### 2_7 Solving Proportions

```2.7 Solving Proportions:
Fraction: A term with numerator and

denominator ( where b ≠ 0) .

Proportion: An equation that
states that two ratios are equal:
We can find the number of red/blue beads using
the following concept:
Cross Product: the products of a proportion:

If
=   ≠ 0 and d ≠ 0,

then
a∙d = b∙c
find out how many we need for a 20 in by using
the following:

.
=

1.25in(x)
2red(20in)
________ = _______
1.25in
1.25in
x = 32 red
We can repeat this process to find the number of
find out how many we need for a 20 in by using
the following:

.
=

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:

=

?

Using cross-product we have the following:
5(y) = 3(3)
Cross product
5y = __
9
___
5 5

Y=

Multiplication
Inverse of Multiplication
Don’t forget to check!
YOU TRY IT:
What is the solution to the proportion:

=

?

Solution:
What is the solution to the proportion:

= ?
4(x) = 3(8)

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
97 mg of vitamin
many milligrams
of vitamin C are
there in a 12-oz
can of orange
juice?
Solution:

=

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:

=
+

?
YOU TRY IT (Solution):

=
+

?
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