൅ǤǤǤǤǤǤǤǤǤǤǤǤൌെͷ͵ (iii) ͳ͹൅ǤǤǤǤǤǤǤǤǤǤǤǤൌͲ

(iv) ሾͳ͵൅ሺെͳʹሻሿ൅ሺǤǤǤǤǤǤǤǤǤǤǤǤሻൌͳ͵൅ሾሺെͳʹሻ൅ሺെ͹ሻሿ

(v) ሺെͶሻ൅ሾͳͷ൅ሺെ͵ሻሿൌሾെͶ൅ͳͷሿ൅ǤǤǤǤǤǤǤǤǤǤǤǤ

Solution:

(i) LHS: െͷ൅ሺെͺሻൌെͳ͵ RHS: െͺ൅ሺെͷሻൌെͳ͵ (commutative property) (ii) െͷ͵൅Ͳൌെͷ͵ (zero additive property) (iii) ͳ͹൅ሺെͳ͹ሻൌͲ (additive identity)

(iv) RHS: ͳ͵൅ሺെͳʹሻ൅ሺെ͹ሻൌͳ͵൅ሺെͳͻሻ (associative property)

ൌെ͸ LHS: ͳ͵൅ሺെͳʹሻ൅ൌെ͸

ͳ൅ሺെ͹ሻൌെ͸

(v) LHS:ሺെͶሻ൅ሾͳͷ൅ሺെ͵ሻሿൌെͶ൅ͳʹ (associative property)

ൌͺ RHS:ሺെͶ൅ͳͷሻ൅ൌͺ

ͳͳ൅െ͵ൌͺ

Exercise: 1.3

1. Find each of the following products:

(a) ͵ൈሺെͳሻ (b) ሺെͳሻൈʹʹͷ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 9 www.embibe.com (c) ሺെʹͳሻൈሺെ͵Ͳሻ

(d) ሺെ͵ͳ͸ሻൈሺെͳሻ (e) ሺെͳͷሻൈͲൈሺെͳͺሻ (f) ሺെͳʹሻൈሺെͳͳሻൈሺͳͲሻ (g) ͻൈሺെ͵ሻൈሺെ͸ሻ (h) ሺെͳͺሻൈሺെͷሻൈሺെͶሻ (i) ሺെͳሻൈሺെʹሻൈሺെ͵ሻൈͶ

(j) ሺെ͵ሻൈሺെ͸ሻൈሺെʹሻൈሺെͳሻ

Solution:

(a) ͵ൈሺെͳሻൌെ͵ (b) ሺെͳሻൈʹʹͷൌെʹʹͷ (c) ሺെʹͳሻൈሺെ͵Ͳሻൌ͸͵Ͳ (d) ሺെ͵ͳ͸ሻൈሺെͳሻൌ͵ͳ͸ (e) ሺെͳͷሻൈͲൈሺെͳͺሻൌͲ

(f) ሺെͳʹሻൈሺെͳͳሻൈሺͳͲሻൌͳ͵ʹͲ

(g) ͻൈሺെ͵ሻൈሺെ͸ሻൌͳ͸ʹ

(h) ሺെͳͺሻൈሺെͷሻൈሺെͶሻൌെ͵͸Ͳ

(i) ሺെͳሻൈሺെʹሻൈሺെ͵ሻൈͶൌെʹͶ

(j) ሺെ͵ሻൈሺെ͸ሻൈሺെʹሻൈሺെͳሻൌ͵͸

2. Verify the following:

(a) ͳͺൈሾ͹൅ሺെ͵ሻሿൌሾͳͺൈ͹ሿ൅ሾͳͺൈሺെ͵ሻሿ

(b) ሺെʹͳሻൈሾሺെͶሻ൅ሺെ͸ሻሿൌሾሺെʹͳሻൈሺെͶሻሿ൅ሾሺെʹͳሻൈሺെ͸ሻሿ

Solution:

(a) ͳͺൈሾ͹൅ሺെ͵ሻሿൌሾͳͺൈ͹ሿ൅ሾͳͺൈሺെ͵ሻሿ (using distributive property)

