7th Standard CBSE Mathematics - Integers Three Marks Questions | QB365

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7th Standard CBSE Mathematics - Integers Three Marks Questions

Published on: 20/09/2019

Integers

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Questions:

Generic 3

15 x 3 = 45

Some points are marked with integers on the following number line. Write these integers in descending order.

Find the product: (-1) x (-1) x (-1) x (-1) x (-1).

Is 10 x [6 + (-2)] = 10 x 6 + 10 x (-2)?

Arushi deposits Rs 2000 per month in her account for six months as saving. But when she is in need, she withdraw Rs 1600 and once again she withdraw Rs 5,000 from her account.
(a) If withdrawal of amount is represented by (-ve) sign and deposition by (+ve) sign, what is the present position (balance) of her account?
(b) Which mathematical concept is used in this problem?
(c) What is its value?

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 each question not attempted.
(a) Mohan gets 6 correct and 4 incorrect answers, what is his score?
(b) Rekha gets 5 correct and 3 incorrect answers and 2 questions she did not attempt. What is her score?
(c) Mayank gets 5 correct and 5 incorrect answers. What is his score?
(d) Jeetu gets 3 correct and 5 incorrect answers. What is his score?

Starting from (- 6) x 3, find (- 6) x (- 7).

If the product of two integers is -512 and one of them is -8, then what is the other integer?

Write a negative integer and a positive integer whose difference is -14.

A certain freezing process requires that room temperature be lowered from 30°C at the rate of 5°C every hour. What will be the room temperature 12 h after the process begins?

10.

Verify -a + (-b) = - (a + b) for the following values of a and b. a =137, b = 49

11.

Verify a + (- b) = a - b for the following values of a and b: a = 137, b = 92

12.

At Srinagar, the temperature was -5° C on Monday and then it dropped by 2° C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

13.

In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were25, - 5, - 10, 15 and 10, what was his total at the end?

14.

Following number line shows the temperature in degree Celsius (^o C ) at different places on a particular day.

Can we say the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

15.

Following number line shows the temperature in degree Celsius (^o C ) at different places on a particular day.

What is the temperature difference between Lahulspiti and Srinagar?

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Answers Key:

Generic 3

15 x 3 = 45

The descending order of these integers is 14, 8, 3, 0, - 4, - 9, - 16.

Since, in the product there are 5 integers of minus sign (i.e., an odd number of integers).
∴ The sign of the product is negative.
Thus, (-1) x (-1) x (-1) x (-1) x (-1) = -1

We have,
L.H.S = 10 x [6 + (-2)] = 10 x 4 = 40
R.H.S = 10 x 6 + 10 x (-2) = 60 - 20 = 40
\(\therefore\) 10 x [6 + (-2)] = 10 x 6 + 10 x (-2)
Now, it is true.

(a) Since, she deposits Rs 2000 per month
∴ Amount deposit by her in six months
= Rs 2000 \(\times\) (6)
= Rs 12,000
She withdraw Rs 1600 and Rs 5000 in need.
So, withdrawal = - (1600 + 5000)
So, present position of account
= 12000- (1600 + 5000)
= 12000- 6600
= 5400
So, she has balance Rs 5400 in her account.
(b) Multiplication and subtraction of integers.
(c) If you save the money you can use it in need.

(a) Score of Mohan= 6 \(\times\) (5) + 4 \(\times\) (- 2)
= 30 + (-8)
=30 - 8 = 22
(b) Rekha's score = 5 \(\times\) (5) + 3 \(\times\) (-2) + 2 \(\times\) 0
= 25 + (-6) + 0
= 25 - 6 = 19
(c) Mayank's score = 5 \(\times\) (5) + 5 \(\times\) (- 2)
= 25 + (-10) = 25 -10 = 15
(d) Jeet's score = 3 \(\times\) (5) + 5 \(\times\) (- 2)
= 15 + (-10) = 15-10 = 5

(- 6) x 3 = -18
(- 6) x 2 = -12 = -18 - (- 6)
(- 6) x 1 = - 6 = -12 - (- 6)
(- 6) x 0 = 0 = - 6 - (- 6)
(-6) x -1 = 6 = 0 - (-6)
(-6) x -2 = 12 = 6 - (-6)
(-6) x -3 = 18 = 12 - (-6)
(-6) x -4 = 24 = 18 -(-6)
(-6) x -5 = 30 = 24-(-6)
(-6) x -6 = 36 = 30 - (-6)
(- 6) x -7 = 42 = 36 - (- 6).

For a negative integer and a positive integer whose difference is -14.
First integer = -11 , Second integer = + 3
\(\therefore\)Difference = -11 - (+3) = -14

As per the given information in the question,
Room temperature = 30° C
Change in temperature per hour = - 5° C
Change in temperature in 12 h = 12 x (-5) = - 60° C
Room temperature after 12 h = 30° C + ( - 60° C)
= -30°C

10.

Given, a = 137, b = 49
Taking LHS,
-a + (-b) = (-137) + (-49)= -137 - 49 = -186
Now, taking RHS,
-(a + b) = -(137 + 49)= -186
Hence, -a + (-b) = -(a + b)

11.

Given, a=137, b=92
Taking LHS,
a + (-b) =137 + (-92) = 45
Now, taking RHS,
a - b = 137 - 92 = 45
Hence, a+(-b) = (a-b)

12.

At Srinagar, temperature on Monday = - 5°C
Bur the temperature dropped 2° C on Tuesday.
\(\therefore\) Temperature on Tuesday = - 5°C - 2°C = -7°C
According to the question,
The temperature increased by 4°C on Wednesday.
Temperature on Wednesday = - 7°C + 4°C = - 3°C
Hence, temperature on Wednesday is - 3° C.

13.

Given, Jack's score ofIst round = 25
Score of IInd round = - 5
Score of IIIrd round = - 10
Score of IVth round = 15
and score of Vth round = 10
Now, total score = Sum of score of all rounds
= 25 + (- 5) + (-10) + 15 + 10 = 25 - 5 -10 + 15 + 10
= (25 + 15 + 10) + (- 5 -10)
=(40+10)+(-15) =50-15=35
Hence, the total score of Jack was 35.

14.

Number line with all numbers is shown below:

Given, temperature of Srinagar - 2° C
and temperature of Shimla = 5°C
\(\therefore\) The sum of the temperature of Srinagar and Shimla is (- 2) + 5 is3°C, but 3°C < 5°C.
Therefore, we can say that the sum of temperature of Srinagar and Shimla is less than the temperature of Shimla.
Now, temperature of Shimla = 5°C and temperature of Srinagar = - 2° C
\(\therefore\) The sum of the temperature of Shimla and Srinagar is 5 + (-2) i.e. 3°C, but 3°C > - 2°C.
Therefore, the temperature of Sri nagar and Shimla taken together is not less than the temperature of Srinagar.

15.

Number line with all numbers is shown below:

We have, the temperature of Lahulspiti = - 8° C
and temperature of Srinagar = - 2° C
\(\therefore\) The temperature difference between Lahulspiti and Srinagar
= Temperature of Srinagar - Temperature of Lahulspiti
= (-2) - (-8)= - 2 +8 = 6°C