- 5.4 Solve Equations with Decimals
- Introduction
- 1.1 Introduction to Whole Numbers
- 1.2 Add Whole Numbers
- 1.3 Subtract Whole Numbers
- 1.4 Multiply Whole Numbers
- 1.5 Divide Whole Numbers
- Key Concepts
- Review Exercises
- Practice Test
- Introduction to the Language of Algebra
- 2.1 Use the Language of Algebra
- 2.2 Evaluate, Simplify, and Translate Expressions
- 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
- 2.4 Find Multiples and Factors
- 2.5 Prime Factorization and the Least Common Multiple
- Introduction to Integers
- 3.1 Introduction to Integers
- 3.2 Add Integers
- 3.3 Subtract Integers
- 3.4 Multiply and Divide Integers
- 3.5 Solve Equations Using Integers; The Division Property of Equality
- Introduction to Fractions
- 4.1 Visualize Fractions
- 4.2 Multiply and Divide Fractions
- 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
- 4.4 Add and Subtract Fractions with Common Denominators
- 4.5 Add and Subtract Fractions with Different Denominators
- 4.6 Add and Subtract Mixed Numbers
- 4.7 Solve Equations with Fractions
- Introduction to Decimals
- 5.1 Decimals
- 5.2 Decimal Operations
- 5.3 Decimals and Fractions
- 5.5 Averages and Probability
- 5.6 Ratios and Rate
- 5.7 Simplify and Use Square Roots
- Introduction to Percents
- 6.1 Understand Percent
- 6.2 Solve General Applications of Percent
- 6.3 Solve Sales Tax, Commission, and Discount Applications
- 6.4 Solve Simple Interest Applications
- 6.5 Solve Proportions and their Applications
- Introduction to the Properties of Real Numbers
- 7.1 Rational and Irrational Numbers
- 7.2 Commutative and Associative Properties
- 7.3 Distributive Property
- 7.4 Properties of Identity, Inverses, and Zero
- 7.5 Systems of Measurement
- Introduction to Solving Linear Equations
- 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
- 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
- 8.3 Solve Equations with Variables and Constants on Both Sides
- 8.4 Solve Equations with Fraction or Decimal Coefficients
- 9.1 Use a Problem Solving Strategy
- 9.2 Solve Money Applications
- 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
- 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
- 9.5 Solve Geometry Applications: Circles and Irregular Figures
- 9.6 Solve Geometry Applications: Volume and Surface Area
- 9.7 Solve a Formula for a Specific Variable
- Introduction to Polynomials
- 10.1 Add and Subtract Polynomials
- 10.2 Use Multiplication Properties of Exponents
- 10.3 Multiply Polynomials
- 10.4 Divide Monomials
- 10.5 Integer Exponents and Scientific Notation
- 10.6 Introduction to Factoring Polynomials
- 11.1 Use the Rectangular Coordinate System
- 11.2 Graphing Linear Equations
- 11.3 Graphing with Intercepts
- 11.4 Understand Slope of a Line
- A | Cumulative Review
- B | Powers and Roots Tables
- C | Geometric Formulas

## Learning Objectives

By the end of this section, you will be able to:

- Determine whether a decimal is a solution of an equation
- Solve equations with decimals
- Translate to an equation and solve

## Be Prepared 5.10

Before you get started, take this readiness quiz.

## Be Prepared 5.11

Evaluate 15 − y 15 − y when y = −5 . y = −5 . If you missed this problem, review Example 3.41 .

## Be Prepared 5.12

Solve n − 7 = 42 . n − 7 = 42 . If you missed this problem, review Example 4.99 .

Determine Whether a Decimal is a Solution of an Equation

## 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.
- If so, the number is a solution.
- If not, the number is not a solution.

## Example 5.40

Determine whether each of the following is a solution of x − 0.7 = 1.5 : x − 0.7 = 1.5 :

ⓐ x = 1 x = 1 ⓑ x = −0.8 x = −0.8 ⓒ x = 2.2 x = 2.2

Since x = 1 x = 1 does not result in a true equation, 1 1 is not a solution to the equation.

Since x = 2.2 x = 2.2 results in a true equation, 2.2 2.2 is a solution to the equation.

