What is an algebraic expression?

A mathematical phrase that contains numbers, variables, and operations

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Algebraic Expressions Quiz - CBSE Class 6 Mathematics

Free practice quiz: Algebraic Expressions (CBSE Class 6 Mathematics). 15 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 15 multiple-choice questions on Algebraic Expressions, and 15 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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Variables and Algebraic Expressions

A variable is a letter, like x or n, that stands for a number that can change.
An algebraic expression joins numbers and variables using +, −, × or ÷. It has no equals sign.
A rule or pattern can be written as an expression using a variable, like a perimeter rule.

Number times variable

\[k \times m = km\]

Perimeter of a square of side s

\[P = 4s\]

Common mistake: Calling something with an equals sign, like x + a = b, an expression. That is an equation, not an expression.

Terms, Coefficients and Constants

Terms are the parts of an expression separated by + or − signs.
The coefficient is the number multiplying the variable. A term with no variable is the constant term.

In ax + b: coefficient of x is a, constant is b

\[ax + b\]

Coefficient of a lone variable is 1

\[x = 1x\]

Common mistake: Dropping the sign of a term. In p − kq, the term is −kq, not kq.

Like Terms and Simplifying

Like terms have the same variable raised to the same power. Only like terms can be added or subtracted.
To combine like terms, add or subtract their coefficients and keep the variable part the same.
To remove brackets, multiply the number outside by every term inside the brackets.

Adding like terms

\[ax + bx = (a + b)x\]

Subtracting like terms

\[ax - bx = (a - b)x\]

Distributive rule

\[a(b + c) = ab + ac\]

Common mistake: Adding unlike terms together, such as writing ap + bq as (a + b)pq. They must stay separate.

Finding the Value of an Expression

To find the value, replace each variable by its given number, then calculate.
Put a negative value inside brackets when you substitute. Do multiplication before addition and subtraction.

Square of a negative number is positive

\[(-k)^2 = k^2\]

Negative times negative is positive

\[(-a) \times (-b) = ab\]

Common mistake: Substituting a negative number without brackets, so −k² is calculated instead of (−k)², which gives the wrong sign.

Solving Simple Equations

An equation says two expressions are equal. Solving means finding the value of the variable that makes it true.
Do the same operation on both sides to keep the balance, until the variable is alone.

Undo addition by subtracting

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

Undo multiplication by dividing

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

Remove brackets first

\[a(x + b) = c \Rightarrow ax + ab = c\]

Common mistake: Moving a term to the other side of the equals sign without changing its sign, for example + becoming + instead of −.

Exam tips

After solving an equation, put your answer back into it to check both sides are equal.
Underline like terms in the same colour before combining them.
When a variable is given a negative value, always use brackets while substituting.

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Sample questions

What is an algebraic expression?
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Answer: B. A mathematical phrase that contains numbers, variables, and operations
An algebraic expression is composed of numbers, variables, and operations (like addition and subtraction) without an equal sign.
In the expression 4y - 7z + 10, what are the terms?
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Answer: B. 4y, -7z, 10
The terms in an algebraic expression are separated by '+' or '-'. Therefore, the terms are 4y, -7z, and 10.
If the expression is x^2 + 3x - 4 and x = -1, what is its value?
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Answer: C. 0
Substituting -1 for x gives: (-1)^2 + 3(-1) - 4 = 1 - 3 - 4 = 0.
What is the result of simplifying the expression 8y - 2y?
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Answer: A. 6y
By combining like terms, you get: 8y - 2y = (8 - 2)y = 6y.
Factor the expression x^2 - 16.
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Answer: A. (x - 4)(x + 4)
x^2 - 16 is a difference of squares, which factors to (x - 4)(x + 4).