Transcript 2_7 Solving Proportions
2.7 Solving Proportions: Fraction:
A term with numerator and denominator (
π π
where b β 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
π π = π π π°π‘π π
β 0 and d β 0, then
aβd = bβc
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:
ππππ π = π.ππππ ππ ππ
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:
πππππ π = π.ππππ ππ ππ
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:
π π =
?
π π
Using cross-product we have the following: 5(y) = 3(3) Cross product 5 5 Y =
π π
Multiplication Inverse of Multiplication Donβt forget to check!
YOU TRY IT: What is the solution to the proportion:
π π = π
?
π
Solution: What is the solution to the proportion: 4(x) = 3(8)
π π = π
?
π
Cross Product 4x = 24 Multiplication 4 4 Inverse of Multiplication
X = 6
Donβt 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:
πππ ππππ
=
ππππ π
Set up proportion
x(8oz) = 97mg(12oz)
Cross Product
8oz(x) =1164mgoz
Multiplication
8oz 8oz
Inverse of multiplication X = 145.5 mg Donβt forget to check!
YOU TRY IT: What is the solution to the following proportion:
π π
=
ππ+π π ?
YOU TRY IT (Solution):
π π
=
ππ+π π ?
Given proportion
n(6) = 5(2n+4) 6n= 5(2n) +5(4)
Cross Product Distributive prop.
6n= 10n +20 -6n -6n 0 = 4n +20 -20 = -20
Move smallest variable Isolate variable
4 4
n = - 5 Inverse of multiplication Donβt forget to check!
VIDEOS:
Proportions
https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/writing proportions https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/find-an unknown-in-a-proportion https://www.khanacademy.org/math/algebra/rati o-proportion-topic/ratios_algebra/v/find-an unknown-in-a-proportion-2
CLASS WORK: