Transcript Ch 2-5 powerpoint

2-5 Solving Proportions
California
Standards
15.0 Students apply algebraic
techniques to solve rate problems, work
problems, and percent mixture problems.
2-5 Solving Proportions
A ratio is a comparison of two quantities. The
ratio of a to b can be written as a:b or ,
where b ≠ 0.
A statement that two ratios are equal, such as
is called a proportion.
2-5 Solving Proportions
In the proportion
the products a  d
and b  c are called cross products. You
can solve a proportion for a missing value
by using the Cross Products Property
2-5 Solving Proportions
Additional Example 3A: Solving Proportions
Solve the proportion.
Use cross
products.
3(m) = 9(5)
3m = 45
Divide both sides by 3.
m = 15
2-5 Solving Proportions
Additional Example 3B: Solving Proportions
Solve the proportion.
Use cross products.
6(7) = 2(y – 3)
42 = 2y – 6
+6
+6
48 = 2y
Add 6 to both sides.
Divide both sides by 2.
24 = y
2-5 Solving Proportions
Check It Out! Example 3a
Solve the proportion. Check your answer.
Use cross products.
–5(8) = 2(y)
–40 = 2y
Divide both sides by 2.
–20 = y
2-5 Solving Proportions
Check It Out! Example 3a Continued
Solve the proportion. Check your answer.
Check
Substitute –20 for y.
–2.5 –2.5

2-5 Solving Proportions
Check It Out! Example 3b
Solve the proportion. Check your answer.
Use cross product.
4(g + 3) = 5(7)
4g + 12 = 35
–12 –12
4g = 23
Subtract 12 from both sides.
Divide both sides by 4.
g = 5.75
2-5 Solving Proportions
Check It Out! Example 3b Continued
Solve the proportion. Check your answer.
Check
Substitute 5.75 for b.
1.75
1.75 
2-5 Solving Proportions
Additional Example 4B: Percent Problems
230 is what percent of 200?
Method 2 Use an equation.
230 = x  200
230 = 200x
1.15 = x
Write an equation. Let x represent
the percent.
Since x is multiplied by 200, divide
both sides by 200 to undo the
multiplication.
The answer is a decimal.
Write the decimal as a percent.
This answer is reasonable; 230
is more than 100% of 200.
230 is 115% of 200.
115% = x
2-5 Solving Proportions
Additional Example 4C: Percent Problems
20 is 0.4% of what number?
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
2000 = 0.4x
Cross multiply.
Since x is multiplied by 0.4,
divide both sides by 0.4.
5000 = x
20 is 0.4% of 5000.
2-5 Solving Proportions
Check It Out! Example 4a
Find 20% of 60.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the part.
100x = 1200
x = 12
20% of 60 is 12.
Find the cross product. Since x
is multiplied by 100, divide
both sides to undo the
multiplication.