Chapter 6 of Class 7 Maths focuses on Integers and their operations, including addition, subtraction, multiplication, and division. Integers are whole numbers that can be positive, negative, or zero. Understanding how to work with integers is fundamental for solving algebraic expressions and equations.
Let’s go through the exercises and solutions to get a better understanding of how to perform operations with integers.
Exercise 6.1: Addition of Integers
Q1.
Add:5+(−3)5 + (-3)5+(−3)
Solution:
When adding a positive number and a negative number, subtract the absolute values and keep the sign of the number with the larger absolute value.5+(−3)=5−3=25 + (-3) = 5 – 3 = 25+(−3)=5−3=2
Q2.
Add:−7+4-7 + 4−7+4
Solution:
−7+4=−3-7 + 4 = -3−7+4=−3
(As the negative number has a larger absolute value.)
Q3.
Add:−12+(−8)-12 + (-8)−12+(−8)
Solution:
When adding two negative integers, add their absolute values and keep the negative sign.−12+(−8)=−12−8=−20-12 + (-8) = -12 – 8 = -20−12+(−8)=−12−8=−20
Q4.
Add:6+96 + 96+9
Solution:
6+9=156 + 9 = 156+9=15
Q5.
Add:−4+7-4 + 7−4+7
Solution:
−4+7=3-4 + 7 = 3−4+7=3
(Here, the positive integer is larger.)
Exercise 6.2: Subtraction of Integers
Q1.
Subtract:8−58 – 58−5
Solution:
8−5=38 – 5 = 38−5=3
Q2.
Subtract:−9−(−4)-9 – (-4)−9−(−4)
Solution:
When subtracting a negative number, it’s the same as adding the positive of that number.−9−(−4)=−9+4=−5-9 – (-4) = -9 + 4 = -5−9−(−4)=−9+4=−5
Q3.
Subtract:−6−2-6 – 2−6−2
Solution:
−6−2=−8-6 – 2 = -8−6−2=−8
(When subtracting a positive integer, we move further in the negative direction.)
Q4.
Subtract:5−(−3)5 – (-3)5−(−3)
Solution:
5−(−3)=5+3=85 – (-3) = 5 + 3 = 85−(−3)=5+3=8
Q5.
Subtract:−7−5-7 – 5−7−5
Solution:
−7−5=−12-7 – 5 = -12−7−5=−12
Exercise 6.3: Multiplication of Integers
Q1.
Multiply:6×(−3)6 \times (-3)6×(−3)
Solution:
When multiplying a positive integer by a negative integer, the result is negative.6×(−3)=−186 \times (-3) = -186×(−3)=−18
Q2.
Multiply:−5×4-5 \times 4−5×4
Solution:
−5×4=−20-5 \times 4 = -20−5×4=−20
Q3.
Multiply:−7×(−2)-7 \times (-2)−7×(−2)
Solution:
When multiplying two negative integers, the result is positive.−7×(−2)=14-7 \times (-2) = 14−7×(−2)=14
Q4.
Multiply:9×(−5)9 \times (-5)9×(−5)
Solution:
9×(−5)=−459 \times (-5) = -459×(−5)=−45
Q5.
Multiply:−8×3-8 \times 3−8×3
Solution:
−8×3=−24-8 \times 3 = -24−8×3=−24
Exercise 6.4: Division of Integers
Q1.
Divide:6÷(−2)6 \div (-2)6÷(−2)
Solution:
When dividing a positive integer by a negative integer, the result is negative.6÷(−2)=−36 \div (-2) = -36÷(−2)=−3
Q2.
Divide:−10÷2-10 \div 2−10÷2
Solution:
−10÷2=−5-10 \div 2 = -5−10÷2=−5
Q3.
Divide:−12÷(−4)-12 \div (-4)−12÷(−4)
Solution:
When dividing two negative integers, the result is positive.−12÷(−4)=3-12 \div (-4) = 3−12÷(−4)=3
Q4.