LHS:ͳͺൈሾ͹൅ሺെ͵ሻሿൌͳͺൈͶ ൌ͹ʹ

RHS: ሾͳͺൈ͹ሿ൅ሾͳͺൈሺെ͵ሻሿൌͳʹ͸൅ሺെͷͶሻ

ൌ͹ʹ ൌǡ hence verified

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 10 www.embibe.com (b) ሺെʹͳሻൈሾሺെͶሻ൅ሺെ͸ሻሿൌሾሺെʹͳሻൈሺെͶሻሿ൅ሾሺെʹͳሻൈሺെ͸ሻሿ

LHS: ሺെʹͳሻൈሾሺെͶሻ൅ሺെ͸ሻሿൌെʹͳൈሺെͳͲሻ

ൌʹͳͲ

RHS: ሾሺെʹͳሻൈሺെͶሻሿ൅ሾሺെʹͳሻൈሺെ͸ሻሿൌͺͶ൅ͳʹ͸

ൌʹͳͲ ൌǡ hence verified

3. (i) For any integer a, what is ሺെͳሻൈ equal to?

(ii) Determine the integer whose product with ሺെͳሻ is ሺሻെʹʹሺሻ͵͹ሺሻͲ

Solution:

(i) For any integer a, ሺെͳሻൈൌെ (additive inverse of an integer property) (ii) ሺሻെͳ is to be multiplied with ʹʹ for the product to be െʹʹ i.e., ሺെͳሻൈʹʹൌെʹʹ ሺሻെͳ is to be multiplied with െ͵͹ for the product to be ͵͹ i.e., ሺെͳሻൈെ͵͹ൌ͵͹ (c) െͳ is to be multiplied with Ͳ for the product to be Ͳ i.e., ሺെͳሻൈͲൌͲ

4. Starting from ሺെͳሻൈͷǡ write various products showing some pattern to show

ሺെͳሻൈሺെͳሻൌͳǤ

Solution:

ሺെͳሻൈͷൌെͷ ሺെͳሻൈͶൌെͶ ሺെͳሻൈ͵ൌെ͵ ሺെͳሻൈʹൌെʹ ሺെͳሻൈͳൌെͳ ሺെͳሻൈͲൌͲ ሺെͳሻൈሺെͳሻൌͳ

5. Find the product, using suitable properties:

(a) ʹ͸ൈሺെͶͺሻ൅ሺെͶͺሻൈሺെ͵͸ሻ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 11 www.embibe.com (b) ͺൈͷ͵ൈሺെͳʹͷሻ

(c) ͳͷൈሺെʹͷሻൈሺെͶሻൈሺെͳͲሻ

(d) ሺെͶͳሻൈͳͲʹ (e) ͸ʹͷൈሺെ͵ͷሻ൅ሺെ͸ʹͷሻൈ͸ͷ (f) ͹ൈሺͷͲെʹሻ (g) ሺെͳ͹ሻൈሺെʹͻሻ (h) ሺെͷ͹ሻൈሺെͳͻሻ൅ͷ͹

Solution:

(a) ʹ͸ൈሺെͶͺሻ൅ሺെͶͺሻൈሺെ͵͸ሻൌെͶͺൈሺʹ͸൅ሺെ͵͸ሻ (distributive

property) ൌെͶͺൈሺെͳͲሻ ൌͶͺͲ

(b) ͺൈͷ͵ൈሺെͳʹͷሻൌͷ͵ൈሺͺൈെͳʹͷሻ(commutative property)

ൌͷ͵ൈሺെͳͲͲͲሻ ൌെͷ͵ͲͲͲ

(c) ͳͷൈሺെʹͷሻൈሺെͶሻൈሺെͳͲሻൌͳͷൈሺെͳͲሻൈሺെʹͷሻൈሺെͶሻ

(commutative property) ൌെͳͷͲൈͳͲͲ ൌെͳͷͲͲͲ

(d) ሺെͶͳሻൈͳͲʹൌሺെͶͳሻൈሺͳͲͲ൅ʹሻ

ൌሺെͶͳൈͳͲͲሻ൅ሺെͶͳൈʹሻ(distributive property)