## Try It 5.79

Determine whether each value is a solution of the given equation.

x − 0.6 = 1.3 : x − 0.6 = 1.3 : ⓐ x = 0.7 x = 0.7 ⓑ x = 1.9 x = 1.9 ⓒ x = −0.7 x = −0.7

## Try It 5.80

y − 0.4 = 1.7 : y − 0.4 = 1.7 : ⓐ y = 2.1 y = 2.1 ⓑ y = 1.3 y = 1.3 ⓒ −1.3 −1.3

## Properties of Equality

## Example 5.41

Solve: y + 2.3 = −4.7 . y + 2.3 = −4.7 .

We will use the Subtraction Property of Equality to isolate the variable.

## Try It 5.81

Solve: y + 2.7 = −5.3 . y + 2.7 = −5.3 .

## Try It 5.82

Solve: y + 3.6 = −4.8 . y + 3.6 = −4.8 .

## Example 5.42

Solve: a − 4.75 = −1.39 . a − 4.75 = −1.39 .

We will use the Addition Property of Equality.

Since the result is a true statement, a = 3.36 a = 3.36 is a solution to the equation.

## Try It 5.83

Solve: a − 3.93 = −2.86 . a − 3.93 = −2.86 .

## Try It 5.84

Solve: n − 3.47 = −2.64 . n − 3.47 = −2.64 .

## Example 5.43

Solve: −4.8 = 0.8 n . −4.8 = 0.8 n .

We will use the Division Property of Equality.

Use the Properties of Equality to find a value for n . n .

Since n = −6 n = −6 makes −4.8 = 0.8 n −4.8 = 0.8 n a true statement, we know we have a solution.

## Try It 5.85

Solve: −8.4 = 0.7 b . −8.4 = 0.7 b .

## Try It 5.86

Solve: −5.6 = 0.7 c . −5.6 = 0.7 c .

## Example 5.44

Solve: p − 1.8 = −6.5 . p − 1.8 = −6.5 .

We will use the Multiplication Property of Equality .

A solution to p −1.8 = −6.5 p −1.8 = −6.5 is p = 11.7 . p = 11.7 .

## Try It 5.87

Solve: c −2.6 = −4.5 . c −2.6 = −4.5 .

## Try It 5.88

Solve: b −1.2 = −5.4 . b −1.2 = −5.4 .

Translate to an Equation and Solve

## Example 5.45

Translate and solve: The difference of n n and 4.3 4.3 is 2.1 . 2.1 .

## Try It 5.89

Translate and solve: The difference of y y and 4.9 4.9 is 2.8 . 2.8 .

## Try It 5.90

Translate and solve: The difference of z z and 5.7 5.7 is 3.4 . 3.4 .

## Example 5.46

Translate and solve: The product of −3.1 −3.1 and x x is 5.27 . 5.27 .

## Try It 5.91

Translate and solve: The product of −4.3 −4.3 and x x is 12.04 . 12.04 .

## Try It 5.92

Translate and solve: The product of −3.1 −3.1 and m m is 26.66 . 26.66 .

## Example 5.47

Translate and solve: The quotient of p p and −2.4 −2.4 is 6.5 . 6.5 .

## Try It 5.93

Translate and solve: The quotient of q q and −3.4 −3.4 is 4.5 . 4.5 .

## Try It 5.94

Translate and solve: The quotient of r r and −2.6 −2.6 is 2.5 . 2.5 .

## Example 5.48

Translate and solve: The sum of n n and 2.9 2.9 is 1.7 . 1.7 .

## Try It 5.95

Translate and solve: The sum of j j and 3.8 3.8 is 2.6 . 2.6 .

## Try It 5.96

Translate and solve: The sum of k k and 4.7 4.7 is 0.3 . 0.3 .

## ACCESS ADDITIONAL ONLINE RESOURCES

- Solving One Step Equations Involving Decimals
- Solve a One Step Equation With Decimals by Adding and Subtracting
- Solve a One Step Equation With Decimals by Multiplying
- Solve a One Step Equation With Decimals by Dividing

## Section 5.4 Exercises

In the following exercises, determine whether each number is a solution of the given equation.

x − 0.8 = 2.3 x − 0.8 = 2.3 ⓐ x = 2 x = 2 ⓑ x = −1.5 x = −1.5 ⓒ x = 3.1 x = 3.1

y + 0.6 = −3.4 y + 0.6 = −3.4 ⓐ y = −4 y = −4 ⓑ y = −2.8 y = −2.8 ⓒ y = 2.6 y = 2.6

h 1.5 = −4.3 h 1.5 = −4.3 ⓐ h = 6.45 h = 6.45 ⓑ h = −6.45 h = −6.45 ⓒ h = −2.1 h = −2.1

