Chapter 2.7 Solve Proportions Using Cross Products
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Chapter 2.7
Solve Proportions Using Cross Products
Cross Product Property
• In a proportion, a cross product is the product of the numerator of one ratio and the denominator of the other ratio. The following property involving cross products can be used to solve proportions.
Use the cross products property EXAMPLE
Write original proportion.
8 15 = x 6
Solve the proportion = . 8
x
6
15
Cross products property
Simplify. 120 = 6x
Divide each side by 6. 20 = x
The solution is 20. Check by substituting 20 for x in the original proportion.
ANSWER
= 8
x
6
15
Use the cross products property EXAMPLE
Substitute 20 for x.
CHECK
Cross products property
Simplify. Solution checks.
8
20
6
15 = ?
8 15 = 20 6 ?
120 = 120
EXAMPLE Standardized Test Practice
What is the value of x in the proportion = ? 4
x
8
3 x –
A – 6 B – 3 C 3 D 6
SOLUTION
4
x =
8
x – 3 Write original proportion.
Cross products property 4(x – 3) = x 8
4x – 12 = 8x Simplify.
Subtract 4x from each side. –12 = 4x
Divide each side by 4. –3 = x
EXAMPLE Standardized Test Practice
The value of x is –3. The correct answer is B.
ANSWER
A B C D
Write and solve a proportion
EXAMPLE
x
280 =
8 amount of food
100 weight of seal
SOLUTION
STEP 1
Write a proportion involving two ratios that compare the amount of
food with the weight of the seal.
Each day, the seals at an aquarium are each fed 8 pounds of food for
every 100 pounds of their body weight. A seal at the aquarium weighs
280 pounds.
How much food should the seal be fed per day?
Seals
Write and solve a proportion
EXAMPLE
STEP 2
Solve the proportion.
8
100
x
280 = Write proportion.
8 280 = 100 x Cross products property
2240 = 100x Simplify.
22.4 = x Divide each side by 100.
ANSWER
A 280 pound seal should be fed 22.4 pounds of food per
day.
EXAMPLE 1
Solve the proportion. Check your solution.
On Your Own
= 4
a
24
30 1.
5 ANSWER
EXAMPLE 2 On Your Own
3
x =
2
x – 6 2.
18 ANSWER
Solve the proportion. Check your solution.
EXAMPLE 2 On Your Own
4
m
5 =
m – 6 3.
18 ANSWER
Solve the proportion. Check your solution.
EXAMPLE 4
Use the scale on a map On Your Own
6. The ship model kits sold at a hobby store have a scale of 1 ft : 600
ft. A completed model of the Queen Elizabeth II is 1.6 feet long.
Estimate the actual length of the Queen Elizabeth II.
Model ships
ANSWER about 960 ft
Related Documents
