Download Class 6 Integers

ID : in-6-Integers [1]
Class 6
Integers
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Answer t he quest ions
(1)
(2)
(3)
Which number in the f ollowing pairs is smaller :
A)
-22, 7
B)
-26, -24
C)
6, 20
D)
-16, -21
Find the predecessor of each of the f ollowing integers:
A)
-45 = ______
B)
-21 = ______
C)
-77 = ______
D)
-77 = ______
E)
-32 = ______
F)
-92 = ______
Find the sum of the f ollowing integers:
A)
86430 and 74206 = ?
B)
22392 and 74546 = ?
C)
-94561 and -77896 = ?
D)
64212 and 60852 = ?
Choose correct answer(s) f rom given choice
(4) T he sum of a two negative integers will be?
a. Positive integer
b. Negative integer
c. Positive if f irst number is larger
d. Negative if f irst number is larger
Fill in t he blanks
(5)
Find the value of f ollowing :
A)
B)
13 × 16 × 16 + ( -18 ) × 12 =
2 × 18 + ( -13 ) × 15 =
(6) Divide :
A)
B)
189 by -7 =
450 by -15 =
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ID : in-6-Integers [2]
(7) If a and b are two integers such that a is the predecessor of b, the value of a - b + 9 will be
.
(8)
Which number in the f ollowing pairs is larger:
A)
D)
B)
-15, -23 =
E)
-14, -15 =
C)
-15, -4 =
F)
22, -18 =
-8, 29 =
-2, 25 =
(9) Find the sum of the f ollowing integers:
A)
-10239 and 61162 =
B)
95834 and -29587 =
C)
21252 and -18599 =
D)
-43259 and 91504 =
E)
-30344 and 62957 =
F)
-27374 and -18305 =
(10) Find the value of the f ollowing :
A)
B)
74 + ( -127 ) + ( -45 ) + 45 + ( -197 ) + ( -151 ) =
200 + ( -152 ) + ( -109 ) + ( -146 ) + ( -134 ) + ( -193 ) + 55 =
Check True/False
(11) T he sum of a number and its negative number is zero
T rue
False
(12) Every negative number is less than every natural number.
T rue
False
(13) Z ero is an integer.
T rue
False
(14) T he absolute value of an integer is less than the integer .
T rue
False
(15) T he additive inverse of a positive number is positive.
T rue
False
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ID : in-6-Integers [3]
Answers
(1)
A)
-22
Step 1
We know that a negative number is smaller than the positive number, theref ore 22 < 7.
Step 2
T heref ore, we can say that the smaller number in the pair -22, 7 is -22.
B)
-26
Step 1
In case of negative numbers, the value of more negative number is smaller as
compared to the less negative number or positive number.
T heref ore, -26 < -24.
Step 2
Now, we can say that the smaller number in the pair -26, -24 is -26.
C)
6
Step 1
If we look at the pair 6, 20, we will notice that 6 < 20.
Step 2
T heref ore, we can say that the smaller number in the pair 6, 20 is 6.
D)
-21
Step 1
In case of negative numbers, the value of more negative number is smaller as
compared to the less negative number or positive number.
T heref ore, -21 < -16.
Step 2
Now, we can say that the smaller number in the pair -16, -21 is -21.
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ID : in-6-Integers [4]
(2)
A)
-46
Step 1
All positive numbers, negative numbers and zero are integer, accept f ractions.
we can write all integers in increasing order as:
Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
Step 2
T he predecessor of -45 is = -45 - 1 = -46.
B)
-22
Step 1
All positive numbers, negative numbers and zero are integer, accept f ractions.
we can write all integers in increasing order as:
Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
Step 2
T he predecessor of -21 is = -21 - 1 = -22.
C)
-78
Step 1
All positive numbers, negative numbers and zero are integer, accept f ractions.
we can write all integers in increasing order as:
Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
Step 2
T he predecessor of -77 is = -77 - 1 = -78.
D)
-78
Step 1
All positive numbers, negative numbers and zero are integer, accept f ractions.
we can write all integers in increasing order as:
Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
Step 2
T he predecessor of -77 is = -77 - 1 = -78.
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ID : in-6-Integers [5]
E)
-33
Step 1
All positive numbers, negative numbers and zero are integer, accept f ractions.
we can write all integers in increasing order as:
Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
Step 2
T he predecessor of -32 is = -32 - 1 = -33.
