2.7 Solving Proportions:

Fraction: A term with numerator and denominator ( where b ≠ 0) .

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: If ≠ 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:

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:

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

Multiplication

___ __ 5 5 Inverse of Multiplication

Y = 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 Inverse of Multiplication___ ____ 4 4 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:Set up proportion =

Cross ProductMultiplication

x(8oz) = 97mg(12oz)8oz(x) =1164mgoz ________ _________ 8oz 8ozX = 145.5 mg Don’t forget to check!

8oz(x) =1164mgoz Inverse of multiplication

YOU TRY IT:

What is the solution to the following proportion:

= ?

YOU TRY IT (Solution):Given proportion = ?

Cross ProductDistributive prop.

Move smallest variable

n(6) = 5(2n+4)6n= 5(2n) +5(4)6n= 10n +20-6n -6n0 = 4n +20-20 = -20 Isolate variable

-20 = 4n___ ____ 4 4 Inverse of multiplicationn = - 5 Don’t forget to check!

VIDEOS: Proportions

https://www.khanacademy.org/math/algebra/ratio-proportion-topic/ratios_algebra/v/find-an-unknown-in-a-proportion

https://www.khanacademy.org/math/algebra/ratio-proportion-topic/ratios_algebra/v/writing-proportions

https://www.khanacademy.org/math/algebra/ratio-proportion-topic/ratios_algebra/v/find-an-unknown-in-a-proportion-2

CLASS WORK:

Pages: 127– 129

Problems: As many as it takes to master the concept.