Grade 7 Integers In

7/26/2019 Grade 7 Integers In

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Class 7

Integers

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Answer the questions

(1) In a competitive exam, there are 60 questions. Students can score 2 marks f or each correct

answer while 1 mark is deducted f or each incorrect answer. If Vinayak answered 40 quest ions

correctly, how many marks did he get?

(2) An integer is divided by 4 and gives a remainder o f 3. The resulting quotient is divided by 6 and

gives a remainder of 3. The resulting quot ient of this is divided by 7 and gives a quot ient of 1

and a remainder of 1. What is t he number?

(3) Find how many integers are there between:

A) -4 and 3 B) -5 and 3

C) -4 and 7 D) -4 and 7

(4) Which number in the f ollowing pairs is larger:

A) -7, 5 B) -29, 29

C) 13, 4 D) 14, -13

(5) Kareem made following transactions on his credit card account :

Opening Balance : Rs. 4483

1) Debited Rs. 2596

2) Credited Rs. 1087


4) Credited Rs. 579

5) Debited Rs. 2224

6) Debited Rs. 1280



If the s tart ing balance on his credit card was Rs. 44 83, what will be the f inal balance on his

credit card account ?

ID : in-7-Integers [1]

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Choose correct answer(s) from given choice

(6) The abso lute value of | a- 19 | if ais less t han 19 is

a.-(a- 19) b.19

c.a d.a- 19

(7) Simplify

(-6324 / 68) + (-4608 / -64) + (-5076 / 54)

a.-119 b.-115

c.-110 d.-113

(8) A railway company makes a pro f it o f Rs. 1474 on per t icket of business class while loses Rs.

154 on every ticket in economy class. If the company sold 3517 t ickets of business class and

45313 tickets o f economy class in the month o f April, what would be the to tal prof it or loss

company will make in that month.

a.-1793144 b.-1794144

c.-6978202 d.5184058

Fill in the blanks

(9) Find the value of f ollowing :

A)6 10 ( -5 ) 1 17 =

B)( -5 ) 13 ( -8 ) 14 7 =

(10)Every integer to the lef t of zero on the number line have value.

(11) Divide :

A)1872 by -52 =

B)1599 by 41 =

(12) Simplify :

A)(5445 / -55) + (-4788 / -63) - (- 5658 / 69) =

B)( -14 ) ( -1 ) 1 - (-1672 / -4 4) + (-1400 / 40) =

(13) Subtract :




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A) -16047 f rom 91916 = B) -81054 f rom -12232 = C) 24125 from -4 0818 =

D) -61445 f rom 29610 = E) -95555 f rom 71854 = F) -22671 f rom -74867 =

(14) The sum of two integers is -4 763. If one of the integers is -3196, the other integer is

Check True/False

(15) The absolute value of an integer is greater than the integer .

True False

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Answers

(1) 60

Step 1

The to tal number of questions in a competitive exam = 60,

Marks obtained for each correct answer = 2 and

Marks deducted f or each incorrect answer = 1

Step 2

Since Vinayak answered 40 questions correctly,

Total marks obtained by Vinayak for correct answers = 2 40 =80

Step 3

Number of incorrect question answered by Vinayak = to tal number of questions in exam -

number of correct quest ions answered by Vinayak = 60 - 40 = 20

Step 4

Now to tal marks obtained by Vinayak in exam = total marks obtained by Vinayak f or co rrect

answers - tot al marks deducted for incorrect answers

= 80 - 20

= 60

Step 5

Therefore Vinayak obtained 60 marks.




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(2) 207

Step 1

If you loo k at t he question carefully, you will notice that an integer is divided by 4 and gives

a remainder of 3. The result ing quotient is divided by 6 and gives a remainder of 3. The

resulting quotient o f this is divided by 7 and gives a quotient o f 1 and a remainder of 1.

Step 2

Lets assume the number or dividend is x.

According to question, Diviso r = 4

Remainder = 3

We know that dividend = divisor quotient + remainder

or

quotient =dividend - remainder

divisor

=

x - 3

4

Step 3

Since the resulting quot ient is divided by 6 and gives a remainder of 3 and hence the

resulting quotient is work as a dividend.

New quotient =dividend - remainder

divisor

New quotient =(

x - 3

4 ) - 3

6

=x - 3 - 12

4

1

6

=x - 15

24

Step 4

Since the resulting quot ient is divided by 7 and gives a quot ient of 1 and a remainder of 1

and hence the resulting quot ient is work as a dividend.

dividend = divisor quotient + remainder

x - 15

24 = 7 1 + 1

x - 15

24 = 7 + 1

x - 1524

= 8

x - 15 = 8 24

x = 192 + 15




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x = 207

Step 5

Therefore the number is 207 .