0.75 k = −3.6 0.75 k = −3.6 ⓐ k = −0.48 k = −0.48 ⓑ k = −4.8 k = −4.8 ⓒ k = −2.7 k = −2.7

In the following exercises, solve the equation.

c + 1.15 = −3.5 c + 1.15 = −3.5

d + 2.35 = −4.8 d + 2.35 = −4.8

j − 1.82 = −6.5 j − 1.82 = −6.5

k − 3.19 = −4.6 k − 3.19 = −4.6

m − 0.25 = −1.67 m − 0.25 = −1.67

q − 0.47 = −1.53 q − 0.47 = −1.53

In the following exercises, solve the equation. Then check your solution.

− 2 5 = x + 3 4 − 2 5 = x + 3 4

− 2 3 = y + 3 8 − 2 3 = y + 3 8

s − 1.75 = −3.2 s − 1.75 = −3.2

r − 1.25 = −2.7 r − 1.25 = −2.7

In the following exercises, translate and solve.

The difference of n n and 1.9 1.9 is 3.4 . 3.4 .

The difference n n and 1.5 1.5 is 0.8 . 0.8 .

The product of −6.2 −6.2 and x x is −4.96 . −4.96 .

The product of −4.6 −4.6 and x x is −3.22 . −3.22 .

The quotient of y y and −1.7 −1.7 is −5 . −5 .

The quotient of z z and −3.6 −3.6 is 3 . 3 .

The sum of n n and −7.3 −7.3 is 2.4. 2.4.

The sum of n n and −5.1 −5.1 is 3.8 . 3.8 .

## Everyday Math

## Writing Exercises

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## Course: 6th grade > Unit 2

## Adding & subtracting decimals word problems

- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text

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## Search form

Solving more decimal word problems.

Answer: The cost of 15.5 weeks of school lunches would be about $200.

Analysis: To solve this problem, we will multiply $11.75 by 21.

Answer: The student will earn $246.75 for gardening this month.

Analysis: To solve this problem, we will multiply 29.7 by 10.45

Answer: Rick can travel 310.365 miles with one full tank of gas.

Analysis: We need to estimate the quotient of 179.3 and 61.5.

Answer: He averaged about 3 miles per day.

Analysis: We will divide 7.11 lbs. by 9 to solve this problem.

Answer: Each jar will contain 0.79 lbs. of candy.

Answer: Paul will make 36 monthly payments of $529.47 each.

Analysis: We will divide 956.4 by 15.9, then round the quotient to the nearest tenth.

Answer: Rounded to the nearest tenth, the average speed of the car is 60.2 miles per hour.

- Estimating decimal products
- Multiplying decimals by whole numbers
- Multiplying decimals by decimals
- Estimating decimal quotients
- Dividing decimals by whole numbers
- Rounding decimal quotients
- Dividing decimals by decimals

## Featured Sites:

Free math worksheets, charts and calculators

## Year 5 Unit 10 Decimals

## Lesson 18- Problems Involving Decimals

Three cylinders weigh 52.4kg, 48.06kg and 63.587kg. What is the total weight of the three cylinders?

Liters of petrol used each day = 1.65L

Liters of petrol used in 12 days = 1.65L x 12

The product of two numbers is 96.75. If one of the numbers is 2.5, find the other number.

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## Decimal Word Problems Simple How-To w/ 13+ Examples!

// Last Updated: October 23, 2020 - Watch Video //

Have you ever found yourself stuck on a decimal word problem and not quite sure what to do?

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

## Steps In Solving Word Problems

All you have to do is remember the FACTS !

