New learning Composite Mathematics Class 7 Solutions Chapter 1
Mamta Mund founder, Owner of https://www.mathsgrade.com/
In Mathematics, numbers play a vital role. In everyday life also numbers play a big role. In the early days, people count herds using stone or sticks. They improved by using finger counting. Then after they give the numbers as a name that is zero(0) for nothing, one object for digit 1, and so on…
Numbers are of different types
- Counting numbers (Natural numbers)- The numbers that used for counting are known as counting or natural numbers.
Ex- 1, 2,3,………….
2. Whole Numbers- consists of natural numbers and 0. The whole number starts with zero(0).
Ex- 0,1,2,3,………….
3. Integers- Integers are positive and Negative.
Positive integers are having a plus sign.
Ex- 1,2,3….
Negative Integers are having a minus sign.
Ex- -1,-2,-3,…………
New Learning Composite Mathematics S K Gupta Anubhuti Gangal class 7 solutions
Mamta Mund, founder-owner of https://www.mathsgrade.com/
Self-practice — 1(A)
1. Write each number as an integer in each of the following situations.
a)Profit of Rs 17,000 in the first year and loss of Rs 5000 in the second year.
Solution- +17000 and -5000
b) Withdrawal of Rs 800 from the bank
Solution- -800
c) 5 degrees above zero degrees.
Solution- +5 degree
d) 2000 m above sea level.
Solution- 2000 m
e) 500 m below sea level.
Solution- -500 m
f) Increase in weight by 5 kg.
Solution- +5 kg
g) Decrease in weight by 2 kg.
Solution- -2 kg
How To represent integers on Number Line-
b) -5 , Opposite of -5 is 5
Comparison Of Integers
How to Compare Integers
3. Compare the integer. Use > or <
a) -10 ……… -15
Solution- Comparing the integers, first look at the integer. The negative sign of the smaller number is the largest than the negative sign of the bigger number.
- 10 > -15
b) — 29 ……… -19
Solution- Comparing the integers, first look at the integer. The negative sign of the larger number is less than the negative sign of the smaller number.
- 29 < -19
c) — 20 ……… 20
Solution- Comparing the integers, first look at the integer. A negative Integer is always smaller than a positive integer.
-20 < 20
d) 7 ……… — 7
Solution- Comparing the integers, first look at the integer. Positive Integer is always greater than the negative integer.
7 > — 7
e) -8,700 ……… — 8,000
Solution- Comparing the integers, first look at the integer. the negative sign of the bigger number is smaller than the negative sign of the smaller number.
- 8,700 < — 8,000
Ordering Of Integers
Absolute Value-
5. Write the absolute value of each.
a) |-27|
Solution- |-27|=27
b) |18|
Solution- | 18|=18
c) |-509|
Solution- |-509|=509
d) |306|
Solution- |306|=306
How To Compare Integers
6. Compare write > ,< or =
a) 35 ……….|35|
Solution- |35|=35
So 35=|35|
b) -19 …….|-27|
Solution- |-27|=27
-19 <27
So -19 <|-27|
c) -|-5| ……….|5|
Solution- |-5|=5 and |5|=5
We know -5<5
so-|-5| <|5|
d) |-200|………-300
Solution- |-200|=200
we know 200>300
So|-200|>-300
e) |-25| ……….|25|
Solution- |-25|=25 and |25|=25
We know 25=25
so |-25|=|25|
f) -|-39|………-35
Solution- |-39|=39
we know -39<-35
So -|-39|<-35
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Opposite Of Integers
7. Write the opposite of
a) |45|
Solution- we know |45|=45
so opposite of |45|=-|45|
b) |-50|
Solution- We know |-50|=50
So Opposite of |-50|=-|-50|
c) -|-25|
Solution- we know |-25|=25
so opposite of — |-25|=|25|
d) -|18|
Solution- We know |18|=18
So Opposite of -|18|=|18|
Addition Of Integers On Number Line
Addition Of Integers
1.When we add integers of equal signs, add the absolute value of the number and place the sign of that number.
2.When we add integers of opposite signs, subtract the smaller number from the bigger number and place the sign of the bigger number.
