1. Chapter 5 Section 3
Solving Linear Equations with Fractions and Decimals by Clearing the Denominators

2. Essential Question
How do you solve linear equations with fractions?

3. Steps for Solving Linear Equations with Fractions
Find the LCD for all terms in the equation
Multiply all terms by the LCD to eliminate the fraction
Solve the equation for the variable
Check your answer for extraneous roots

4. Practice Solving Equations with Fractions

5. Solving Word Problems with Fractions

6. Solving Equations with Decimals

7. Practice Solving Equations
If the quotient of a number and four is decreased by 20, the result is 5. Find the number
Twice the difference between a number and five is equal to 14 more than six times that number. What is the number?
The perimeter of a triangle is 19 centimeters. If two sides are of equal length and the third side is four centimeters longer, what is the length of each side of the triangle?

8. Practice Solving Equations
A real estate agent says that the home you are looking to buy is 20 years old and that its current value is $80,000 more than twice its original value when it was new. If the current price is $260,000, what did the original owner pay for this house?

9. Practice Solving Equations
Mary sells both small and large paintings at an art fair. The small paintings sell for $50 each and the large sell for $175 each. By the end of the day, Mary lost track of how many of each size she sold. However, she knows that she sold a total of 14 paintings for $1200. Determine the number of small and the number of large paintings that she sold that day.

10. Practice Solving Equations
Jason is considering buying an apartment. His monthly rent is $890. If he makes a $31,350 down payment on the apartment, his monthly mortgage payments would be $560. How many months would it take for his down payment plus his monthly mortgage payments to equal the amount he spends on rent?

11. Practice Solving Equations – Simple Interest
I = PRT I=Interest, P= Principal, R = Rate, T =Time A $1000 investment is made for two and a half years at 6.25%. Find the amount of interest.

12. Rate and Work Amount of work completed = rate of work x time worked
W = RT
A & B working together
A’s work + B’s work = 1 completed job
(A’s rate x A’s time) + (B’s rate x B’s time) = 1 completed job
A & B working in opposition
A’s work – B’s work = 1 completed job
(A’s rate x A’s time) – (B’s rate x B’s time) = 1 completed job

13. Example of Rate and Work
Pipe 1 fills a tank in 6 min and pipe 2 fills the same tank in 8 min. How long does it take for both pipes to fill the tank?
A faucet fills a tank in 6 min. A drain empties the tank in 8 min. If both the faucet and drain are open, in how many minutes will the tank start to overflow if the faucet is not turned off?