- Focus on what you know and not on what you don’t know. Sometimes just looking at word problems can overwhelm us even before we’ve read a single word. The key to problem-solving, especially problem solving with decimals, is to focus on what you know.
- Actively participate . This means you need to circle or underline keywords or phrases, write down important information that the problem is presenting. Once you write down or mark up the word problem, you will quickly realize that you are always given a ton of information to work with, now you just need to …
- Choose a method and go for it! What keywords pop out at you? Does it tell you to add or subtract decimals? Multiply, divide, or compare? Maybe you need to approximate so that rounding may be the best method. Or do you need to use more than one method or operation to calculate the correct answer? What is the problem asking, and what is provided that will help you get there?
- And once you’ve chosen your method, all that’s left is to try it ! Don’t give up, even if it’s challenging. The best thing you can do is try! So, try your method of choice and locate the answer you need.
- Lastly, you need to Scrutinize your work . All this means is that you need to ask yourself, “does my answer make sense?”

## Step-by-Step Example

Helen’s monthly salary is $5463.79.

Her monthly expenses are as follows:

After paying all of her expenses, how much money does Helen have left?

Words And Phrases To Math Symbols

Now we CHOOSE our method, which will involve two steps:

And finally, we ask ourselves, does our answer make SENSE ?

Yes, Helen has $413.46 remaining after paying all of her bills.

## Worksheet (PDF) — Hands on Practice

Practice Problems Step-by-Step Solutions

## Decimal Word Problems – Lesson & Examples (Video)

- Introduction to Video: Problem Solving with Decimals
- 00:00:37 – Review of Keywords and Overview of Problem Solving Steps: FACTS
- 00:08:02 – Solve each one-step problem using decimals (Examples #1-4)
- 00:24:10 – Solve the one-method word problem with decimals (Examples #5-8)
- 00:46:24 – Solve the application problem using two-methods (Examples #9-10)
- 01:02:18 – Solve the decimal word problem using more than one technique (Examples #11-12)
- 01:13:36 – Solve using estimation (Examples #13-14)
- Practice Problems with Step-by-Step Solutions
- Chapter Tests with Video Solutions

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## Decimal Word Problems (2-step)

Related Topics: More Math Word Problems More Lessons on Singapore Math Algebra Word Problems

Step 1: Find the total length of cloth used to make the 4 banners.

The total length of cloth used to make the 4 banners was 7.8 m.

Step 2: Find the total length of cloth Lily used altogether.

Lily used 9.04 m of cloth altogether.

Step 1: Find the total volume of orange juice in the 5 bottles.

The total volume of orange juice in the 5 bottles was 6.75 liters.

Step 2: Find the volume of orange juice in 1 bottle.

The volume of orange juice in 1 bottle was 1.35 liters.

MultiStep Decimal Word Problems Examples:

- One day at the farmer’s market, a customer purchased a box of mangoes for $3.25 plus $.26 tax. If she uses $20, how much will she get back in change?
- In an effort to save money for a car, Irving started walking to work instead of spending $1.25 for the bus each way to and from work. After 17 days of work, how much money has he saved?

How to Solve Multi-Step Word Problems Involving Decimals? Examples:

- The Gomez family drove to the beach for a vacation. They drove 2.5 hours at an average of 49 miles per hour, 1.25 hours at an average of 52 miles per hour, and 5 hours at an average speed of 38 miles per hour. How far did the Gomez family drive to get to the beach?
- Darya and Kana are practicing for a race. During practice, Kana swam 11 laps with an average of 27.02 seconds per lap. Darya swam 12 laps, with an average of 20.5 seconds per lap. How much longer did it take Kana to swim 11 laps than Darya to swim 12 laps?
- Last week during practice, Kamil swam 24 laps in 14.3 minutes. This week at swim practice, Kamil swam 22 laps in 14.8 minutes. What is the difference between the average lap time this week and last week? Write the answer in terms of minutes per lap.

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## Pre-Algebra : One-Step Equations with Decimals

The goal is to isolate the variable on one side.

## Example Question #2 : One Step Equations With Decimals

## Example Question #3 : One Step Equations With Decimals

## Example Question #4 : One Step Equations With Decimals

Subtract 1.75 from both sides of the equation:

The opposite operation of division is multiplication, therefore , multiply each side by 0.15:

The left hand side can be reduced by recalling that anything divided by itself is equal to 1:

The identity law of multiplication takes effect and we get the solution as:

## Example Question #7 : One Step Equations With Decimals

The opposite operation of subtraction is addition so add 0.23 to each side:

Simplifying, we get the final solution:

## Example Question #8 : One Step Equations With Decimals

The opposite operation of subtraction is addition so add 1.94 to each side:

The opposite operation of addition is subtraction so subtract 0.001 from each side:

## Example Question #10 : One Step Equations With Decimals

The opposite operation of addition is subtraction so subtract 8.11 from each side:

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## COMMENTS

If you missed this problem, review Example 3.6.12. Solve \(\dfrac{n}{−7}\) = 42. If you missed this problem, review Example 4.12.5. Determine Whether a Decimal is a Solution of an Equation. Solving equations with decimals is important in our everyday lives because money is usually written with decimals. When applications involve money, such ...