Sum of Integers
10. Find each sum.
a) (-15)+(-7)
Solution- We know 15+7=22
-15+(-7)= -22
b) 13+27
Solution- 13+27=40
c) (-44)+4
Solution- We know 44–4 = 40
- 44+4 = — 40
d) 36+(-60)
Solution- We know 60–36=24
So 36+(-60)= -24
e) (- 94)+(-6)
Solution- We know 94 +6 = 100
- 94+(-6) = — 100
f) 39+(- 9)
Solution- We know 39–9=30
So 39+(-9)= 30
g) 50-|-50|
Solution- We know |-50|=50
50-|-50|=50–50=0
11. Find each sum.
a) (-18)+29+(-11)
Solution- (-18)+29+(-11)
=(-18)+(-11)+29
=-29+29
=0
So (-18)+29+(-11)=0
b) |-25|+9-|-4|
Solution- |-25|+9-|-4|
=25+9–4 [|-25|=25 and |-4|=4]
=34–4
=30
So |-25|+9-|-4|=30
Subtraction Of Integers
- When we subtract integers of opposite signs, subtract the smaller number from the bigger number and place the sign of the bigger number.
12. Find each difference.
a) 8–15
Solution- We know 15–8=7
So 8–15=-7
b) -7-(-12)
Solution- -7-(-12)=-7+12=5
c) 3-(-7)
Solution- We know 3-(-7)=3+7=10
So 3-(-7)=10
d) 8-(-15)
Solution- 8-(-15)=8+15=23
So 8-(-15)=23
e) -8–12
Solution- We know 8+12=20
So -8–12=-20
f) 9-(-9)
Solution- 9-(-9)=9+9=18
So 9-(-9)=18
g) 89-(-11)
Solution- We know 89-(-11)=89+11=100
So 89-(-11)=100
h) -129-(-130)
Solution- -129-(-130)=-129+130=1
So -129-(-130)=1
Word Problems On Integers
13. If the deepest point in the sea is 11,600 m below sea level and the highest mountain top is 8,846 m above sea level. Then the difference in their elevation is
a) 2,754 m b) 20,446 m c) 21,406 m d) 2,952 m
Solution- Difference in the elevation between mountain top and deepest point in se level
=8,846-(-11,600)m
=8,846+11,600 m
=20,446 m
So option b) is correct
14. The sum of two integers is 50. If one of them is -38, the other is :
a) 88 b) 12 c) -88 d) -12
Solution- Given one integer is -38
The Sum of two integers is 50
Let the other number be x
-38+x=50
⇒x=50+38
⇒x=88
So other number is 88
So option a) is correct
15. If p and q are two integers such that p is the predecessor of q. then p-q is equal to
a) 1 b) 0 c) 2 d) -1
Solution- Given p is the predecessor of q.
We know the predecessor is before a number of a number.
The predecessor of q will be q — 1
given p = q — 1
So p — q= -1
16. Which sum is not negative?
a) -40+(-30) b) -70+65 c) -63+82 d) -49+0
Solution- a) We know 40+30=70
So -40+(-30)=-70
b) We know 70–65=5
So -70+65=-5
Solution- c) We know 82–63=19
So -63+82=19
d) We know any integer added with zero we get the number itself.
- 49+0=-49
So option c) is correct
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Properties Of Integers
- Closure Property- if a, and b are integers then a+b is also an integer. Integers are closed over addition
- Commutative Property- If a, and b are integers then a+b=b+a. Integers of addition are commutative.
- Associative Property- If a, b, and c are three integers,
then a+(b+c)=(a+b)+c
4. Distributive Property of integers- If a, b, and c are three integers, then
5. Additive Identity- if a is an integer then
a+0=a
0 is the additive identity of integers.
6. Additive Inverse- If a is an integer, then a+(-a)=0
-a is the additive Inverse or Negative of an integer.
3) (-18)+0=……
Solution- (-18)+0=(-18)
This is known as Additive Identity or the zero property of integers.
4) -25+……….=0
Solution- -25+25=0
This is known as Additive Inverse property
5) 0+………=-68
Solution- 0+(-68)=(-68)
This is known as Additive Identity property
6) 27-……….=27
Solution- 27–0=27
This is known as the Closure property of Integers.
