Download Lesson 7-1

Lesson 7-1
Ratios and Proportions
Ratio: comparison of two quantities using division
• Can be expressed as:
• a to b
• a:b
• 𝑎𝑏 𝑤ℎ𝑒𝑟𝑒 𝑏≠0
Extended ratios: comparison of three or more quantities.
a:b:c
Example:
• A video game store has 60 games to choose from, including 40 sports
games. What is the ratio of sports games to video games?
𝑔𝑎𝑚𝑒𝑠
• We are comparing 𝑠𝑝𝑜𝑟𝑡𝑠
=
𝑡𝑜𝑡𝑎𝑙 𝑔𝑎𝑚𝑒𝑠
40
60
= 23
• In 2015, David Ortiz had 37 homeruns and was at bat 528. What is his
ratio of homeruns to at bats?
• We are comparing ℎ𝑜𝑚𝑟𝑢𝑛𝑠
=
𝑎𝑡 𝑏𝑎𝑡𝑠
37
528
or about 0.07
Extended Ratio problem:
• In a triangle, the ratio of the measures of the sides is 3:3:8 and the
perimeter is 392 inches. Find the length of the largest side.
• First set up the equation: 3x + 3x + 8x = 392
14x = 392
x = 28
Now we need to plug in x for the longest side
8x = 8(28)
So the longest side is 224 inches.
Cross Product:
Example for solving proportions using Cross Product.
𝑤
1
•
=
6.4
2
• 2𝑤 = 6.4(1)
• 2w = 6.4
•
2𝑤
2
=
6.4
2
• W=3.2
4𝑥
56
=
24 112
(4x)(112)=(24)(56)
448x = 1344
x=3
3𝑥 − 6 4𝑥 − 2
=
2
4
(3x-6)(4) = (2)(4x-2)
12x-24 = 8x-4
4x-24 = -4
4x = 20
X=5