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3. Use proportions to solve problems
Objective
Use proportions to solve problems
Example 4-3b

4. An equation stating that two rates are equivalent
Vocabulary
Proportion
An equation stating that two rates are equivalent
1 2 =
2 4
Example 4-3b

5. Property of Proportions The cross products of a proportion are equal
Vocabulary
Property of Proportions
The cross products of a proportion are equal
a/b = c/d then ad = bc
a c =
b d
Example 4-3b

6. Vocabulary Cross products
Multiplying the denominator of one ratio by the numerator of the equivalent ratio
a c =
b d
Example 4-3b

7. Example 1 Identify a Proportion Example 2 Solve a Proportion
Example 3 Use a Proportion to Solve a Problem
Lesson 4 Contents

8. Determine whether the ratios form a proportion.
Write the proportion
Cross multiply
Multiply the numerator of one ratio with the denominator of the other ratio
9  27
= 12  18
243
= 216
Multiply 9  27
Multiply 12  18
Products are not equal
Answer: The ratios do not form a proportion.
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Example 4-1a

9. Determine whether the ratios form a proportion.
Answer: The ratios form a proportion
1/3
Example 4-1b

10. Find the cross products.
Solve
Write the equation.
Find the cross products.
Bring down 20x =
20x
= 4(7)
Multiply 4  7
20x = 28
Ask “what is being done to the variable?”
Variable is being multiplied by 20
Do the inverse on both sides of the equal sign
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Example 4-2a

11. Use Identify Property to multiply 1  x
Solve
Bring down 20x = 28
Divide 20x by 20
Divide 28 by 20
20x
= 4(7)
Combine “like” terms
20x = 28
Use Identify Property to multiply 1  x
1  x = 1.4
1  x =
x = 1.4
Answer: x = 1.4
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Example 4-2a

12. Solve
Answer: x = 2.75
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Example 4-2b

13. 10 people and calls for 3 cups
COOKING A recipe serves 10 people and calls for 3 cups of flour. If you want to make the recipe for 15 people, how many cups of flour should you use?
10 people and calls for 3 cups
of flour
15 people
how many cups of flour
people served 10
Write first ratio
cups of flour 3
Write second ratio keeping units in same location
people served 15
cups of flour x
Write a proportion with the first ratio equal to the second ratio
10 15 =
3 x
3/3
Example 4-3a

14. Ask “what is being done to the variable?”
people served
10 15
Cross multiply =
cups of flour
3 x
Bring down =
Cross multiply
10x =
10x
10x = 3(15)
Bring down 10x =
10x = 45
10x =
Multiply 3  15
Ask “what is being done to the variable?”
Variable is being multiplied by 10
Do the inverse on both sides of the equal sign
3/3
Example 4-3a

15. Do the inverse on both sides of the equal sign
people served
10 15 =
Bring down 10x = 45
cups of flour
3 x
Divide 10x by 10
10x
10x = 3(15)
10x =
Divide 45 by 10
10x = 45
10x =
Combine “like” terms
10x = 45
Use Identify Property to multiply 1  x 10 10
Add dimensional analysis
1  x = 4.5
1  x =
Answer:
cups of flour
x = 4.5
3/3
Example 4-3a

16. Answer: x = 7.5 cups of sugar*
COOKING A recipe serves 12 people and calls for 5 cups of sugar. If you want to make the recipe for 18 people, how many cups of sugar should you use?
Answer: x = 7.5 cups of sugar
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Example 4-3b

17. Assignment
Lesson 4:4
Solving Proportions
All
End of Lesson 4