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Introduction Quiz - CBSE Class 7 Mathematics

Free practice quiz: Introduction (CBSE Class 7 Mathematics). 14 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 14 multiple-choice questions on Introduction, and 14 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Learn the key ideas first ↓

Learn the key ideas Beta

Equation, Variable and Solution

An equation says two expressions are equal. The left side (LHS) must equal the right side (RHS).
A variable like x stands for an unknown number we must find.
The solution is the value of the variable that makes LHS equal to RHS.

Equation form

\[\text{LHS} = \text{RHS}\]

Sides can swap

\[b = ax \iff ax = b\]

Common mistake: Thinking an equation is solved without checking. Always put your value back into the equation to see if LHS equals RHS.

Keep the Balance

An equation is like a balanced scale. Whatever you do to one side, do to the other.
You may add, subtract, multiply or divide both sides by the same number, but never divide by zero.

Add to both sides

\[a = b \Rightarrow a + c = b + c\]

Subtract from both sides

\[a = b \Rightarrow a - c = b - c\]

Multiply both sides

\[a = b \Rightarrow ac = bc\]

Divide both sides

\[a = b \Rightarrow \frac{a}{c} = \frac{b}{c},\ c \neq 0\]

Common mistake: Changing only one side of the equation, for example adding a number to the LHS but forgetting to add it to the RHS.

Transposing: Do the Opposite

Moving a term to the other side changes its operation to the opposite one.
Plus becomes minus, minus becomes plus, times becomes divide, divide becomes times.

Undo addition

\[x + a = b \Rightarrow x = b - a\]

Undo subtraction

\[x - a = b \Rightarrow x = b + a\]

Undo multiplication

\[ax = b \Rightarrow x = \frac{b}{a}\]

Undo division

\[\frac{x}{a} = b \Rightarrow x = ab\]

Common mistake: Moving a term across the equals sign without changing its sign or operation, such as keeping plus as plus.

Two-Step Equations

When an equation has both multiplication and addition or subtraction, undo the addition or subtraction first.
Then undo the multiplication or division to get the variable alone.

Form ax + b = c

\[ax + b = c \Rightarrow x = \frac{c - b}{a}\]

Form ax - b = c

\[ax - b = c \Rightarrow x = \frac{c + b}{a}\]

Common mistake: Dividing first and forgetting to divide the added or subtracted number too. Remove the constant before dividing by the coefficient.

Exam tips

Check every answer by substituting it back into the original equation.
If the variable is on the right side, simply swap the two sides first.
A fraction like x over a means x divided by a, so multiply by a.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the solution of the equation 5 + x = 9?
Show answer
Answer: B. 4
To find the solution, subtract 5 from both sides of the equation, which gives x = 4.
Find the value of x in the equation x/2 = 10.
Show answer
Answer: D. 20
Multiply both sides by 2 to solve for x, giving x = 20.
Solve the equation: 8 = 2x.
Show answer
Answer: B. 4
Divide both sides by 2 to find x = 4.
If 7x = 49, what is x?
Show answer
Answer: B. 7
Divide 49 by 7 to find x = 7.
If x/4 = 3, what is x?
Show answer
Answer: B. 12
Multiply both sides by 4 to get x = 12.

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