7) 24+[(-15+2)]=[24+……]+2
Solution- 24+[(-15+2)]=[24+(-15)]+2
This is known as Associative property of integers.
8) (59+11)+(-30)=………..+[11+(-30)]
Solution- (59+11)+(-30)=59+[11+(-30)]
This is known as Associative property of integers.
9) -9+[17+(-4)]=(-9+17)+……….
Solution- -9+[17+(-4)]=(-9+17)+(-4)
This is known as the Associative property of integers.
10)Predecessor of -12 is……….
Solution- Predecessor of -12 is -12–1=-13
This is known as the Closure property of Subtraction of integer.
Multiplication Of Integers
Rules for multiplication of Integers having signs
Self Practice 1(C)
1. Determine whether the product is positive or negative.
a) 2×5
Solution- 2×5=10 is positive
b) -2×5
Solution- -2×5=-10 is negative
As positive x negative=negative
c) 2×-5
Solution- 2×(-5)=-10 is negative
d) -2×-5
Solution- -2×-5=10 is positive
As negative x negative = positive
e) -25×-16
Solution- -25×-16=400 is positive
As negative x negative = positive
f) -80×14
Solution- -80×14=-1120 is negative
g) -803×-17
Solution- -803×-17=13651 is positive
As negative x negative = positive
h) 38×(-11)
Solution- 38×(-11)=-418 is negative
As positive x negative= negative
2. Find each product.
a) 8×5
Solution- 8×5=40 is positive
b) 6×(-7)
Solution- 6×(-7)=-42 is negative
c) -6×9
Solution- -6×9=-54 is negative
d) -9×10
Solution- -9×10=-90 is negative
e) 9×(-8)
Solution- 9×(-8)=-72 is negative
f) 4×(-15)
Solution- 4×(-15)=-60 is negative
g) -23×5
Solution- -23×5=-115 is negative
h) -12×7
Solution- -12×7=-84 is negative
3. Find each product.
a) -7×-8
Solution- -7×-8=56 is positive
b) -9×-10
Solution- -9×-10=90 is positive
c) -15×-4
Solution- -15×-4=60 is positive
d) -19×5
Solution- -19×5=-95 is negative
e) -12×-12
Solution- -12×-12=144 is positive
f) 23×-30
Solution- 23×-30=-690 is negative
g) -16×-12
Solution- -16×-12=192 is positive
h) -50×-50
Solution- -50×-50=2500 is positive
Properties of Multiplication of Integers
- Closure Property — if a, and b are integers, then
is also an integer.
2. Commutative Property- If a, and b are integers. then
3. Associative property- If a,b, and c are three integers. then
4. Distributive Property- If a,b, and c are three integers. then
5. Multiplicative Identity- if a is an integer. then
1 is called the Multiplicative identity of integers.
6. Multiplicative Inverse Property- If a is an integer. then
is called the multiplicative Inverse of integer a
4. Find each product.
a)2×5×6
Solution- 2×5×6
=(2×5)×6 (Associative property)
=10×6
=60
b) 8×-6×-7
Solution- 8×-6×-7
=[8×(-6)]×(-7) (Associative property)
=-48×(-7)
=336
c) -9×-5×-2
Solution- -9×-5×-2
=[-9×(-5)]×(-2) (Associative property)
=45×(-2)
=-90
d) -4×-6×-10
Solution- -4×-6×-10
=[-4×(-6)]×(-10) (Associative property)
=24×(-10)
=-240
e) -5×4×-9
Solution- -5×4×-9
=[-5×4]×(-9) (Associative property)
=-20×(-9)
=180
f) -2×3×-4×-5
Solution- -2×3×-4×-5
=(-2×3×-4)×(-5)
=[[(-2)×3]×(-4)]×(-5)
=-6×(-4)×(-5)
=[(-6)×(-4)]×(-5)=24×(-5)=-120
g) -1×-2×3×-4
Solution- -1×-2×3×-4
=(-1×-2×3)×(-4)
=[[(-1)×(-2)]×(3)]×(-4)
=[2×3]×(-4)
=6×(-4)=-24
h) -1×-1×-1×-1
Solution- -1×-1×-1×-1
=(-1×-1×-1)×(-1)
=[[(-1)×(-1)]×(-1)]×(-1)
=[1×(-1)]×(-1)
=-1×(-1)=1
Division Of Integers
How to divide two integers
Self Practice 1(D)
1. Determine whether each quotient is positive or negative.
a) 18÷9
Solution- 18÷9=2 is positive
As 18 and 9 are both positive, so quotient will also be positive.
