Algebra 1 Common Core Student Edition, Grade 8-9

G o t It? 1. W hat is th e solution of the p ro p o rtio n f

In th e p ro p o rtio n f = j , th e p ro d u cts ad a n d be are c a lle d cross pro d u c ts. You can use

the following property of cross p ro d u c ts to solve proportions.

11 lij. pr0perfy Cross Products Property of a Proportion

Words The cross p roducts of a p ro p o rtio n are equal.

Algebra If | = jj, where b ¥= 0 a n d d + 0, t h e n ad = be.

Example | = so 3(12) = 4(9), or 36 = 36.

V

Think
Which property
should you use?
The Cross Products
Property can be easier to
use w h e n th e va ria b le is
in th e denom inator. If you
use the M u ltip lic a tio n
Property, you must
multiply each side by 3x.

Here's W hy It W orks You can u se th e M ultiplication P roperty of Equality to

prove th e Cross Products Property.

a£b d (^) A s s u m e th is e q u a tio n is tru e.
bd • | = bd • ^ Multiplication Property of Equality
bd • | = bd • ^ Divide the common factors.
da = be Simplify.
ad = be Commutative Property of M ultiplication
For this p roportion, a and d are called th e extremes of th e p ro p o rtio n an d b an d c are
called th e means. Notice th a t in th e Cross P roducts P roperty th e p ro d u c t of th e m eans
equals th e p ro d u c t of th e extrem es.
Solving a Proportion Using the Cross Products Property
What is the solution of the proportion^4 3 =^8
4 8
3 x
Ax = 3(8) Cross Products Property
Ax = 24 Multiply.
x=6 Divide each side by 4 and simplify.
G o t It? 2. a. W hat is th e solution of th e pro p o rtio n | = |?
b. Reasoning W ould you ra th e r use the Cross P roducts Property or the
M ultiplication P roperty of Equality to solve^3 5 = y? Explain.^13
Problem 2
c
| Lesso n 2-7 So l v i n g Pr o p o r t i o n s 125