ൌെͶͳͲͲ൅ሺെͺʹሻ ൌെͶͳͺʹ

(e) ͸ʹͷൈሺെ͵ͷሻ൅ሺെ͸ʹͷሻൈ͸ͷൌሺ͸ʹͷሻൈሺെ͵ͷሻ൅ሺെ͸ͷሻ

(distributive property) ൌ͸ʹͷൈሺെͳͲͲሻ ൌെ͸ʹͷͲͲ

(f) ͹ൈሺͷͲെʹሻൌሺ͹ൈͷͲሻെሺ͹ൈʹሻ

ൌ͵ͷͲെͳͶ ൌ͵͵͸(distributive property)

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 12 www.embibe.com (g) ሺെͳ͹ሻൈሺെʹͻሻൌെͳ͹ൈሺെ͵Ͳ൅ͳሻ

ൌሺെͳ͹ൈെ͵Ͳሻ൅ሺെͳ͹ൈͳሻ(distributive property)

ൌͷͳͲ൅ሺെͳ͹ሻ ൌͶͻ͵

(h) ሺെͷ͹ሻൈሺെͳͻሻ൅ͷ͹ൌሺെͷ͹ሻൈሺെͳͻሻ൅ͷ͹ൈͳ (distributive

property) ൌͷ͹ൈሺͳͻ൅ͳሻ ൌͷ͹ൈʹͲ ൌͳͳͶͲ

6. A certain freezing process requires that room temperature be lowered from ͶͲι

at the rate of ͷι every hour. What will be the room temperature ͳͲ hours after the process begins?

Solution:

Present room temperature ൌͶͲι

Temperature to be reduced every hour ൌͷι

Therefore, the room temperature after ͳͲ hours ൌͶͲιെሺͳͲൈͷιሻ

ൌͶͲιെͷͲι ൌെͳͲι

7. In a class test containing ͳͲ questions, ͷ marks are awarded for every correct

answer and ሺെʹሻ marks a re awarde d for every incorr ect a nswer and Ͳ for questions not attempted. (i) Mohan gets four correct and six incorrect answers. What is his score? (ii) Reshma gets five correct answers and five incorrect answers, what is her score? (iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Solution:

Four correct answers ൌͶൈͷൌʹͲ Six incorrect answers ൌ͸ൈሺെʹሻൌെͳʹ

Therefore, ൌʹͲെͳʹ

ൌͺ Five correct answersൌͷൈͷൌʹͷ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 13 www.embibe.com Five incorrect answers ൌͷൈሺെʹሻൌെͳͲ

ൌʹͷെͳͲ ൌͳͷ Two correct answers ൌʹൈͷൌͳͲ Five incorrect answers ൌͷൈሺെʹሻൌെͳͲ scores ൌͳͲെͳͲ ൌͲ

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

of Rs per bag of grey cement sold. (a) The company sells ͵ǡͲͲͲ bags of white cement and ͷǡͲͲͲ bags of grey cement in a month. What is its profit or loss? 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 ͸ǡͶͲͲ bags?

Solution:

Profit @ Rs ͺ on ͵ͲͲͲ bags of white cement ൌ͵ͲͲͲൈͺ ൌʹͶͲͲͲ Loss@ Rs ͷ on ͷͲͲͲ bags of grey cement ൌͷͲͲͲൈͷ ൌʹͷͲͲͲ The difference ൌʹͶͲͲͲെʹͷͲͲͲ ൌെͳͲͲͲ ׵

Number of grey bags sold ൌ͸ͶͲͲ

֜ ൌ͵ʹͲͲͲ To have neither profit nor loss, the profit on white bags should equal the loss on grey bags i.e., Rs ͵ʹͲͲͲ Therefore, number of white bags to be sold @ Rs 8=32000÷8 ൌͶͲͲͲ

