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Practice Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions based on the NCERT syllabus. Solve fresh MCQs on solving equations, transposition, verification, variables, and simple word problems.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 2
Difficulty Level: Easy to Moderate
Based On: NCERT Syllabus
Introduction
Simple equations help us find unknown quantities using mathematical relationships. An equation contains an equal sign and states that two mathematical expressions have the same value.
For example:
$$2x+3=11$$
Here, $x$ is the unknown variable. We can find its value by performing suitable operations on both sides of the equation.
In Practice Set 2, students will practise equations involving addition, subtraction, multiplication, division, and simple real-life situations.
What You Will Learn
✔ Solving equations with addition and subtraction
✔ Solving equations involving multiplication
✔ Finding unknown quantities
✔ Applying inverse operations
✔ Verifying solutions
✔ Forming equations from statements
Why This Topic Is Important
Simple equations are one of the basic building blocks of algebra. They help students convert verbal statements into mathematical equations and solve unknown quantities logically.
These skills are also useful in word problems involving ages, numbers, costs, and quantities.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ State Board Exams
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ NCERT-Based Practice
✔ Mathematics Revision
Q1. Find the value of $x$:
$$x+15=32$$
A) $15$
B) $16$
C) $17$
D) $18$
Answer:
C) $17$
Useful Concept
To remove a number added to the variable, subtract the same number from both sides.
Solution
Given:
$$x+15=32$$
Subtract $15$ from both sides:
$$x+15-15=32-15$$
Therefore:
$$x=17$$
Verification
Substitute $x=17$:
$$17+15=32$$
$$32=32$$
Therefore, the solution is correct.
Hence, the correct answer is:
C) $17$
Q2. If
$$x-18=25,$$
then the value of $x$ is:
A) $7$
B) $25$
C) $43$
D) $45$
Answer:
C) $43$
Useful Concept
When a number is subtracted from a variable, add the same number to both sides.
Solution
Given:
$$x-18=25$$
Add $18$ to both sides:
$$x-18+18=25+18$$
Therefore:
$$x=43$$
Verification
$$43-18=25$$
$$25=25$$
Hence, the correct answer is:
C) $43$
Q3. Which value of $x$ satisfies the equation
$$7x=56?$$
A) $6$
B) $7$
C) $8$
D) $9$
Answer:
C) $8$
Useful Concept
When a variable is multiplied by a number, divide both sides by that number to find the variable.
Solution
Given:
$$7x=56$$
Divide both sides by $7$:
$$\frac{7x}{7}=\frac{56}{7}$$
Therefore:
$$x=8$$
Verification
$$7(8)=56$$
$$56=56$$
Thus, $x=8$ is the correct solution.
Hence, the correct answer is:
C) $8$
Q4. The quotient of a number and $5$ is $9. Which equation represents the statement?
A) $x+5=9$
B) $x-5=9$
C) $5x=9$
D) $\frac{x}{5}=9$
Answer:
D) $\frac{x}{5}=9$
Useful Concept
The word quotient indicates division. If a number is represented by $x$, then the quotient of the number and $5$ is:
$$\frac{x}{5}$$
Solution
Let the unknown number be:
$$x$$
According to the statement:
The quotient of a number and $5$ is $9$.
Therefore:
$$\frac{x}{5}=9$$
Thus, the equation is:
$$\frac{x}{5}=9$$
Hence, the correct answer is:
D) $\frac{x}{5}=9$
If we solve it:
$$x=9\times5$$
$$x=45$$
Verification:
$$\frac{45}{5}=9$$
So the equation is correct.
Q5. Riya has some pencils. After buying 8 more pencils, she has 23 pencils in total. If $x$ represents the number of pencils she had initially, which equation represents the situation?
A) $x-8=23$
B) $x+8=23$
C) $8x=23$
D) $x+23=8$
Answer:
B) $x+8=23$
Useful Concept
When an amount is increased by a certain quantity, we use addition.
Solution
Let the initial number of pencils be:
$$x$$
Riya buys $8$ more pencils.
