1. 2.7 Solving Proportions:
Fraction: A term with numerator and denominator ( 𝒂 𝒃 where b ≠ 0) .
Proportion: An equation that states that two ratios are equal:

2. Beaded Necklace:

3. We can find the number of red/blue beads using the following concept:
Cross Product: the products of a proportion: If 𝒂 𝒃 = 𝒄 𝒅 𝐰𝐡𝐞 𝐛 ≠ 0 and d ≠ 0, 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 𝟏.𝟐𝟓𝒊𝒏 = 𝒙 𝟐𝟎 𝒊𝒏
1.25in(x) = 2red(20in)
________ _______ in in
x = 32 red

4. 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 𝟏.𝟐𝟓𝒊𝒏 = 𝒙 𝟐𝟎 𝒊𝒏
1.25in(x) = 3blue(20in)
________ ______ in in
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.

5. 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
Multiplication
___ __
Inverse of Multiplication
Y = 𝟗 𝟓
Don’t forget to check!

6. What is the solution to the proportion:
YOU TRY IT:
What is the solution to the proportion:
𝟒 𝟑 = 𝟖 𝒙 ?

7. X = 6 Solution: What is the solution to the proportion: 𝟒 𝟑 = 𝟖 𝒙 ?
Cross Product
4x = 24
Multiplication
4x = 24
___ ____
Inverse of Multiplication
X = 6
Don’t forget to check!!

8. 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?

9. Inverse of multiplication ________ _________ 8oz 8oz
Solution:
𝟖𝒐𝒛 𝟗𝟕𝒎𝒈 = 𝟏𝟐𝒐𝒛 𝒙
Set up proportion
x(8oz) = 97mg(12oz)
Cross Product
8oz(x) =1164mgoz
Multiplication
8oz(x) =1164mgoz
Inverse of multiplication
________ _________
8oz oz
X = mg
Don’t forget to check!

10. YOU TRY IT: What is the solution to the following proportion:
𝒏 𝟓 = 𝟐𝒏+𝟒 𝟔 ?

11. Move smallest variable -6n -6n
YOU TRY IT (Solution):
𝒏 𝟓 = 𝟐𝒏+𝟒 𝟔 ?
Given proportion
n(6) = 5(2n+4)
Cross Product
6n= 5(2n) +5(4)
Distributive prop.
6n= 10n +20
Move smallest variable
-6n -6n
0 = 4n +20
Isolate variable
-20 =
Inverse of multiplication
-20 = 4n
___ ____
n = - 5
Don’t forget to check!

12. VIDEOS:
Proportions

13. Problems: As many as it takes to master the concept.
CLASS WORK:
Pages: 127– 129
Problems: As many as it takes to master the concept.