b) -32÷4
Solution- -32÷4=-8 is negative
As -32 and 4 are of different signs, so quotient will be a negative sign.
c)45÷(-9)
Solution- 45÷(-9)=-5 is negative
As 45 and -9 are different signs, so quotient will be negative.
d) -65÷(-13)
Solution- -65÷(-13)=5 is positive
As -65 and -13 are of the same signs, so quotient will be a positive sign.
e) -62÷7
Solution- -62÷7=-8 R 6 Quotient is negative
As -62 and 7 are of different signs, so quotient will be negative.
f) 28÷(-7)
Solution- 28÷(-7)=-4 is negative
As 28 and -7 are different signs, so quotient will be a negative sign.
g) -56÷(-8)
Solution- -56÷(-8)=7 Quotient is positive
As -56 and -8 are of different signs, so quotient will be positive.
h) -91÷(-7)
Solution- -91÷(-7)=13 is positive
As -91 and -7 are of the same signs, so quotient will be a positive sign
2. Divide and find each quotient.
a) 38÷2
Solution- 38÷2=19 Quotient is positive
As 38 and 2 are of the same signs, so quotient will be positive.
b) -6÷3
Solution- -6÷3=-2 is negative
As -6 and 3 are of different signs, so quotient will be a negative sign.
c) -16÷8
Solution- -16÷8=-2 Quotient is negative
As -16 and 8 are of different signs, so quotient will be negative.
d) 36÷(-4)
Solution- 36÷(-4)=-9 is negative
As 36 and -4 are of different signs, so quotient will be a negative sign.
e) 49÷(-7)
Solution- 49÷(-7)=-7 Quotient is negative
As 49 and -7 are of different signs, so quotient will be negative.
f) -70÷14
Solution- -70÷14=-5 is negative
As -70 and 14 are of different signs, so quotient will be a negative sign.
g) -100÷10
Solution- -100÷10=-10 Quotient is negative
As -100 and 10 are of different signs, so quotient will be negative.
h) 80÷(-16)
Solution- 80÷(-16)=-5 is negative
As 80 and -16 are of different signs, so quotient will be a negative sign.
3. Divide and find each quotient.
a) -8÷(-4)
Solution- -8÷(-4)=2 Quotient is positive
As -8 and -4 are of the same signs, so quotient will be positive.
b) -63÷(-9)
Solution- -63÷(-9)=7 is positive
As -63 and -9 are of the same signs, so quotient will be a positive sign
c) 128÷(-16)
Solution- 128÷(-16)=-8 Quotient is negative
As 128 and -16 are of different signs, so quotient will be negative.
d) -52÷(-13)
Solution- -52÷(-13)=4 is positive
As -52 and -13 are of the same signs, so quotient will be a positive sign.
e) -27÷3
Solution- -27÷3=-9 Quotient is negative
As -27 and 3 are of different signs, so quotient will be negative.
f) 84÷(-14)
Solution- 84÷(-14)=-6 is negative
As 84 and -14 are different signs, so quotient will be negative.
g) -126÷(-18)
Solution- -128÷(-18)=7 Quotient is positive
As -126 and -18 are of the same signs, so quotient will be positive.
h) -400÷(-16)
Solution- -400÷(-16)=25 is positive
As -400 and -16 are of the same signs, so quotient will be positive.
