6th Grade Math Textbook, Progress

Proportions

11-4

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? 
? 
? 

A proportion is an equation that shows

two ratios are equivalent.

John made trail mix using 2 cups of nuts and

6 cups of dried fruit. Marcy used 3 cups of nuts

and 9 cups of dried fruit. Are the two mixes

the same?

To determine if the two mixes are the same,

check if the ratios form a proportion.



6

2

c

c

d

n

r

u

ie

ts

d

m

f

m

ru

n

it

 

3

9

c

c

n

d

u

ri

t

e

s

d

m

fr

m

u

n

it



There are two ways to check if two ratios form a proportion.


 Write the ratios as fractions in simplest form.

If the fractions are the same, the ratios are equivalent.



2

6

 

3

9

 

2

6




1

3

and

3

9




1

3

 

1

3




1

3





2

6




3

9

is a proportion because both ratios equal one third.

 Use the cross-products rule:

Two ratios form a proportion if their cross productsare equal.

2  9 6  3

18 
 18

The trail mixes are the same because the ratios form a proportion.

a: b
c: d a d 
b c

Cross-Products Rule

a : b
c : dwhenb, d  0

 
 

 1

ad
bc

a 
d

b c

d

c

c

d

d

c

a

b

c

d

a

b

Write the ratios in

fraction form.

Numerator and

denominator are equal

since their quotient is 1.

Multiply both

sides by .dc

cdand dcare

multiplicative inverses.

extremes

means



2

6

 

3

9



2 and 9 are

the extremes.

6 and 3 are

the means.

The product of the extremes is

equal to the product of the means.

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