EQ - Solve Equations with Decimals Lesson

Solve Equations with Decimals

In this lesson, you will learn to solve equations containing decimals. Let us begin with an activity involving mental math and estimation. In the following mathematical sentences, use mental math to find the missing number.

1. 14.75 + _____ = 30

- - Solution: 15.25

2. 10 - _____ = 5.5

- - Solution: 4.5

3. 3 * _____ = 7.5

- - Solution: 2.5

4. _____ ÷ 0.5 = 6

- - Solution: 3.0

In the following equations, use a calculator to find the value of x.

5. 14.75 + x = 30

- - Solution: 15.25

6. 10 - x = 5.5

- - Solution: 4.5

7. 3 * x = 7

- - Solution: 2.5

8. x ÷ 0.5 = 6

- - Solution: 3.0

Notice that the answers in both sections are the same.

Investigate

Students on the cross-country team were running 50-yard dashes as part of a fitness test. The slowest time on the team was 3.62 seconds slower than the fastest time of 7.4 seconds. You can write an equation to represent this situation. The slowest time s minus 3.62 is equal to the fastest time of 7.4 seconds.

Slowest time minus 3.62 is 7.4
S - 3.62 = 7.4

Example 1

plus and minus Solve equations by adding or subtracting.

$LaTeX: s-3.62=7.4 \\ \text{Use the Addition Property of Equality}\\ s-3.62=7.4\\ +3.62\:\:\: +3.62\: \text{Add 3.62 to both sides.}\\ s=11.02$ $s-3.62=7.4 \\ \text{Use the Addition Property of Equality}\\ s-3.62=7.4\\ +3.62\:\:\: +3.62\: \text{Add 3.62 to both sides.}\\ s=11.02$

equation image indicator $LaTeX: x+15.52=25 \\ \text{Use the Subtraction Property of Equality}\\ x+15.52=25 \\ -15.52\:\:\: -15.52\: \text{Subtract 15.52 to both sides.}\\ x=9.48$ $x+15.52=25 \\ \text{Use the Subtraction Property of Equality}\\ x+15.52=25 \\ -15.52\:\:\: -15.52\: \text{Subtract 15.52 to both sides.}\\ x=9.48$

Example 2

multiply and divide Solve equations by multiplying or dividing.

$LaTeX: \frac{n}{2.8}=2.2\\ \text{Use the Multiplication Property of Equality}\\ 2.8\cdot \frac{n}{2.8}=2.2\cdot 2.8 \text{Multiply by 2.8 to both sides.}\\ n=6.16$ $\frac{n}{2.8}=2.2\\ \text{Use the Multiplication Property of Equality}\\ 2.8\cdot \frac{n}{2.8}=2.2\cdot 2.8 \text{Multiply by 2.8 to both sides.}\\ n=6.16$

equation image indicator $LaTeX: 5=2.6y\\ \text{Use the Division Property of Equality}\\ \frac{5}{2.6}=\frac{2.6y}{2.6}\:\:\text{Divide by 2.6 on both sides.}\\ \frac{5}{2.6}=y\:\:\text{Think 5 ÷ 2.6 = 50 ÷ 26 (Great strategy for solving decimal division!)} \\ y=1.92$ $5=2.6y\\ \text{Use the Division Property of Equality}\\ \frac{5}{2.6}=\frac{2.6y}{2.6}\:\:\text{Divide by 2.6 on both sides.}\\ \frac{5}{2.6}=y\:\:\text{Think 5 ÷ 2.6 = 50 ÷ 26 (Great strategy for solving decimal division!)} \\ y=1.92$

Investigate

person on wakeboard Kayce wants to purchase a new wakeboard that costs $350.00. If she earns $9.75 per hour at work, how many hours must she work to earn enough money to buy the wakeboard?

Strategy

First, rewrite the question as a statement.

Find the number of hours Kayce must work to earn the $350.00. Translate the words into math. Use a variable to represent the number of hours.

LaTeX: 9.75x=350 $9.75x=350$

Solution

$LaTeX: \frac{9.75x}{9.75}=\frac{350}{975}\:\text{(Divide both sides by 9.75 (Think 35000 divided by 975)}$ $\frac{9.75x}{9.75}=\frac{350}{975}\:\text{(Divide both sides by 9.75 (Think 35000 divided by 975)}$

x = 35.89 Kayce will have to work 36 hours to earn enough to purchase the wakeboard.

Equations with Decimals Practice

Solve Equations with Decimals Homework

Now that you have spent some time learning strategies for solving equations with decimal numbers, you are ready to complete your Equations: Solving Equations with Decimals Homework. Download your homework by CLICKING HERE. Links to an external site.

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key Links to an external site..

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