Download Grade 6 Integers

ID : pk-6-Integers [1]
Grade 6
Integers
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Answer t he quest ions
(1)
What is the absolute value of | a + 16 | if a is greater than -16
(2)
Find the value of the f ollowing expression:
(3)
A)
- 100 + ( -77 ) - ( -61 ) - 27 - 188 - 14
B)
- ( -78 ) + 133 - ( -44 ) - 91 + ( -121 ) - 73 - 200
In a competitive exam, there are 70 questions. Students can score 3 marks f or each correct
answer while 2 marks are deducted f or each incorrect answer. If Sanober answered 22
questions correctly, how many marks did she get?
Choose correct answer(s) f rom given choice
(4) T he product of 2 given numbers is 240. T he two numbers are each divisible by 4, but neither of
them is 4. Which is the larger of these two numbers?
(5)
a. 20
b. 24
c. 16
d. 28
T he sum of a two negative integers will be?
a. Positive if f irst number is larger
b. Positive integer
c. Negative integer
d. Negative if f irst number is larger
Fill in t he blanks
(6) Find the sum of the f ollowing integers:
A)
C)
B)
75108 and -30514 =
D)
-64940 and -69798 =
-6269 and -85114 =
5089 and -64945 =
(7) Find how many integers are there between:
A)
C)
(8)
-3 and 2 =
-3 and 1 =
B)
D)
-4 and 7 =
-5 and 4 =
Subtract :
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ID : pk-6-Integers [2]
(9)
A)
8765 f rom -60894 =
B)
-36153 f rom -55242 =
C)
-87476 f rom 8565 =
D)
-47541 f rom -7178 =
E)
-59823 f rom -95150 =
F)
-65599 f rom -69204 =
Every integer to the lef t of zero on the number line have
value.
(10) Find the absolute value of f ollowing integers:
A)
D)
(11)
| -1 | =
| -5 | =
B)
E)
C)
|4 |=
F)
| -16 | =
| -5 | =
|9|=
If a and b are two integers such that a is the predecessor of b, the value of a - b will be
.
Check True/False
(12) T he absolute value of an integer is greater than the integer .
T rue
False
(13) T he additive inverse of a positive number is positive.
T rue
False
(14) T he sum of a negative integer and a positive integer is always a negative integer.
T rue
False
(15) T he smallest integer is zero.
T rue
False
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ID : pk-6-Integers [3]
Answers
(1)
a + 16
Step 1
|a + 16| = a + 16 if, a + 16 >= 0,
|a + 16| = -(a + 16) if, a + 16 < 0
Step 2
Above can also be written as,
|a + 16| = a + 16 if, a >= -16 ,
|a + 16| = -(a - 16) if, a < -16
Step 3
Since it is given that a is greater than -16, theref ore
|a + 16| = a + 16
(2)
A)
-345
Step 1
T he given expression can be expressed as:
- 100 + ( -77 ) - ( -61 ) - 27 - 188 - 14
= - 100 -77 + 61 - 27 - 188 - 14
= -345
Step 2
T heref ore the value of expression - 100 + ( -77 ) - ( -61 ) - 27 - 188 - 14 is 345.
B)
-230
Step 1
T he given expression can be expressed as:
- ( -78 ) + 133 - ( -44 ) - 91 + ( -121 ) - 73 - 200
= + 78 + 133 + 44 - 91 -121 - 73 - 200
= -230
Step 2
T heref ore the value of expression - ( -78 ) + 133 - ( -44 ) - 91 + ( -121 ) - 73 200 is -230.
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ID : pk-6-Integers [4]
(3)
-30
Step 1
T he total number of questions in a competitive exam = 70,
Marks obtained f or each correct answer = 3 and
Marks deducted f or each incorrect answer = 2
Step 2
Since Sanober answered 22 questions correctly,
T otal marks obtained by Sanober f or correct answers = 3 × 22 =66
Step 3
Number of incorrect question answered by Sanober = total number of questions in exam number of correct questions answered by Sanober = 70 - 22 = 48
Step 4
Now total marks obtained by Sanober in exam = total marks obtained by Sanober f or
correct answers - total marks deducted f or incorrect answers
= 66 - 96
= -30
Step 5
T heref ore Sanober obtained -30 marks.
(4) a. 20
Step 1
Since numbers are divisible by 4, lets assume numbers are 4x and 4y.
Also, since numbers are not equal to 4, x and y cannot be 1
Step 2
It is given that their product is 240
(4x) (4y) = 240
⇒ 16 xy = 240
⇒ xy =
240
16
⇒ xy = 15
Step 3
Since x and y cannot be 1, only possible f actors of xy = 15, are 5 and 3
Step 4
T heref ore numbers are (5 × 4 = 20) and (3 × 4 = 12)
Step 5
Larger of two numbers = 20
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ID : pk-6-Integers [5]
(5)
c. Negative integer
Step 1
We know that negative numbers are less than 0 and are on lef t hand side of 0 on number
line.
Above number line shows two negative numbers a = -3 and b = -1
Step 2
When we add a positive number, number on number line shif ts to the right and if we add a
negative number, it shif ts to lef t on number line
Step 3
For example if we add b(-1) to a(-3), a shif ts to f urther lef t on number line,
Step 4
Since sum of two negative numbers will be on lef t side of 0 on number line, sum will always
be negative.