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

(a) ሺെ͵ሻൈ̴̴̴̴̴ൌʹ͹ (b) ͷൈ̴̴̴̴̴ൌെ͵ͷ (c) ̴̴̴̴̴ൈሺെͺሻൌെͷ͸

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 14 www.embibe.com (d) ̴̴̴̴̴ൈሺെͳʹሻൌͳ͵ʹ

Solution:

(a) ሺെ͵ሻൈ̴̴̴̴̴ൌʹ͹ ֜ െ͵ൌെͻ ሺെ͵ሻൈሺെͻሻൌʹ͹ (b) ͷൈ̴̴̴̴̴ൌെ͵ͷ ֜

ͷൌെ͹

ͷൈሺെ͹ሻൌെ͵ͷ (c) ̴̴̴̴̴ൈሺെͺሻൌെͷ͸ ֜ െͺൌ͹ ͹ൈሺെͺሻൌെͷ͸ (d) ̴̴̴̴̴ൈሺെͳʹሻൌͳ͵ʹ ֜ െͳʹൌെͳͳ ሺെͳͳሻൈሺെͳʹሻൌͳ͵ʹ

Exercise: 1.4

1. Evaluate each of the following:

(a) ሺെ͵ͲሻൊͳͲ (b) ͷͲൊሺെͷሻ (c) ሺെ͵͸ሻൊሺെͻሻ (d) ሺെͶͻሻൊሺͶͻሻ (e) ͳ͵ൊሾሺെʹሻ൅ͳሿ (f) Ͳൊሺെͳʹሻ

(g) ሺെ͵ͳሻൊሾሺെ͵Ͳሻ൅ሺെͳሻሿ

(h) ሾሺെ͵͸ሻൊͳʹሿൊ͵

(i) ሾሺെ͸ሻ൅ͷሻሿൊሾሺെʹሻ൅ͳሿ

Solution:

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 15 www.embibe.com (a) ሺെ͵ͲሻൊͳͲൌെ͵

(b) ͷͲൊሺെͷሻൌെͳͲ (c) ሺെ͵͸ሻൊሺെͻሻൌͶ (d) ሺെͶͻሻൊሺͶͻሻൌെͳ

(e) ͳ͵ൊሾሺെʹሻ൅ͳሿൌͳ͵ൊሺെͳሻൌെͳ͵

(f) ͲൊሺെͳʹሻൌͲ

(g) ሺെ͵ͳሻൊሾሺെ͵Ͳሻ൅ሺെͳሻሿൌሺെ͵ͳሻൊሺെ͵ͳሻൌͳ

(h) ሾሺെ͵͸ሻൊͳʹሿൊ͵ൌሺെ͵ሻൊ͵ൌെͳ

(i) ሾሺെ͸ሻ൅ͷሻሿൊሾሺെʹሻ൅ͳሿൌሺെͳሻൊሺെͳሻൌͳ

2. Verify that ൊሺ൅ሻ്ሺൊሻ൅ሺൊሻ for each of the following values of

ǡ and .

(a) ܽൌͳʹǡܾൌെͶǡܿ (b) ܽൌሺെͳͲሻǡܾൌͳǡܿ

Solution:

(a) To verify ൊሺ൅ሻ്ሺൊሻ൅ሺൊሻ LHS:ൊሺ൅ሻൌͳʹൊሺെͶሻ൅ʹ ൌͳʹൊെʹ ൌെ͸

RHS: ሺൊሻ൅ሺൊሻൌͳʹൊሺെͶሻ൅ሺͳʹൊʹሻ

ൌെ͵൅͸ ൌ͵ ്, Hence verified (b) To verify ൊሺ൅ሻ്ሺൊሻ൅ሺൊሻ LHS: ൊሺ൅ሻൌሺെͳͲሻൊሺͳ൅ͳሻ ൌെͳͲൊʹ ൌെͷ

RHS:ሺൊሻ൅ሺൊሻൌሺെͳͲሻൊͳ൅ሺെͳͲሻൊͳ

ൌሺെͳͲሻ൅ሺെͳͲሻ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 16 www.embibe.com ൌെʹͲ ്ǡ Hence verified