F)
-93
Step 1
All positive numbers, negative numbers and zero are integer, accept f ractions.
we can write all integers in increasing order as:
Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
Step 2
T he predecessor of -92 is = -92 - 1 = -93.
(3)
A)
160636
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of 86430 and 74206
Step 2
Now 86430 + 74206 = 160636
Step 3
T heref ore the sum of 86430 and 74206 = 160636
B)
96938
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of 22392 and 74546
Step 2
Now 22392 + 74546 = 96938
Step 3
T heref ore the sum of 22392 and 74546 = 96938
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ID : in-6-Integers [6]
C)
-172457
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of -94561 and -77896
Step 2
Now -94561 + (-77896) = -94561 -77896
= -172457
Step 3
T heref ore the sum of -94561 and -77896 = -172457
D)
125064
Step 1
If you look at the question caref ully, you will notice that you have to f ind the sum
of 64212 and 60852
Step 2
Now 64212 + 60852 = 125064
Step 3
T heref ore the sum of 64212 and 60852 = 125064
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ID : in-6-Integers [7]
(4) b. 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.
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ID : in-6-Integers [8]
(5)
A)
3112
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
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
Now 13 × 16 × 16 + ( -18 ) × 12 can be expressed as:
13 × 16 × 16 + ( -18 ) × 12
= (3328) + (-216)
= 3328 -216
= 3112
Step 3
T heref ore the value of 13 × 16 × 16 + ( -18 ) × 12 is 3112.
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ID : in-6-Integers [9]
B)
-159
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
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
Now 2 × 18 + ( -13 ) × 15 can be expressed as:
2 × 18 + ( -13 ) × 15
= (36) + (-195)
= 36 -195
= -159
Step 3
T heref ore the value of 2 × 18 + ( -13 ) × 15 is -159.
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ID : in-6-Integers [10]
(6)
A)
-27
Step 1
Division of a positive 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 positive number.
For example (-4)/(-2) = 2
Step 2
Let's divide 189 by 7,
Dividend↴
Divisor→ 7 ) 1 8 9 ( 27 ←Quotient
1 4
4 9
4 9
Remainder←
0
Step 3
T heref ore (189) &div; (-7) = -27
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ID : in-6-Integers [11]
B)
-30
Step 1
Division of a positive 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 positive number.
For example (-4)/(-2) = 2
Step 2
Let's divide 450 by 15,
Dividend↴
Divisor→ 15 ) 4 5 0 ( 30 ←Quotient
4 5
0
0
Remainder← 0
Step 3
T heref ore (450) &div; (-15) = -30
(7)
8
Step 1
If you look at the question caref ully, you will notice that a is the predecessor of b
T heref ore a = b - 1
Step 2
Now a - b + 9 = b - 1 - b + 9
[Since a = b - 1]
= -1 + 9
=8
Step 3
T heref ore the value of a - b + 9 = 8
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ID : in-6-Integers [12]
(8)
A)
-15
Step 1
In case of negative numbers, the value of more negative number is smaller as
compare to the less negative number or positive number,T heref ore -15 > -23
Step 2
Now we can say that the larger number in pair -15, -23 is -15
B)
-4
Step 1
In case of negative numbers, the value of more negative number is smaller as
compare to the less negative number or positive number,T heref ore -4 > -15
Step 2
Now we can say that the larger number in pair -15, -4 is -15
C)
29
Step 1
In case of negative numbers, the value of more negative number is smaller as
compare to the less negative number or positive number,T heref ore 29 > -8
Step 2
Now we can say that the larger number in pair -8, 29 is -8
D)
-14
Step 1
In case of negative numbers, the value of more negative number is smaller as
compare to the less negative number or positive number,T heref ore -14 > -15
Step 2
Now we can say that the larger number in pair -14, -15 is -14
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ID : in-6-Integers [13]
E)
22
Step 1
In case of negative numbers, the value of more negative number is smaller as