Therefore, the total number of pencils becomes:
$$x+8$$
According to the question, the total is $23$:
$$x+8=23$$
Therefore, the required equation is:
$$x+8=23$$
Hence, the correct answer is:
B) $x+8=23$
We can also find the initial number:
$$x=23-8$$
$$x=15$$
Verification:
$$15+8=23$$
Therefore, the equation is correct.
Important Formulas & Concepts
Addition Equation
If:
$$x+a=b$$
then:
$$x=b-a$$
Subtraction Equation
If:
$$x-a=b$$
then:
$$x=b+a$$
Multiplication Equation
If:
$$ax=b$$
then:
$$x=\frac{b}{a}$$
where $a\ne0$.
Division Equation
If:
$$\frac{x}{a}=b$$
then:
$$x=ab$$
where $a\ne0$.
Inverse Operations
Addition and subtraction are inverse operations.
Multiplication and division are inverse operations.
These operations help us isolate the variable.
Verification
To verify a solution, substitute the obtained value into the original equation.
If both sides are equal, the solution is correct.
Related Practice Questions
Q1. Solve:
$$x+18=35$$
Q2. Find $x$:
$$x-12=28$$
Q3. Solve:
$$6x=42$$
Q4. Solve:
$$\frac{x}{7}=8$$
Q5. A number increased by $9$ is $31$. Form an equation and find the number.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find $x$:
$$x+13=29$$
A) $14$
B) $15$
C) $16$
D) $17$
Q2. Find $x$:
$$x-16=20$$
A) $34$
B) $35$
C) $36$
D) $37$
Q3. If:
$$8x=72,$$
then $x$ is:
A) $7$
B) $8$
C) $9$
D) $10$
Q4. Which equation represents “a number divided by $6$ is $7$”?
A) $x+6=7$
B) $x-6=7$
C) $6x=7$
D) $\frac{x}{6}=7$
Q5. If $x=12$, which equation is true?
A) $x+5=16$
B) $x-5=7$
C) $2x=24$
D) $x+8=18$
Exam Tips
✔ Identify the operation used in the equation.
✔ Use the inverse operation to isolate the variable.
✔ Write each step clearly.
✔ Keep both sides of an equation balanced.
✔ Pay attention to words such as sum, difference, product, quotient, increased, decreased.
✔ Verify the final answer whenever possible.
✔ In word problems, define the unknown quantity before forming the equation.
Quick Revision Notes
✔ Addition and subtraction are inverse operations.
✔ Multiplication and division are inverse operations.
✔ $x+a=b$ gives:
$$x=b-a$$
✔ $x-a=b$ gives:
$$x=b+a$$
✔ $ax=b$ gives:
$$x=\frac{b}{a}$$
✔ $\frac{x}{a}=b$ gives:
$$x=ab$$
✔ Verification means substituting the answer into the original equation.
Common Mistakes Students Make
❌ Using subtraction when division is required.
❌ Forgetting to reverse the operation while isolating the variable.
❌ Making arithmetic mistakes while calculating.
❌ Confusing product with sum.
❌ Confusing quotient with difference.
❌ Not reading word problems carefully.
❌ Skipping verification when the calculation is complicated.
Key Takeaways
✔ Equations can be solved using inverse operations.
✔ Addition is reversed by subtraction.
✔ Subtraction is reversed by addition.
✔ Multiplication is reversed by division.
✔ Division is reversed by multiplication.
✔ Word statements can be converted into equations.
✔ Verification confirms the correctness of a solution.
FAQs
Q. What are inverse operations?
Answer:
Inverse operations undo the effect of each other. Addition and subtraction are inverse operations, while multiplication and division are inverse operations.
Q. How do we solve $x+15=30$?
Answer:
Subtract $15$ from both sides:
$$x=30-15$$
Therefore:
$$x=15$$
Q. How do we solve $x-10=20$?
Answer:
Add $10$ to both sides:
$$x=20+10$$
Therefore:
$$x=30$$
Q. How do we solve $5x=40$?
Answer:
Divide both sides by $5$:
$$x=\frac{40}{5}=8$$
Q. How do we solve $\frac{x}{4}=9$?
Answer:
Multiply both sides by $4$:
$$x=9\times4=36$$
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh practice on solving equations using inverse operations, forming equations from statements, and applying equations to simple real-life situations.
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