Lesson 4: Solve Equations with Decimals

New Concept

This lesson applies the Properties of Equality to solve equations involving decimals. You'll learn to find unknown values, check if a decimal is a solution, and translate real-world problems into equations to solve.

What’s next

Next, you'll tackle interactive examples showing how to apply each property. Then, test your skills with a series of practice problems.

Property

Determine whether a number is a solution to an equation.

Step 1. Substitute the number for the variable in the equation.

Step 2. Simplify the expressions on both sides of the equation.

Property

Subtraction Property of Equality: For any numbers $a$, $b$, and $c$, if $a = b$, then $a - c = b - c$.

Addition Property of Equality: For any numbers $a$, $b$, and $c$, if $a = b$, then $a + c = b + c$.

Use these properties to isolate the variable by performing the inverse operation on both sides of the equation.

Property

The Division Property of Equality: For any numbers $a$, $b$, and $c$, and $c \neq 0$, if $a = b$, then $\frac{a}{c} = \frac{b}{c}$.

The Multiplication Property of Equality: For any numbers $a$, $b$, and $c$, if $a = b$, then $ac = bc$.

Use these properties to isolate the variable by performing the inverse operation on both sides of the equation.

Property

Translate word sentences into algebraic equations by identifying keywords for operations.

• Sum indicates addition (+).
• Difference indicates subtraction (-).
• Product indicates multiplication (⋅).
• Quotient indicates division (÷).
• Is or is equal to indicates equality (=).

Examples

• 'The difference of $n$ and $4.3$ is $2.1$' translates to the equation $n - 4.3 = 2.1$. Solving by adding $4.3$ to both sides gives $n = 6.4$.