Divide:15÷(−3)15 \div (-3)15÷(−3)
Solution:
15÷(−3)=−515 \div (-3) = -515÷(−3)=−5
Q5.
Divide:−20÷5-20 \div 5−20÷5
Solution:
−20÷5=−4-20 \div 5 = -4−20÷5=−4
Exercise 6.5: Word Problems on Integers
Q1.
The temperature in a city dropped from 5°C to -3°C. What is the change in temperature?
Solution:
The change in temperature is calculated by subtracting the final temperature from the initial temperature:5−(−3)=5+3=85 – (-3) = 5 + 3 = 85−(−3)=5+3=8
So, the change in temperature is 8°C.
Q2.
A football team lost 10 points in one match and then gained 15 points in the next. What is their net change in points?
Solution:
The net change in points is:−10+15=5-10 + 15 = 5−10+15=5
So, the net change is +5 points.
Q3.
A submarine is at a depth of 150 meters below sea level and rises by 50 meters. What is its new position?
Solution:
The new position of the submarine is:−150+50=−100-150 + 50 = -100−150+50=−100
So, the submarine is now at a depth of 100 meters below sea level.
Q4.
The bank balance of a person is $500. He withdraws $200 and later deposits $100. What is his current balance?
Solution:
The current balance is:500−200+100=400500 – 200 + 100 = 400500−200+100=400
So, the person’s current balance is $400.
Q5.
In a game, a player earns 50 points in the first round, loses 30 points in the second round, and gains 40 points in the third round. What is the total score?
Solution:
The total score is:50−30+40=6050 – 30 + 40 = 6050−30+40=60
So, the total score is 60 points.
Additional Practice Questions:
1.
Add:−8+6-8 + 6−8+6
Solution:−8+6=−2-8 + 6 = -2−8+6=−2
2.
Add:−5+(−9)-5 + (-9)−5+(−9)
Solution:−5+(−9)=−14-5 + (-9) = -14−5+(−9)=−14
3.
Add:12+(−3)12 + (-3)12+(−3)
Solution:12+(−3)=912 + (-3) = 912+(−3)=9
4.
Add:−15+7-15 + 7−15+7
Solution:−15+7=−8-15 + 7 = -8−15+7=−8
5.
Add:0+(−4)0 + (-4)0+(−4)
Solution:0+(−4)=−40 + (-4) = -40+(−4)=−4
6.
Subtract:5−(−3)5 – (-3)5−(−3)
Solution:5−(−3)=5+3=85 – (-3) = 5 + 3 = 85−(−3)=5+3=8
7.
Subtract:−10−6-10 – 6−10−6
Solution:−10−6=−16-10 – 6 = -16−10−6=−16
8.
Subtract:−20−(−5)-20 – (-5)−20−(−5)
Solution:−20−(−5)=−20+5=−15-20 – (-5) = -20 + 5 = -15−20−(−5)=−20+5=−15
9.
Subtract:7−127 – 127−12
Solution:7−12=−57 – 12 = -57−12=−5
10.
Subtract:−5−(−8)-5 – (-8)−5−(−8)
Solution:−5−(−8)=−5+8=3-5 – (-8) = -5 + 8 = 3−5−(−8)=−5+8=3
11.
Multiply:−6×4-6 \times 4−6×4
Solution:−6×4=−24-6 \times 4 = -24−6×4=−24
12.
Multiply:7×(−3)7 \times (-3)7×(−3)
Solution:7×(−3)=−217 \times (-3) = -217×(−3)=−21
13.
Multiply:−8×(−2)-8 \times (-2)−8×(−2)
Solution:−8×(−2)=16-8 \times (-2) = 16−8×(−2)=16
14.
Multiply:0×50 \times 50×5
Solution:0×5=00 \times 5 = 00×5=0
15.
Multiply:9×(−6)9 \times (-6)9×(−6)
Solution:9×(−6)=−549 \times (-6) = -549×(−6)=−54
16.
