Introduction to Solving Equations with Decimals

What you’ll learn to do: Solve equations with decimals using properties of addition and subtraction

A female swimmer wearing googles and a yellow cap doing the freestyle stroke in one lane of a pool

To calculate the difference between two swimmers’ race times, you’ll need to write an equation with decimals.

Kim and Alyssa are on the same high school swim team, and they’re always competing for the fastest time in the 50-meter freestyle event. In the last race, the difference between Kim’s time and Alyssa’s time was 1.36 seconds. If Alyssa swam the race in 36.79 seconds, what was Kim’s time? To solve this problem, you’ll need to translate the information given to an equation and then solve it. Read on to find out more about solving equations with decimals.

Before you get started, take this readiness quiz.

readiness quiz

If you missed this problem, review the example below.

Evaluate [latex]y-\Large\frac{5}{6}[/latex] when [latex]y=-\Large\frac{2}{3}[/latex]

Show Solution

If you missed this problem, review the following example.

Evaluate [latex]20-z\text{ when}[/latex]

[latex]z=12[/latex]
[latex]z=-12[/latex]

Show Solution

If you missed this problem, review this video.

	[latex]y-\Large\frac{5}{6}[/latex]
Substitute [latex]\color{red}{--\Large\frac{2}{3}}[/latex] for y.	[latex]\color{red}{--\Large\frac{2}{3}} -\Large\frac{5}{6}[/latex]
Rewrite as equivalent fractions with the LCD, [latex]6[/latex].	[latex]-\Large\frac{4}{6}-\frac{5}{6}[/latex]
Subtract.	[latex]-\Large\frac{9}{6}[/latex]
Simplify.	[latex]-\Large\frac{3}{2}[/latex]

[latex]20--z[/latex]
[latex]\text{Substitute }\color{red}{12}\text{ for }z[/latex]	[latex]20--\color{red}{12}[/latex]
Subtract.	[latex]8[/latex]

[latex]20--z[/latex]
[latex]\text{Substitute }\color{red}{--12}\text{ for }z[/latex]	[latex]20--(\color{red}{--12})[/latex]
Subtract.	[latex]32[/latex]

Module 5: Decimals