(3) A) 6

Step 1Number of integers between any two integers is equal to one less than the

dif f erence between the two integers.

Step 2

Thus, the to tal number of integers that are there between -4 and 3 = 3 - (-4 ) - 1

= 3 + 3

= 6

B) 7

Step 1

Number of integers between any two integers is equal to one less than the


Step 2

Thus, the to tal number of integers that are there between -5 and 3 = 3 - (-5) - 1

= 3 + 4

= 7

C) 10

Step 1



Step 2

Thus, the to tal number of integers that are there between -4 and 7 = 7 - (-4 ) - 1

= 7 + 3= 10




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D) 10

Step 1



Step 2

Thus, the to tal number of integers that are there between -4 and 7 = 7 - (-4 ) - 1= 7 + 3

= 10

(4) A) 5

Step 1

The value of more negative number is smaller as compared to a less negative

number or any positive number.

Step 2

Thus, we can say that the larger number in the pair -7, 5 is 5.

B) 29

Step 1



Step 2

Thus, we can say that the larger number in the pair -29, 29 is 29 .

C) 13

Step 1

Both numbers 13 and 4 are positive.

Step 2

The positive number 13 is larger than the positive number 4.

D) 14

Step 1



Step 2

Thus, we can say that the larger number in the pair 14, -13 is 14 .




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(5) Rs. 9879

Step 1

If you look at the quest ion carefully, you will notice that t he starting balance on Kareem's

credit card was Rs. 4483.

to tal number of Rs. credited by Kareem = 1087 + 4547 + 579 + 2052 + 3231 = Rs. 11496

to tal number of Rs. debited by Kareem = 2596 + 2224 + 1280 = Rs. 6100

Step 2

Now the f inal balance on his credit card = t he starting balance on Kareem credit card - to tal

number of Rs. debited by Kareem + total number of Rs. credited by Kareem

= 4483 - 6100 + 11496

= Rs. 9879

(6) a.-(a- 19)

Step 1

Since the value of 'a' is less than 19, the value of a- 19 will be negative.

Step 2

Therefore the abso lute value of | a- 19 | is -(a- 19)

(7) b.-115

Step 1

We can divide two numbers by the f ollowing steps:

1.First of all we have to divide sign of the numbers. we use negative sign before the

negative numbers and we can't use any sign before the positive numbers.

We can divide sign as:

+ + = +

+ - = -

- - = +

2.Now we have to divide numbers.

f or example 4 2 = 2,

4 (-2) = (-2),

(-4 ) 2 = (-2),

(-4 ) (-2) = 2.

Step 2

Now (-6324 / 68) + (-4608 / -64) + (-5076 / 54) can be simplif ied as:

(-6324 / 68) + (-4608 / -64) + (-5076 / 54)

= (-93) + 72 + (-94)

= -115




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(8) b.-1794144

Step 1

The company so ld 3517 tickets o f business class. Since the prof it on per ticket of

business class is Rs. 1474 .

Therefore the prof it on 3517 t ickets of business class = 3517 1474 = 5184058

Step 2

The company so ld 45313 tickets o f economy class. Since the loss on per ticket o f

economy class is Rs. 154.

Therefore the loss on 45313 tickets o f economy class = 45313 154 = 6978202

Step 3

Therefore the tot al prof it or loss company will make in that month = 5184058 - 6978202 =

Rs. -1794144

(9)A) -5100

Step 1

We can multiply two numbers by the f ollowing steps:

1.First of all we have to multiply sign of the numbers. we use negative sign

before t he negative numbers and we can't use any sign before t he posit ive

numbers.

We can multiply sign as:

+ + = +

+ - = -

- - = +

2.Now we have to multiply numbers.


3 (-2) = (-6),

(-3) 2 = (-6),

(-3) (-2) = 6.

Step 2

To solve 6 10 ( -5 ) 1 17, f irst of all we have to multiply f irst two numbers

af ter that we have to multiply result with the next number and so on as shown

below:

6 10 ( -5 ) 1 17

= 60 ( -5 ) 1 17

= -300 1 17

= -300 17

= -5100

Step 3

Therefore the value of 6 10 ( -5 ) 1 17 is -5100.




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B)50960

Step 1

We can multiply two numbers by the f ollowing steps:

1.First of all we have to multiply sign of the numbers. we use negative sign

before t he negative numbers and we can't use any sign before t he posit ive

numbers.We can multiply sign as:

+ + = +

+ - = -

- - = +

2.Now we have to multiply numbers.


