Algebra 1 Common Core Student Edition, Grade 8-9

Objective To solve an d apply p roportions

Getting Ready!

You've used ratios

to compare. This

problem involves

equal ra tio s.

MATHEMATICAL j 1

PRACTICES-

You a re making beaded necklaces, using a p a tte rn in which 2 large red

beads are followed by 3 small blue beads. Each set of 5 beads adds

14 in. to the length of the necklace. How many of each color bead will

you need fo r a 2 0 - in. necklace? Explain your answ er.

Lesson

Vocabulary

proportion

cro ss p ro d uct s

Cr o ss Pr o d u c t s

Pr o p er t y

In th e Solve It, th e n u m b e r of red b eads a n d th e n u m b e r of blue b ea d s are quantities

th at have a p roportional relationship. This m ean s th a t th e ratio of the quantities is

co n stan t even th o u g h th e quantities them selves can change. For example, as you are

m aking th e necklace you will have 2 red b eads a n d 3 blue beads, th e n 4 red b eads an d

6 blue beads, th e n 6 red b eads an d 9 blue beads, a n d so on. At each stage, th e ratio of

red b eads to blue b eads rem ains constant, 2 :3.

A proportional relationship can p roduce an infinite n u m b e r of equivalent ratios. Any

two of these can be u sed to write a p roportion. A proportion is a n e q u a tio n th a t states

th at two ratios are equal. For example, | = w here b Y= 0 and d + 0, is a proportion.

You read this as “a is to b as c is to d"

Solving Proportions

Common Core State Standards

A-REI.B.3 Solve linear equations and inequalities

in one variable, including equations w ith coefficients

represented by letters. Also N-Q.A.1, A-CED.A.1

MP 1, MP3, MP4, MP 8

Essential U nderstanding If two ratios are eq u al a n d a q uantity in one of the

ratios is unknow n, you can write an d solve a p ro p o rtio n to find th e u nknow n quantity.

H o w is th is p ro b le m

related to problems

you've solved before?

Solving this proportion

is s im ila r to s o lving a

one-step equation using

m u ltip lic a tio n. You can

simply multiply by 12 to

isolate m.

Problem 1 Solving a Proportion Using the M ultiplication Property

What is the solution of the proportion | =

7 _ m

8 ~ 12

12 • | = 12 • jk Multiply each side by 12.

(^84) T = m
10.5 = m
Simplify.
Divide.
124 Ch ap t er 2 So lvin g Eq u at i o n s