3. Fill in the blanks:

(a) ͵͸ͻൊ̴̴̴̴̴ൌ͵͸ͻ (b) ሺെ͹ͷሻൊ̴̴̴̴̴ൌെͳ (c) ሺെʹͲ͸ሻൊ̴̴̴̴̴ൌͳ (d) െͺ͹ൊ̴̴̴̴̴ൌͺ͹ (e) ̴̴̴̴̴ൊͳൌെͺ͹ (f) ̴̴̴̴̴ൊͶͺൌെͳ (g) ʹͲൊ̴̴̴̴̴ൌെʹ (h) ̴̴̴̴̴ൊሺͶሻൌെ͵

Solution:

(a) ͵͸ͻൊͳൌ͵͸ͻ (b) ሺെ͹ͷሻൊ͹ͷൌെͳ (c) ሺെʹͲ͸ሻൊሺെʹͲ͸ሻൌͳ (d) ሺെͺ͹ሻൊሺെͳሻൌͺ͹ (e) ሺെͺ͹ሻൊͳൌെͺ͹ (f) ሺെͶͺሻൊͶͺൌെͳ (g) ʹͲൊሺെͳͲሻൌെʹ (h) ሺെͳʹሻൊͶൌെ͵

4. Write five pairs of integers ሺǡሻ such that ൊൌെ͵Ǥ One such pair is ሺ͸ǡെʹሻ

because ͸ൊሺെʹሻൌሺെ͵ሻ

Solution:

Five pairs of integers ሺǡሻ such that ൊൌെ͵ (i) ሺെͻǡ͵ሻ֜ (ii) ሺͳʹǡെͶሻ֜ (iii) ሺെʹͳǡ͹ሻ֜ (iv) ሺ͵ǡെͳሻ֜ (v) ሺെͳͷǡͷሻ֜

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 17 www.embibe.com 5. The temperature at ͳʹ noon was ͳͲι above zero. If it decreases at the rate of ʹι

per hour until midnight, at what time would the temperature be ͺι below zero?

What would be the temperature at mid-night?

Solution:

The temperature at ͳʹ noon ൌͳͲιܿ

It decreases at the rate of ʹι per hour

Let us assume the time taken for decrease in the temperature to be ֜ ׵ for temperature to be െͺι֜ െʹൌെͳͺ ൌെͳͺ െʹ ൌͻ Thus, the temperature would be 8°C below zero at 9 pm

6. In a class test ሺ൅͵ሻ marks are given for every correct answer and ሺെʹሻ marks are

given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored ʹͲ marks. If she has got ͳʹ correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores െͷ marks in this test, though she ha s got 7 correc t answers. How many questions ha s she attempted incorrectly?

Solution:

(i) Marks given for every correct answerൌ͵ Marks given for every wrong answer ൌെʹ

Marks scored by Radhika ൌʹͲ

Number of correct answers ൌͳʹ֜

i.e., marks scored for correct answers ൌ͵͸ ֜ ൌെͳ͸ ׵ ൌͺ (ii) Marks given for every correct answer ൌ͵ Marks given for every wrong answer ൌെʹ

Class- VII-CBSE-Mathematics Integers

Practice more on Integers Page - 18 www.embibe.com Marks scored by Mohini ൌെͷ

Number of correct answers ൌ͹֜

i.e., marks scored for correct answers ൌʹͳ marks scored for incorrect answers ൌሺെͷሻെʹͳ ൌെʹ͸ ׵ ൌͳ͵

7. An elevator descends into a mine shaft at the rate of ͸ m/min. If the descent starts

from ͳͲ m above the ground level, how long will it take to reach െ͵ͷͲ.

Solution:

The elevator descends at the rate of ͸m per min The descend starts at ͳͲ m above the ground leveland it needs to cover ͵ͷͲ m below ground. Therefore, total distance ൌͳͲ൅͵ͷͲ ൌ͵͸Ͳ ׵ ൌ͸Ͳ i.e., ͳ hour

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