Proportions
11-4
? ? ? ?
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: bc: d a d b c
Cross-Products Rule
a : bc : dwhenb, d 0
1
adbc
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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