2.7 Solving Proportions:
Fraction: A term with numerator and
𝒂
denominator ( where b ≠ 0) .
𝒃
Proportion: An equation that
states that two ratios are equal:
Beaded Necklace:
We can find the number of red/blue beads using
the following concept:
Cross Product: the products of a proportion:
𝒂
𝒄
If
= 𝐰𝐡𝐞 𝐛 ≠ 0 and d ≠ 0,
𝒃
𝒅
then
a∙d = b∙c
Since we have 2 read beads every 1.25 in, we can
find out how many we need for a 20 in by using
the following: 𝟐𝒓𝒆𝒅
𝒙
𝟏.𝟐𝟓𝒊𝒏
=
𝟐𝟎 𝒊𝒏
1.25in(x)
2red(20in)
________ = _______
1.25in
1.25in
x = 32 red
We can repeat this process to find the number of
blue beads:
Since we have 3 read beads every 1.25 in, we can
find out how many we need for a 20 in by using
the following: 𝟑𝒃𝒍𝒖𝒆
𝒙
𝟏.𝟐𝟓𝒊𝒏
=
𝟐𝟎 𝒊𝒏
1.25in(x)
3blue(20in)
________= ______
1.25in
1.25in
x = 48 blue
Thus if we are following the same pattern, we will
need 32 red and 48 blue beads to make a 20 in
necklace.
We use cross-product to solve problems
involving proportions with unknowns (variables
Ex:
What is the solution to the proportion:
𝒚
𝟑
=
𝟑
?
𝟓
Using cross-product we have the following:
5(y) = 3(3)
Cross product
5y = __
9
___
5 5
𝟗
Y=
𝟓
Multiplication
Inverse of Multiplication
Don’t forget to check!
YOU TRY IT:
What is the solution to the proportion:
𝟒
𝟑
=
𝟖
?
𝒙
Solution:
What is the solution to the proportion:
𝟒
𝟖
= ?
4(x) = 3(8)
𝟑
𝒙
Cross Product
4x = 24
Multiplication
4x =____
24
___
4
4
Inverse of Multiplication
X=6
Don’t forget to check!!
REAL-WORLD:
An 8-oz can of
orange juice
contains about
97 mg of vitamin
C. About how
many milligrams
of vitamin C are
there in a 12-oz
can of orange
juice?
Solution:
𝟖𝒐𝒛
𝟗𝟕𝒎𝒈
=
𝟏𝟐𝒐𝒛
𝒙
Set up proportion
x(8oz) = 97mg(12oz) Cross Product
8oz(x) =1164mgoz Multiplication
8oz(x)
________ =1164mgoz
_________
8oz
8oz
X = 145.5 mg
Inverse of
multiplication
Don’t forget to check!
YOU TRY IT:
What is the solution to the following
proportion:
𝒏
𝟓
=
𝟐𝒏+𝟒
𝟔
?
YOU TRY IT (Solution):
𝒏
𝟓
=
𝟐𝒏+𝟒
𝟔
?
n(6) = 5(2n+4)
6n= 5(2n) +5(4)
Given proportion
Cross Product
Distributive prop.
6n= 10n +20
-6n -6n
Move smallest variable
0 = 4n +20
-20 =
-20
___ =____
-20
4n
n=-5
4
4
Isolate variable
Inverse of multiplication
Don’t forget to check!
VIDEOS:
Proportions
https://www.khanacademy.org/math/algebra/rati
o-proportion-topic/ratios_algebra/v/writingproportions
https://www.khanacademy.org/math/algebra/rati
o-proportion-topic/ratios_algebra/v/find-anunknown-in-a-proportion
https://www.khanacademy.org/math/algebra/rati
o-proportion-topic/ratios_algebra/v/find-anunknown-in-a-proportion-2
CLASS WORK:
Pages: 127– 129
Problems: As many as it takes
to master the
concept.