4. Evaluate.
a) 10+(-40)÷8
Solution- 10+(-40)÷8
=10–5 (Division has high precedence than
addition)
=5
b) -7×15÷(-5)
Solution- -7×15÷(-5)
=-105÷(-5) (multiplication perform first)
=21
c) -72÷(-9)×5
Solution- -72÷(-9)×5
=8×5 (Division perform first)
=40
d) 20+7×8÷(-2)
Solution- 20+7×8÷(-2)” “
=20+56÷(-2) (multiplication perform first)
=20+(-28)
=20–28
=-8
properties Of Multiplication
Self Practice 1(E)
1. Verify and name the property used.
a)18×(-15)=(-15)×18
Solution- LHS- 18×(-15)=-270
RHS — (-15)×18=-270
So LHS=RHS
This is the commutative property of multiplication
b) 15×[3×(-12)]=(15×3)×(-12)
Solution- LHS- 15×[3×(-12)]
=15×(-36)
=-540
RHS — (15×3)×(-12)
=45×(-12)
=-540
So LHS=RHS
This is the Associative property of multiplication
c) 20×[75+(-15)]=(20×75)+20×(-15)
Solution- LHS- 20×[75+(-15)]
=20×60
=1200
RHS — (20×75)+20×(-15)
=1500+(-300)
=1500–300
=1200
So LHS=RHS
This is the Distributive property of multiplication over addition
d) -12×[(-7)+5]=(-12)×(-7)+(-12)×5
Solution- LHS- -12×[(-7)+5]
=-12×(-2)
=24
RHS -(-12)×(-7)+(-12)×5
=84–60
=24
So LHS=RHS
This is the Distributive property of multiplication over addition
2. Fill in the blanks
a) 28×……….=28
Solution- 28×1=28
This property is known as the Identity property of multiplication
b) -16×………=16
Solution- -16×(-1)=16
1 is the multiplicative identity. When we multiply integers of the same signs, the result will be positive.
c) 285×……….=0
Solution- 285×0=0
This property is known as the zero property of Integer
d) 0÷63=………
Solution- 0÷63=0
e) -95÷……….=-1
Solution- -95÷95=-1
The result will be a negative sign when we multiply integers of different signs.
f) -50×…….=50
Solution- -50×(-1)=50
The result will be a positive sign when we multiply integers of the same sign.
3. Evaluate by using suitable properties.
a) 37×(-58)+(-58)×(-27)
Solution- 37×(-58)+(-58)×(-27)
=(-58)×[37+(-27)] (Distributive Property)
=(-58)×10
=-580
b) -45×103
Solution- -45×103
=-45×(100+3)
=(-45)×100+(-45)×3 (Distributive property)
=-4500–135
=-4635
c) 4×87×(-25)
Solution- 4×87×(-25)
=87×4×(-25) (Commutative property)
=87×[4×(-25)] (Associative property)
=87×(-100)
=-8700
d) 19×(-25)×(-4)×(-8)
Solution- 19×[(-25)×(-4)]×(-8)
(Associative property)
=19×[100×(-8)]
=19×(-800)
=-15200
e) -16×(-39)
Solution- -16×(-39)
=-16×(-40+1)
=(-16)×(-40)+(-16)×1 (Distributive property)
=640–16
=624
f) -68×(-19)+68
Solution- -68×(-19)+68
=68×19×(-1)×(-1)+68
=68×19×1+68
=68×19+68×1
=68×(19+1) (Distributive property)
=68×20
=1360
Mental Maths Questions On Integers
1)(-5)×(-4)
Solution- (-5)×(-4)=20
2) 0÷398
Solution- 0÷398=0
3) 298÷1
Solution- 298÷1=298
4)(-28)÷4
Solution- (-28)÷4=(-7)
5) (-64)÷(-8)
Solution- (-64)÷(-8)=8
6) 2986×0
Solution- 2986×0=0
7) (89)÷89
Solution- 89÷89=1
8) (-67)÷67
Solution- (-67)÷67=-1
9) (-3)×5×(-2)
Solution- (-3)×5×(-2)=30
10) 35÷7×4
Solution- 35÷7×4=5×4=20
Multiple Choice Questions on Integers
1) (-20)÷5 is not the same as
a) 5÷(-20)
b) -(20÷5)
c) 20÷(-5)
d) -4
Solution- a) 5÷(-20)=-1÷4=-1/4
b) -(20÷5)=-4
c) 20÷(-5)=-4
So option (a) is the answer. As all option has value -4 which is equal to the value of (-20)÷5
2) Which of the following does not represent an integer
a) 0÷(-8) b) 15÷(-3) c) (-4)×(-5) d) 8÷3
Solution- a) 0÷(-8)=0
b) 15÷(-3)=-5
c) (-4)×(-5)=20
d) 8÷3=8/3
So option (d) is the answer. As all option has a value which is an integer but option d) has a value which is not an integer
3) Which of the following is different from others.
a) (-7)×(-1)
b) -49÷(-7)
c) 27÷3–2
d) 28÷(-4)
Solution- a) (-7)×(-1)=7
b) -49÷(-7)=7
C) 27÷3–2 =9–2=7
d) 28÷(-4)=-7
So option (d) is the answer. As all option has positive integer but option (d) has a negative value
4) Which of the expressions are equal to -30?
