IM 8 Ch 5.1.2 How Can I Eliminate Fractions In Equationsmaestrodeyo.weebly.com/uploads/1/7/1/0/17102056/im...IM 8 Ch 5.1.2 How Can I Eliminate Fractions In Equations 511 Rewriting

IM 8 Ch 5.1.2 How Can I Eliminate Fractions In Equations

CPM Materials modified by Mr. Deyo

What is a solution to an equation?

What does it look like?

What is the growth pattern?

What is the yintercept?

Common Core Standard: 8.EE.7b


By the end of the period, I will solve equations with fraction and decimal coefficients by changing the coefficients to integers.

I will demonstrate this by completing Four‑Square notes and by solving problems in a pair/group activity.

Learning TargetTitle: IM8 ‑ Ch. 5.1.2 How Can I Eliminate Fractions in Equations? Date:


Home Work: Sec. 5.1.2Desc. Date Due

Review & Preview

2 Problems: 5‑18, 5‑22



Vocabulary1) growth factor

2) yintercept

3) proportion

4) multiplicative inverse



5.1.2 How Can I Eliminate Fractions in Equations?Earlier in this course, you worked with proportions such as . One way to begin solving a proportion is to eliminate the fractions and create an equivalent equation. When you eliminate the fractions, it is easier to solve.

Fraction elimination is not just for proportions, however. It also applies to other equations with fractions. In this lesson, you will learn how to eliminate fractions in equations. Then you will be able to use what you learned about solving equations to complete the problems.


510 Hannah wants to solve 0.04x + 1 = 2.2 . “I think that I need to use my calculator because of the decimals,” she told Michael. Suddenly Hannah blurted out, “No, wait! What was the way we learned to rewrite a proportion equation without fractions? Maybe we can use that idea here to get rid of the decimals.”What is Hannah talking about? Explain what she means. Then rewrite the equation so that it has no decimals.

0.04x + 1 = 2.2 turns into >Now solve the new equation (the one with no decimals). Check your solution.


511 Rewriting 0.04x + 1 = 2.2 in the previous problem gave you a new, equivalent equation that was easier to solve. If needed, review the Math Notes box in this lesson for more information about equivalent equations.On the following pages, how can each equation below be rewritten so that it is easier to solve? With your team, find an equivalent equation for each equation below. If the original equation has large numbers, make sure the equivalent equation has smaller numbers. If the original equation has fractions or decimals, eliminate the fractions or decimals in the equivalent equation. Solve each new equation and check your answer.


Explanation

• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse

511a Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.

2.1x + 0.6 = 17.4

Solve for x


Explanation


511b Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.

100x + 250 = −400

Solve for x


Explanation


511c Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.

Solve for x

2x 30 3 1=


Explanation• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse

511d Solve for the indicated variable. Write down each of your steps algebraically.

Solve for x x 5 + 1 = 6


512a,b,c Examine the equation below and then answer the questions below.

a) Multiply each term by 3. What happened? Do any fractions remain?

x 3 = 16 x

5+

b) If you had multiplied each term in the original equation by 5 instead of 3, would you have eliminated all of the fractions? Why?

c) Find a number that you can use to multiply by all of the terms that will get rid of all of the fractions. How is this number related to the numbers in the equation?


512d Solve the equation below and then check your answer.

x 3 = 16 x

5+




513a Solve for the indicated variable. Write down each of your steps algebraically.

Solve for a a 7 = 10 a

3+



513b Solve for the indicated variable. Write down each of your steps algebraically.

Solve for y 3y 5 = 3

2+ 7y 10



513c Solve for the indicated variable. Write down each of your steps algebraically.

Solve for x (2x 3) 6 = 1

2+ 2x 3



513d Solve for the indicated variable. Write down each of your steps algebraically.

Solve for b b + 3 6 = b2 2 b 4


514 Sam can paint an apartment living room in 3 hours, and Pam can paint the same room in 2 hours. The solution to the equation below describes how long it will take them to paint the living room if they work together. Before solving this problem, make a guess about the answer. Then solve the equation. How did your guess compare? Most people are surprised with the correct solution!

x 3 = 1+ x 2

Guess:


515a&b Review your solution to part (b) of problem 513. You probably multiplied each fraction by the lowest (least) common denominator (LCD), which, in this case, is 10. But what would you do if you could not determine the LCD? You will explore this idea in parts (a) through (e).a) Multiply the three denominators: 5 · 2 · 10 3y

5 = 3 2+ 7y

10b) Multiply both sides of the equation by the product you got in part (a). This gives you an equivalent equation. Have your partner multiply both sides of the equation by 10 and find a different equivalent equation.


515c,d,e Review your solution to part (b) of problem 513. You probably multiplied each fraction by the lowest (least) common denominator (LCD), which, in this case, is 10. But what would you do if you could not determine the LCD? You will explore this idea in parts (a) through (e).c) Now, solve your equation for y and check your answer. While you solve your equation, your partner will be solving his or her equation.

d) Compare your result with your partner’s.

60y + 150 = 70y

e) Why do both your method and your partner’s method work? That is, why do both using the product of the denominators and using the LCD of 10 both successfully eliminate fractions from equations?


516. Fill in each of the lines labeled (a) through (e) to explain how the equation to its left was obtained from the equation above it.



In your Learning Log, describe how to create an equivalent equation from an equation that has fractions or decimals. Explain how to decide what number to use to multiply. Also explain any other important things to remember when using this process.

517. LEARNING LOG “Solving Equations With Fractions” Date ______


a)

518 Solve each of the following equations for x. Then check each solution.

x x2 6

b) 1 3= 7 =

http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch5/lesson/5.1.2/problem/518

+ x 9 + 2x

2

http://homework.cpm.org/cpm-homework/homework/category/CC/textbook/CC3/chapter/Ch5/lesson/5.1.2/problem/5-18


519 Fisher thinks that any two lines must have a point of intersection. Is he correct? If so, explain how you know. If not, produce a counterexample and explain your reasoning. (In this case, a counterexample would be an example of two lines that do not have a point of intersection.)




520 In the last election, candidate B received twice as many votes as candidate A. Candidate C received 15,000 fewer votes than candidate A. If a total of 109,000 votes were cast, how many votes did candidate B receive? http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/

chapter/Ch5/lesson/5.1.2/problem/520

Candidate B received votes.



521 Jamila wants to play a game called “Guess My Line.” She gives you the following hint: “Two points on my line are (1, 1) and (2, 4).”

What is the rule? y = ( )x + ( )

Graph

Where's the yintercept?

( , )

What's the rate of growth?




Explanation


522a Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.

2(3x − 4) = 22

Solve for x




Explanation


522b Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.

6(2x − 5) = −(x + 4)

Solve for x




Explanation


522c Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.

2 − (y + 2) = 3y

Solve for y




Explanation


522d Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.

3 + 4(x + 1) = 159

Solve for x



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IM 8 Ch 5.1.2 How Can I Eliminate Fractions In Equationsmaestrodeyo.weebly.com/uploads/1/7/1/0/17102056/im...IM 8 Ch 5.1.2 How Can I Eliminate Fractions In Equations 511 Rewriting