1. Solve Equations with Rational Coefficients

2. Main Idea and New Vocabulary
Key Concept: Inverse Property of Multiplication
Example 1: Real-World Example
Example 2: Real-World Example
Example 3: Decimal Coefficients
Example 4: Real-World Example
Lesson Menu

3. Solve equations with rational coefficients.
multiplicative inverse
Main Idea/Vocabulary

4. Key Concept

5. Fractional Coefficients
Write the equation.
Simplify.
Answer: So, t = 35.
Example 1

6. A. a = 9
B. a = 15
C. a = 25
D. a = 27
Example 1 CYP

7. Fractional Coefficients
You want to find how many curtains Antonio can make. Let c represent the number of curtains. Then write and solve an equation.
Example 2

8. Fractional Coefficients
Write the equation.
Simplify.
Answer: So, Antonio can make 6 curtains.
Example 2

9. A. 21 pets
B. 28 pets
C. 36 pets
D. 42 pets
Example 2 CYP

10. –6.2 = 0.4r Division Property of Equality 0.4 0.4 –15.5 = r Simplify.
Decimal Coefficients
Solve –6.2 = 0.4r.
–6.2 = 0.4r Write the equation.
–6.2 = 0.4r Division Property of Equality
–15.5 = r Simplify.
Answer: So, r = –15.5.
Example 3

11. Solve 10.8 = 0.9n.
A. n = 1.2
B. n = 9
C. n = 10.7
D. n = 12
Example 3 CYP

12. Fractional Coefficients
CYCLING A circular bike trail is 2.6 kilometers long. Isabella rode a total distance of 23.4 kilometers on the trail. Write and solve an equation to determine the number of times Isabella rode around the trail.
Isabella rode a total of 23.4 km. The bike trail is 2.6 km long. Let t represent the number of times she rode around the trail. Then write and solve an equation.
2.6t = Write the equation.
2.6t = Division Property of Equality
t = 9 Simplify.
Answer: Isabella rode around the bike trail 9 times.
Example 4

13. CYCLING A bike trail is made up flat land and hills. There are 2
CYCLING A bike trail is made up flat land and hills. There are 2.5 miles of hills which is 40% of the trail. How long is the bike trail ?
A mi
B mi
C mi
D mi
Example 4 CYP

14. Solve Equations with Rational Coefficients