This document contains examples of solving one-step equations with decimal and fraction coefficients. It provides step-by-step explanations for solving equations such as 16 = 0.25n, x = 1/5, -d = 5, and n = 3/4x. It demonstrates using the division property of equality to isolate the variable and check the solution by substituting it back into the original equation. Understanding how to solve these one-step equations lays the foundation for solving more complex multi-step equations.

1. Solve each equation. Check your solution.
1. 5x = 35
2. –8z = 48
3.
4.
5. A package of 8 juice bottles costs $12. What is
the price per bottle?
7
4
n

15
3
t


Course 2, Lesson 6-3

2. Course 2, Lesson 6-3
ANSWERS
1. x = 7
2. z = –6
3. n = 28
4. t = –45
5. $1.50

3. WHAT does it mean to say
two quantities are equal?
Expressions and Equations
Course 2, Lesson 6-3

4. • 7.EE.4
Use variables to represent quantities in a real-world or mathematical
problem, and construct simple equations and inequalities to solve
problems by reasoning about the quantities.
• 7.EE.4a
Solve real-world problems leading to equations of the form px + q = r
and p(x + q) = r, where p, q, and r are specific rational numbers. Solve
equations of these forms fluently. Compare an algebraic solution to an
arithmetic solution, identifying the sequence of operations used in each
approach.
Course 2, Lesson 6-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

5. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course 2, Lesson 6-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

6. • To solve equations with
decimal coefficients
• To solve equations with
fraction coefficients
Course 2, Lesson 6-3
Expressions and Equations

7. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. Solve 16 = 0.25n. Check your solution.
Write the equation.16 = 0.25n
Division Property of Equality
Simplify.64 = n
Write the original equation.Check 16 = 0.25n
Replace n with 64.16 = 0.25 • 64
This sentence is true.16 = 16
The solution is 64.
?

8. Answer
Need Another Example?
Solve 10 = 0.5x. Check your solution.
20

9. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
2. Jaya’s coach agreed to buy ice cream for all of the team members.
Ice cream cones are $2.40 each. Write and solve an equation to
find how many cones the coach can buy with $30.
Write the equation; $2.40 = 2.4.2.4n = 30
Division Property of Equality
n = 12.5 Simplify.
Let n represent the number of cones the coach can buy.
Since the number of ice cream cones must be a whole
number, there is enough money for 12 ice cream cones.

10. Answer
Need Another Example?
Jamie wants to cut pieces of siding that are each
3.5 feet long to fit between a window and the end of
the house. If the original piece of siding is 21 feet
long, write and solve an equation to find the total
number of 3.5 foot long pieces he can cut.
3.5x = 21; 6 pieces

11. Need Another Example?
Step-by-Step Example
3. Solve x = .
1
2
3
4
Write the equation.
x =
1
Simplify. Check the solution.
Divide by common factors.
1 1 4
1 1 1 5
Multiply each side by the reciprocal of , .

12. Answer
Need Another Example?
Solve x = . Check your solution.

13. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
4. Solve – d = 5. Check your solution.
Write the equation.
Check
Divide by common factors.
1 1
1 1
Simplify.
Write the original equation.
Multiply each side by the reciprocal of – , – .
Simplify.
This sentence is true.
Write 5 as .
Replace d with – .

14. Answer
Need Another Example?
Solve – x = 12. Check your solution.
–18

15. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
5. Valerie needs yard of fabric to make each hat for the
school play. Write and solve an equation to find how
many hats she can make with 6 yards of fabric.
Write the equation.
n = 9 Simplify.
Write and solve a multiplication equation.
Let n represent the number of hats.
Valerie can make 9 hats.
Multiply each side by .

16. Answer
Need Another Example?
Samantha answered of the questions on her
science quiz correctly. If she answered 8 questions
correctly, write and solve an equation to determine
how many questions were on the quiz.
x = 8; 10 questions

17. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-3
Expressions and Equations

18. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-3
Expressions and Equations
Sample answer:
• The same properties can be used to solve equations
with decimal and fraction coefficients.

19. Explain how what you
have learned about solving
one-step equations will help
you solve two-step equations.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2 Lesson 6-3