Practice Variables in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A symbol (usually a letter like xx) that represents an unknown or changing quantity in a mathematical expression.

Like a box that can hold any number. 'x+5=12x + 5 = 12' asks: what's in the box?

Showing a random 20 of 50 problems.

Example 1

medium
Evaluate 2x+6x\frac{2x + 6}{x} when x=2x = 2.

Example 2

easy
Do 2x2x and xโ‹…2x \cdot 2 mean the same thing?

Example 3

medium
Why does xโˆ’x=0x - x = 0 for every value of xx?

Example 4

challenge
If nn is even, explain why n2n^2 is even using a variable.

Example 5

medium
If pp is the price of one pencil in dollars, write an expression for the cost of 1212 pencils.

Example 6

easy
Write an expression for 'a number nn doubled, then added to 55'.

Example 7

challenge
Distinguish the roles of xx in f(x)=x2f(x) = x^2 versus f(3)=9f(3) = 9.

Example 8

easy
If x=4x = 4, evaluate x+7x + 7.

Example 9

medium
If y=3xy = 3x and xx increases from 22 to 33, how much does yy increase?

Example 10

hard
Evaluate x2โˆ’2xy+y2x^2 - 2xy + y^2 when x=4,y=1x = 4, y = 1.

Example 11

easy
Fill in: a ____ is a symbol that stands for an unknown or changing quantity.

Example 12

medium
Evaluate x+yxโˆ’y\frac{x + y}{x - y} when x=7,y=3x = 7, y = 3.

Example 13

easy
If aa stands for apples and bb for bananas, what does a+ba + b count?

Example 14

medium
A taxi charges a $3 flat fee plus $2 per mile. Write an expression for the cost of mm miles.

Example 15

medium
A variable pp represents a price in dollars. Why can't p=โˆ’4p = -4 here?

Example 16

hard
A bag has nn red marbles and 2n+32n + 3 blue marbles. Write an expression for the total marbles.

Example 17

hard
If A=ฯ€r2A = \pi r^2 and r=3r = 3, find AA in terms of ฯ€\pi.

Example 18

easy
If 2n=182n = 18, what is the value of nn?

Example 19

medium
If T=2ฯ€L/gT = 2\pi\sqrt{L/g}, which symbols are variables and which is a constant?

Example 20

hard
The sum of three consecutive integers is 4848. Let the smallest be nn. Write and solve an equation for nn.
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