Variable Expressions

Grade 5 Math — Complete Notes & Formulae

1. Write Variable Expressions

A variable expression is a mathematical phrase combining numbers, variables (like x, y), and operation symbols without an equal sign.

4 + x : "Four plus a number x"
n - 7 : "Seven less than n"
5y : "Five times y"
m ÷ 3 : "A number m divided by 3"

2. Write Variable Expressions: Word Problems

Convert word phrases into variable expressions:

"Three more than a number t" → t + 3
"Twice a number k" → 2k
"Half of p" → p ÷ 2
"A number y decreased by nine" → y - 9

3. Evaluate Variable Expressions

To evaluate an expression, replace the variable with a given value and solve:

Example: What is 6 + x when x = 4?
6 + 4 = 10

General Formula: A + B (if A and B are variables)
Substitute values: A = a, B = b

4. Write Variable Equations: Word Problems

An equation sets two expressions equal. Word problems often ask you to create equations:

"The sum of x and three is nine": x + 3 = 9
"y divided by 5 equals 2": y ÷ 5 = 2
"Twice a number a is 16": 2a = 16

5. Find a Value Using Two-Variable Equations

Equations with two variables let you find values for one variable when you know the other.

Standard form: ax + by = c
Example: If 3x + 4y = 24 and x = 4, find y.
3(4) + 4y = 24 → 12 + 4y = 24 → 4y = 12 → y = 3

6. Complete a Table for a Two-Variable Relationship

List possible values for two variables in a table, using an equation or a rule.

x	y	Rule
1	5	y = x + 4
2	6	y = x + 4
3	7	y = x + 4

7. Complete a Table from a Graph

From a graph, list the (x, y) pairs in a table:

x	y
0	3
1	5
2	7

Rule: y = 2x + 3

8. Graph Patterns Using Rules

To graph a rule: make a table of x values, calculate y for each, and plot the points.

Rule Example: y = 3x
If x = 1, y = 3. If x = 2, y = 6. If x = 3, y = 9. Plot points (1,3), (2,6), (3,9).

Graph these points to see the pattern!

9. Graph a Two-Variable Relationship

Equations like y = 2x + 1 can be represented on a graph. Each point (x, y) that fits the equation is on the line.

Find different x values, solve for y, and plot each (x,y) pair.

10. Write a Two-Variable Equation

A two-variable equation relates x and y by a rule:

y = x + 2
y = 5x
3x + 2y = 18
x - y = 4

General Formula for a Line: y = mx + b
m: slope, b: y-intercept

💡 Quick Reference: Formulas & Tips

Write an expression: Use variables and numbers, no "="" sign
Evaluate: Substitute values for variables, solve using order of operations
Equation: Has "=" and shows two sides are equal
Two-variable equation: Relates x and y; solved for values of one if the other is known
Table: List several possible values for both variables according to the equation/rule.
Graph: Plot points from the equation on coordinate plane to visualize relationships

🌟 Practice converting words to expressions & equations, and try solving real-world problems!

Variable Expressions | 5th Grade Math