Solve Equations with Rational Coefficients

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

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

Key Concept

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

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

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

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

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

–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 0.4 0.4 –15.5 = r Simplify. Answer: So, r = –15.5. Example 3

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

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 = 23.4 Write the equation. 2.6t = 23.4 Division Property of Equality 2.6 2.6 t = 9 Simplify. Answer: Isabella rode around the bike trail 9 times. Example 4

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. 4.52 mi B. 6.25 mi C. 7.25 mi D. 8.65 mi Example 4 CYP

Solve Equations with Rational Coefficients