compare to the less negative number or positive number,T heref ore 22 > -18
Step 2
Now we can say that the larger number in pair 22, -18 is 22
F)
25
Step 1
In case of negative numbers, the value of more negative number is smaller as
compare to the less negative number or positive number,T heref ore 25 > -2
Step 2
Now we can say that the larger number in pair -2, 25 is -2
(9)
A)
50923
Step 1
Sum of -10239 and 61162
= (-10239) + (61162)
= 61162 - 10239
Step 2
Let's subtract 10239 f rom 61162
6 1 1 6 2
- 1 0 2 3 9
5 0 9 2 3
Step 3
T heref ore,
Sum = 61162 - 10239 = 50923
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ID : in-6-Integers [14]
B)
66247
Step 1
Sum of 95834 and -29587
= (95834) + (-29587)
= 95834 - 29587
Step 2
Let's subtract 29587 f rom 95834
9 5 8 3 4
- 2 9 5 8 7
6 6 2 4 7
Step 3
T heref ore,
Sum = 95834 - 29587 = 66247
C)
2653
Step 1
Sum of 21252 and -18599
= (21252) + (-18599)
= 21252 - 18599
Step 2
Let's subtract 18599 f rom 21252
2 1 2 5 2
- 1 8 5 9 9
2 6 5 3
Step 3
T heref ore,
Sum = 21252 - 18599 = 2653
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ID : in-6-Integers [15]
D)
48245
Step 1
Sum of -43259 and 91504
= (-43259) + (91504)
= 91504 - 43259
Step 2
Let's subtract 43259 f rom 91504
9 1 5 0 4
- 4 3 2 5 9
4 8 2 4 5
Step 3
T heref ore,
Sum = 91504 - 43259 = 48245
E)
32613
Step 1
Sum of -30344 and 62957
= (-30344) + (62957)
= 62957 - 30344
Step 2
Let's subtract 30344 f rom 62957
6 2 9 5 7
- 3 0 3 4 4
3 2 6 1 3
Step 3
T heref ore,
Sum = 62957 - 30344 = 32613
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ID : in-6-Integers [16]
F)
-45679
Step 1
Sum of -27374 and -18305,
= (-27374) + (-18305)
= - (27374 + 18305)
Step 2
Let's add 27374 and 18305
2 7 3 7 4
+ 1 8 3 0 5
4 5 6 7 9
Step 3
T heref ore,
Sum = - (27374 + 18305) = -45679
(10) A)
-401
Step 1
T he value of 74 + ( -127 ) + ( -45 ) + 45 + ( -197 ) + ( -151 ) can be f ound by
the f ollowing steps:
Step 2
Separating positive and negative terms like as:
74 + 45 + ( -127 -45 -197 -151 )
Step 3
Adding positive and negative terms separately.
119 + ( -520 )
Step 4
Subtracting the sum of negative terms f rom the positive terms.
119 -520 = -401.
Step 5
T heref ore the value of 74 + ( -127 ) + ( -45 ) + 45 + ( -197 ) + ( -151 ) is -401.
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ID : in-6-Integers [17]
B)
-479
Step 1
T he value of 200 + ( -152 ) + ( -109 ) + ( -146 ) + ( -134 ) + ( -193 ) + 55 can be
f ound by the f ollowing steps:
Step 2
Separating positive and negative terms like as:
200 + 55 + ( -152 -109 -146 -134 -193 )
Step 3
Adding positive and negative terms separately.
255 + ( -734 )
Step 4
Subtracting the sum of negative terms f rom the positive terms.
255 -734 = -479.
Step 5
T heref ore the value of 200 + ( -152 ) + ( -109 ) + ( -146 ) + ( -134 ) + ( -193 ) +
55 is -479.
(11) T rue
Step 1
Let us assume that n is any positive number and negative number of n is -n
Step 2
T he sum of n and -n = n + (-n)
=n-n
=0
Step 3
T heref ore we can say that the sum of a number and its negative number is zero.
T heref ore the answer is true.
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ID : in-6-Integers [18]
(12) T rue
Step 1
We know that if a number is on right hand side of another number on number line, f irst
number is greater other number.
T heref ore a > b, as a is on right side of b.
Step 2
Following picture shows that negative numbers are on lef t hand side of 0 on number line,
while natural numbers are on right hand side of 0
Step 3
From above number line, we can see that natural numbers are greater than negative
numbers.
T heref ore, given statement is true
(13) T rue
Step 1
Integers are the set of whole numbers (0, 1, 2, 3, ...) and their opposites (0, -1, -2, -3, ....).
Step 2
We can see that zero is an integer, theref ore given statement is true.
(14) 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 less than the integer"
is f alse.
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ID : in-6-Integers [19]
(15) 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.
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