I)(-5)×6
II) -60÷(-2) I
II) -30×1
IV) -8×3–6
a) I only
b) I and II
c) I, III
and IV d) I, II, III, IV
Solution- I) (-5)×6=-30
II) -60÷(-2)=30
III)-30×1 =-30
IV)-8×3–6=-24–6=-30
So option ( c) is the answer. As all option, I, III, And IV have Negative integer -30 but option II has a value which is positive.
5) Which expression has a value greater than the value of -40÷(-8)?
a)30÷(-5)
b) -80÷8
c) -35÷(-7)
d) -54÷(-9)
Solution- We know -40÷(-8)=5 which is positive as both 40 and 8 have the same sign. So the result will be positive.
a) 30÷(-5)=-6
b) -80÷8=-10
c) -35÷(-7) =5
d) -54÷(-9)=6
We know 6 > 5
So option (d) is the answer. As all option, a, b, AND c have a value which is less than the value of the expression — 40÷(-8)
6) The value of 80÷5×(-3) is
a)65
b) 95
c) -48
d) -19
Solution-
80÷5×(-3)
=16×(-3) (Division perform first)
=-48
So option c) is the answer
7) The value 8÷(-1) does not lie between
a)0 and -10
b) 0 and 10
c) -1 and -10
d) -5 and -9
Solution-
8÷(-1)=-8 is a negative integer
So -8 does not lie between 0 and 10
So option b) is the answer
8)-69×103 is not the same as
a)-69×(100+3)
b) (-69)×100+(-69)×3
c) -69×3+100
d) (-60–9)×103
Solution- We can write -69×103 as
-69×103=-69×(100+3)
And -69×103=(-69)×100+(-69)×3 which is the distributive property of multiplication
We can write -69×103 as
-69×103=(-60–9)×103
And -69×3+100=-207+100=-107 which is not the same as any of the above options.
So option c) is the answer
9) -56×(-99)+56 is equal to
a)5600
b) -5600
c) 5544
d) 5488
Solution- We can write (-56)×(-99)+56 as
(-56)×(-99)+56
=56×99×(-1)×(-1)+56
=56×99×1+56
=56×99+56
=56×(99+1)
=56×100
=5600
So option a) is the answer
10) Which of the following is the odd one?
a)80÷(-5)
b) -48÷3
c) 112÷7
d) (-8)×2
Solution- All option a), b) and d) have negative integer -16 except option c) which has positive integer 16
So option c) is the answer
11) Which of the following expression has a different value?
a)(-3)×4×5×(-8)
b) 3×(-4)×(-5)×8
c) 3×(-4)×5×(-8)
d) (-3)×(-4)×5×(-8)
Solution-
a)(-3)×4×5×(-8)=3×4×5×8=480
b) 3×(-4)×(-5)×8=3×4×5×8=480
(c) 3×(-4)×5×(-8)=3×4×5×8=480
d) (-3)×(-4)×5×(-8)=(-1)×3×4×5×8=-480
So option d) is the answer as it has a negative integer
12) Which of the following is the odd one out?
a)0÷816
b) 16÷1
c) 635×0
d) -36÷9+4
Solution-
a)0÷816=0
b)16÷1=16
c) 635×0=0
d) -36÷9+4=-4+4=0
So option b) is the answer as it has a value of 16 but all other options have zero value
New Learning Composite Mathematics Class 7 Solutions
d) If a,b,c are any three integers , then a(b+c)=……. Signs.
Solution- ab+bc
e) The Identity element of multiplication and division is ………..
