Algebra
Lesson 3-6
Vocabulary:
•Ratio- A comparison of two numbers by division
•Proportion- An equation in the form of a/b = c/d, which states that two ratios are equivalent
•Extremes- In the ratio w/x = y/z, w and z are the extremes
•Means- In the ratio c/d = e/f, d and e are the means
•Rate- The ratio of two measurements having different units of measure
•Scale- A ratio or rate used when making a model that is either too big or too small to show as its actual size
Examples:
4/5 = x/20
1. First you find the cross products, which is 5(x) = 4(20)
2. Then you simplify that into 5x = 80
3. Finally, divide each side by 5 to get x = 16
Here is another one
65/2.5=j/30
find cross products (2.5j=1950)
divide each side by 2.5 (2.5j/2.5=1950/2.5)
and it comes out as this J = 780
Using cross products:
Determine whether it forms a proprtion or not.
0.4/0.8=0.7/1.4
Take cross products. 0.4(1.4)=0.8(0.7)
Simplify. 0.56=0.56
It is equal so these two ratios form a proportion.
Another one:
6/8=24/28
Take cross products. 6(28)=8(24)
Simplify. 168 and 192
They are not equal so these two ratios do not form a proportion.
Using Rates:
A blueprint for a house states that 2.5 inches equals 10 feet. If the length of a wall is 12 feet, how long is the wall in the blueprint?
2.5 inches = x
10 feet = 12 feet
2.5(12)=10x
30=10x
Then you divide by 10 on both sides getting 3=x.
2.5 inches on the blueprint equals 3 inches on the wall.
Your answer would be 3 inches.
Seth earns $152 in 4 days. At that rate, how many days will it take him to earn $532?
$152 = $532
4 = x
So you take 152x = 532(4)
Getting...152x = 2128
Then you divide by 152 on both sides getting x = 14.
Your answer would be it will take Seth 14 days.
Additional Information:
Online resources:
This page by: Amanda Tate, Nick, and Courtney