(6)
A)
44594
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of 75108 and -30514
Step 2
Now 75108 + (-30514) = 75108 -30514
= 44594
Step 3
T heref ore the sum of 75108 and -30514 = 44594
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ID : pk-6-Integers [6]
B)
-91383
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of -6269 and -85114
Step 2
Now -6269 + (-85114) = -6269 -85114
= -91383
Step 3
T heref ore the sum of -6269 and -85114 = -91383
C)
-134738
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of -64940 and -69798
Step 2
Now -64940 + (-69798) = -64940 -69798
= -134738
Step 3
T heref ore the sum of -64940 and -69798 = -134738
D)
-59856
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of 5089 and -64945
Step 2
Now 5089 + (-64945) = 5089 -64945
= -59856
Step 3
T heref ore the sum of 5089 and -64945 = -59856
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ID : pk-6-Integers [7]
(7)
A)
4
Step 1
Number of integers between any two integers is equal to one less than the
dif f erence between the two integers.
Step 2
T hus, the total number of integers that are there between -3 and 2 = 2 - (-3) - 1
=2+2
=4
B)
10
Step 1
Number of integers between any two integers is equal to one less than the
dif f erence between the two integers.
Step 2
T hus, the total number of integers that are there between -4 and 7 = 7 - (-4) - 1
=7+3
= 10
C)
3
Step 1
Number of integers between any two integers is equal to one less than the
dif f erence between the two integers.
Step 2
T hus, the total number of integers that are there between -3 and 1 = 1 - (-3) - 1
=1+2
=3
D)
8
Step 1
Number of integers between any two integers is equal to one less than the
dif f erence between the two integers.
Step 2
T hus, the total number of integers that are there between -5 and 4 = 4 - (-5) - 1
=4+4
=8
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ID : pk-6-Integers [8]
(8)
A)
-69659
Subtracting 8765 f rom -60894 = -60894 - 8765 = -69659
B)
-19089
Subtracting -36153 f rom -55242 = -55242 - (-36153) = -55242 + 36153 = -19089
C)
96041
Subtracting -87476 f rom 8565 = 8565 - (-87476) = 8565 + 87476 = 96041
D)
40363
Subtracting -47541 f rom -7178 = -7178 - (-47541) = -7178 + 47541 = 40363
E)
-35327
Subtracting -59823 f rom -95150 = -95150 - (-59823) = -95150 + 59823 = -35327
F)
-3605
Subtracting -65599 f rom -69204 = -69204 - (-65599) = -69204 + 65599 = -3605
(9)
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. T heref ore numbers to the lef t of 0,
should have values which are smaller than 0
Step 3
We know that numbers which are smaller than 0, are negative numbers. T heref ore, every
integer to the lef t of 0 on the number line will have negative value.
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ID : pk-6-Integers [9]
(10) A)
1
Step 1
T he absolute value (or modulus) of a integer x is x's numerical value without
regard to its sign.
Step 2
T heref ore the absolute value of | -1 | = 1.
B)
4
Step 1
T he absolute value (or modulus) of a integer x is x's numerical value without
regard to its sign.
Step 2
T heref ore the absolute value of | 4 | = 4.
C)
5
Step 1
T he absolute value (or modulus) of a integer x is x's numerical value without
regard to its sign.
Step 2
T heref ore the absolute value of | -5 | = 5.
D)
5
Step 1
T he absolute value (or modulus) of a integer x is x's numerical value without
regard to its sign.
Step 2
T heref ore the absolute value of | -5 | = 5.
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ID : pk-6-Integers [10]
E)
16
Step 1
T he absolute value (or modulus) of a integer x is x's numerical value without
regard to its sign.
Step 2
T heref ore the absolute value of | -16 | = 16.
F)
9
Step 1
T he absolute value (or modulus) of a integer x is x's numerical value without
regard to its sign.
Step 2
T heref ore the absolute value of | 9 | = 9.
(11)
-1
Step 1
Because a is predecessor of b theref ore the value of a = b - 1
Step 2
T he value of a - b = b - 1 - b
=b-b-1
= -1
(12) False
Step 1
Absolute Value is the value of the number without regards to its' sign. T he value is always a
positive number.
For positive numbers, absolute value is same as number. e.g. |5| = 5.
For negative numbers, absolute value is reverse of the number. e.g. |-5| = 5.
Step 2
We can see that absolute value of a number if either equal to the number (f or positive
numbers), or it is larger than the number (f or negative numbers).
Hence the given statement "T he absolute value of an integer is greater than the
integer" is f alse.
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ID : pk-6-Integers [11]
(13) False
Step 1
T he additive inverse of a number a is the number that, when added to a, yields zero.
Step 2
T he additive inverse is the opposite of a number theref ore the additive inverse of a
positive number is negative and a negative number is positive.
For example, the additive inverse of 14 is –14.
T he additive inverse of –5 is 5.
Step 3
T heref ore the given statement is f alse.
(14) False
Step 1
Let us assume that n is a positive integer and -m is a negative integer.
Step 2
T he sum of integer n and -m = n + (-m)
=n-m
If m is less than n then the value of n - m is positive and
if m is greater than the n, then the value of n - m is negative.
Step 3
T heref ore we can say that the sum of a negative integer and a positive integer is not
always a negative integer. It will depends on the value of the numbers.
Step 4
T heref ore the answer is f alse.
(15) False
Step 1
We know that integers can be negative {-1, -2,-3, -4, -5, ... }, positive {1, 2, 3, 4, 5, ... }, or
zero {0}. Z ero is greater than the all negative values and smaller than the all positive values,
theref ore we can say that zero is not the smallest integer.
Step 2
Hence the answer is f alse.
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