Divide:−36÷9-36 \div 9−36÷9
Solution:−36÷9=−4-36 \div 9 = -4−36÷9=−4
17.
Divide:−81÷(−9)-81 \div (-9)−81÷(−9)
Solution:−81÷(−9)=9-81 \div (-9) = 9−81÷(−9)=9
18.
Divide:42÷(−6)42 \div (-6)42÷(−6)
Solution:42÷(−6)=−742 \div (-6) = -742÷(−6)=−7
19.
Divide:25÷(−5)25 \div (-5)25÷(−5)
Solution:25÷(−5)=−525 \div (-5) = -525÷(−5)=−5
20.
Divide:−56÷7-56 \div 7−56÷7
Solution:−56÷7=−8-56 \div 7 = -8−56÷7=−8
21.
Solve the expression:−3+5×2-3 + 5 \times 2−3+5×2
Solution:
First, multiply:5×2=105 \times 2 = 105×2=10
Now, add:−3+10=7-3 + 10 = 7−3+10=7
22.
Solve the expression:4×(−6)+24 \times (-6) + 24×(−6)+2
Solution:
First, multiply:4×(−6)=−244 \times (-6) = -244×(−6)=−24
Now, add:−24+2=−22-24 + 2 = -22−24+2=−22
23.
Solve the expression:10−4×210 – 4 \times 210−4×2
Solution:
First, multiply:4×2=84 \times 2 = 84×2=8
Now, subtract:10−8=210 – 8 = 210−8=2
24.
Solve the expression:(−3)×3+5(-3) \times 3 + 5(−3)×3+5
Solution:
First, multiply:(−3)×3=−9(-3) \times 3 = -9(−3)×3=−9
Now, add:−9+5=−4-9 + 5 = -4−9+5=−4
25.
Solve the expression:−7+4×(−3)-7 + 4 \times (-3)−7+4×(−3)
Solution:
First, multiply:4×(−3)=−124 \times (-3) = -124×(−3)=−12
Now, add:−7+(−12)=−19-7 + (-12) = -19−7+(−12)=−19
26.
Solve the equation:x+8=−10x + 8 = -10x+8=−10
Solution:
Subtract 8 from both sides:x=−10−8=−18x = -10 – 8 = -18x=−10−8=−18
27.
Solve the equation:−5x=25-5x = 25−5x=25
Solution:
Divide both sides by -5:x=25−5=−5x = \frac{25}{-5} = -5x=−525=−5
28.
Solve the equation:3x+7=−23x + 7 = -23x+7=−2
Solution:
Subtract 7 from both sides:3x=−2−7=−93x = -2 – 7 = -93x=−2−7=−9
Now, divide by 3:x=−93=−3x = \frac{-9}{3} = -3x=3−9=−3
29.
Solve the equation:x−4=6x – 4 = 6x−4=6
Solution:
Add 4 to both sides:x=6+4=10x = 6 + 4 = 10x=6+4=10
30.
Solve the equation:x+3=−7x + 3 = -7x+3=−7
Solution:
Subtract 3 from both sides:x=−7−3=−10x = -7 – 3 = -10x=−7−3=−10
Summary:
These 30 additional questions cover a variety of operations with integers, including addition, subtraction, multiplication, division, and solving simple equations. Working through these problems will help reinforce your understanding of how to manage and manipulate integers in different scenarios. Keep practicing to improve your skills!
Integers are essential in various mathematical concepts. Whether it is adding, subtracting, multiplying, or dividing integers, mastering these operations will provide a solid foundation for further studies in algebra and arithmetic.
Through consistent practice and solving word problems, you can strengthen your understanding of how to work with integers. Keep practicing and refer to these solutions for better clarity on solving integer-based problems!
Also Read: Class 7 Maths – Chapter 4: Simple Equations Solutions
Class 7 Maths Chapter 5 Worksheet with Answers: Simple Equations
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