Writing a number as a fraction and decimal. Rewriting decimals as fractions: 0.15. Rewriting decimals as fractions: 0.8. Rewriting decimals as fractions: 0.36. Rewriting tricky fractions to decimals.

If you missed this problem, review Example 3.41. Be Prepared 5.12. Solve n − 7 = 42. n − 7 = 42. If you missed this problem, review Example 4.99. Determine Whether a Decimal is a Solution of an Equation. Solving equations with decimals is important in our everyday lives because money is usually written with decimals. When applications ...

Adding & subtracting decimals word problems. Google Classroom. Rosa is building a guitar. The second fret is 33.641\,\text {mm} 33.641mm from the first fret. The third fret is 31.749\,\text {mm} 31.749mm from the second fret.

Solving Decimal Word Problems. Example 1: If 58 out of 100 students in a school are boys, then write a decimal for the part of the school that consists of boys. Analysis: We can write a fraction and a decimal for the part of the school that consists of boys. Example 2: A computer processes information in nanoseconds.

Step 1: Step 2: Answer: Rounded to the nearest tenth, the average speed of the car is 60.2 miles per hour. Summary: In this lesson we learned how to solve word problems involving decimals. We used the following skills to solve these problems: Estimating decimal products. Multiplying decimals by whole numbers.

At the end of this lesson, students should be able to understand and solve word problems involving decimals. Decimal word problems are just like any other word problems except that they involve decimal numbers and not whole numbers. Example 1. Three cylinders weigh 52.4kg, 48.06kg and 63.587kg. What is the total weight of the three cylinders?

The answer to this problem is 5.1099. Multiplication. 1. 5.888 x 1.2 The answer is 7.0656. Notice how it has four numbers after the decimal point, because the first number has three digits after the decimal point and the second number has one digit in the tens column, resulting in four numbers total. 2. 12.01 x 3.3 The solution is 39.633.

Problem 20. Write \displaystyle \frac {127} {1000} 1000127 as decimal number. Problem 21. Write \displaystyle 3\frac {59} {100} 310059 as decimal number. Problem 22. Write "eight tenths" as a decimal number. Problem 23. Write "thirteen hundredths" as a decimal number. Problem 24.

Practice Problems Step-by-Step Solutions. Decimal Word Problems - Lesson & Examples (Video) 1 hr 22 min. Introduction to Video: Problem Solving with Decimals; 00:00:37 - Review of Keywords and Overview of Problem Solving Steps: FACTS; 00:08:02 - Solve each one-step problem using decimals (Examples #1-4) 00:24:10 - Solve the one-method ...

HOW TO: SOLVE EQUATIONS WITH FRACTION COEFFICIENTS BY CLEARING THE FRACTIONS. Step 1. Find the least common denominator of all the fractions in the equation. Step 2. Multiply both sides of the equation by that LCD. This clears the fractions. Step 3. Solve using the General Strategy for Solving Linear Equations.

Then, take your success and apply it to your current problem. For example, if you are good with money and know right away whether something adds up or not, you can think of decimals in terms of ...

Example Solutions Practice Questions How to Solve Multistep Word Problems Involving Decimals Step 1: Using keywords in the word problem, write the equation that will yield the answer to the question.

Word Problems With Decimals. Solve word problems involving addition, subtraction, multiplication and division of decimal numbers. Examples: Stan compares his checkbook record with his monthly bank statement that says he has $876.47. Stan sees that checks for $32.85, $97.10 and $158.78 have not been cashed yet.

Here are some examples of decimal word problems. We will illustrate how block diagrams can be used to help you to visualize the decimal word problems in terms of the information given and the data that needs to be found. Block diagrams are used in Singapore Math. Example: Lily used some cloth to make 4 banners and a tablecloth.

Algebra. Equation Solver. Step 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result!

Free practice questions for Pre-Algebra - One-Step Equations with Decimals. Includes full solutions and score reporting.