3 (-2) = (-6),

(-3) 2 = (-6),

(-3) (-2) = 6.Step 2

To so lve ( -5 ) 13 ( -8 ) 14 7, f irst o f all we have to multiply f irst two

numbers af ter that we have to multiply result with the next number and so on as

shown below:

( -5 ) 13 ( -8 ) 14 7

= -65 ( -8 ) 14 7

= 520 14 7

= 7280 7

= 50960

Step 3

Therefore the value of ( -5 ) 13 ( -8 ) 14 7 is 50960.

(10)negative

Step 1

Following pitcure shows number line which has negative, zero(0), and positive numbers.

Step 2

On number line, numbers increases f rom lef t to right. Therefore numbers to the lef t o f 0,

sho uld have values which are smaller than 0

Step 3

We know that numbers which are smaller than 0, are negative numbers. Therefore, every

integer to the lef t of 0 on the number line will have negative value.




11/14

(11) A)-36

Step 1

Division of a pos itive number by a negative number results in a negative number.

For example 4/(-2) = - 2

Division of a negative number by a positive number results in a negative number.

For example -4/2 = - 2

Division of a negative number by a negative number results in a pos itive number.

For example (-4)/(-2) = 2

Step 2

Therefore if we divide 1872 by -52, result will be negative

1872

-52 = -36

B)39

Step 1

Division of a pos itive number by a negative number results in a negative number.

For example 4/(-2) = - 2

Division of a negative number by a positive number results in a negative number.

For example -4/2 = - 2

Division of a negative number by a negative number results in a pos itive number.

For example (-4)/(-2) = 2

Step 2

Therefore if we divide 1599 by 41, result will be pos itive

1599

41 = 39




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(12) A)59

Step 1

We can multiply/divide two numbers by the f ollowing steps:

1.First of all we have to multiply/divide sign of the numbers. we use negative

sign before the negative numbers and we can't use any sign before the posit ive


+ + = +

+ - = -

- - = +


+ + = +

+ - = -

- - = +

2.Now we have to multiply/divide numbers.f or example 3 2 = 6,

3 (-2) = (-6),

(-3) 2 = (-6),

(-3) (-2) = 6.

and 4 2 = 2,

4 (-2) = (-2),

(-4 ) 2 = (-2),

(-4 ) (-2) = 2.

Step 2

Now (5445 / -55) + (-4 788 / -63) - (-5658 / 69) can be simplif ied as:

(5445 / -55) + (-47 88 / -63) - (-5658 / 69)

= (-99) + 76 - (-82)

= 59




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B)-59

Step 1

We can multiply/divide two numbers by the f ollowing steps:

1.First of all we have to multiply/divide sign of the numbers. we use negative

sign before the negative numbers and we can't use any sign before the posit ive


+ + = +

+ - = -

- - = +


+ + = +

+ - = -

- - = +

2.Now we have to multiply/divide numbers.f or example 3 2 = 6,

3 (-2) = (-6),

(-3) 2 = (-6),

(-3) (-2) = 6.

and 4 2 = 2,

4 (-2) = (-2),

(-4 ) 2 = (-2),

(-4 ) (-2) = 2.

Step 2

Now ( -14 ) ( -1 ) 1 - (- 1672 / -44) + (-1400 / 40) can be simplif ied as:

( -14 ) ( -1 ) 1 - (-1672 / -4 4) + (-1400 / 40)

= 14 - 38 + (-35)

= -59

(13) A)107963

Subtracting -16047 f rom 91916 = 91916 - (-16047) = 91916 + 16047 = 107963

B)68822

Subtracting -81054 f rom -12232 = -12232 - (-81054) = -12232 + 81054 = 68822

C)-64943

Subtracting 24125 f rom -40818 = - 40818 - 24125 = -64943




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D)91055

Subtracting -6144 5 f rom 29610 = 29610 - (-61445) = 29610 + 61445 = 91055

E)167409

Subtracting -95555 f rom 71854 = 71854 - (-95555) = 71854 + 95555 = 167409

F)-52196

Subtracting -22671 f rom -74867 = -74867 - (- 22671) = -7 4867 + 22671 = -

52196

(14)-1567

Step 1

The sum of two integers is -47 63

One of the integer is -3196

Step 2

The other integer,

= The sum of two integers - One of the integer

= (-4763) - (-3196)

= -4 763 + 3196

= -1567

(15) False

Step 1

Abso lute Value is t he value o f the number without regards to its ' sign. The value is always a

positive number.

For posit ive numbers, absolute value is same as number. e.g. |5| = 5.

For negative numbers, abso lute value is reverse o f the number. e.g. |-5| = 5.

Step 2

We can see that abso lute value of a number if either equal to the number (for positive

numbers), or it is larger than the number (f or negative numbers).

Hence the given statement "The absolute value of an intege r is greate r than the

integer"is false.


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Grade 7 Integers In