Solution- 1
2) State True or False
a) For any integer a, a÷0=0
Solution- False It is undefined
b) For all integers a, and b, a÷b≠b÷a
Solution- True Division is not commutative
c) When an integer is divided by itself, the quotient is 1
Solution- True
d) (-57)÷(-19)=-3
Solution- False When the integers both are of the same sign, the result will be positive. It will be 3
e) The product of two integers is -56, if one of the integers is 8, then the other integer is 7
Solution- False -56÷8=-7
3) Find the value of
a) (-18)×(-30)
Solution- 540 When the integers both are of the same sign, the result will be positive.
b) (-89)×(-237)×0×18
Solution- 0
c)-1728÷12
Solution- -144 When both integers are of different signs, then the result will be negative.
d)(-38970)÷(-1)
Solution- 38970 When the integers both are of the same sign, the result will be positive. Dividing any number by 1 we get the number itself
e) (-1×-4×-4×-10×5)÷80×(-1)
Solution- 800÷80×(-1)
=10×(-1)
=-10
4) Insert > or < in the box to mke it a correct statement.
a) (-49)÷7 ………(-96)÷12
Solution- (-49)÷7=-7 and (-96)÷12=-8
We know -7>-8
So (-49)÷7 >(-96)÷12
b) (-5)×15 ………1800÷(-25)
Solution- (-5)×15=-75 and 1800÷(-25)=-72
We know -75<-72
So(-5)×15 <1800÷(-25)
c) 27–81÷3 ………-8×9÷(3)
Solution- 27–81÷3=27–27=0
and -8×9÷3=-72÷3=-24
We know 0>-24
So 27–81÷3>-8×9÷(3)
d) -110÷(-2) ………-8×(-7)
Solution- -110÷(-2)=55
and -8×(-7)=56
We know 55<56
So -110÷(-2)<-8×(-7)
5) Bunty is playing a game with a regular die, If the number that turns up is even, he will gain four times, the number that came up. if it is odd, he will lose 10 times the number that comes up. Bunty tosses the game 10 times in the game. What will be his final score?
He tosses : 6,3, 1, 5, 4, 2, 6,3,2, 4 in ten throws.
Solution- if the number of the dice is even, he gains 4 times the number
If the number of the dice is odd, he losses 10 times the number
10 tosses of Bunty is 6,3, 1, 5, 4, 2, 6, 3, 2, 4
Even numbers score is
4×6+4×4+4×2+4×6+4×2+4×4
=24+16+8+24+8+16
=96
The odd number score is
-10×3+(-10)×1+(-10)×5+(-10)×3
=-30–10–50–30
=-120
Final score is
96–120
=-24
6) Evaluate :
a) (-187)×(-35)+(-187)×(-65)
Solution- (-187)×(-35)+(-187)×(-65)
=(-187)×[(-35)+(-65)]
=(-187)×(-100)
=18700
b) (-54)÷9×(-7)×(-1)
Solution- (-54)÷9×(-7)×(-1)
=(-6)×(-7)×(-1)
=(-42)
7) Evaluate :
[(-36)÷9]÷(-2) is
a) -2
b) 2
c) 4
d) -4
Solution-[(-36)÷9]÷(-2)
=(-4)÷(-2)
=2
8) If a, and b are integers , which of the following may not be an integer?
a) a+b
b) a-b
c) a×b
d) a÷b
Solution- d) a÷b=a/b may be a rational number.
So option d) is correct
9) Which expression has a value smaller than
[-30÷(-5)]×(-10)
a)-12×4
b) 50÷(-2)
c) (-280)÷4
d) [(-30)×(-6)]÷(-9)
Solution- [-30÷(-5)]×(-10)
=6×(-10)
=-60
a)-12×4=-48
b) 50÷(-2)=-25
c)(-280)÷4=-70
d) [(-30)×(-6)]÷(-9)
=180÷(-9)
=-20
We know -48>-60, -25>-60
-70<-60 and -20 >-60
So option c) is correct
10) A 1-kilogram rock dropped into an ocean, would take 37 minutes to reach -6660 m. If the rock dropped steadily. How far will it fall in 1 minute?
a)167m
b) -167 m
c) -180 m
d) -188 m
Solution- In 1-minute rock will fall in the ocean is
6660 m ÷37 min=-180 m
So option c) is the correct answer.
