Unit 9 Notes: Proportions, Exercises of Algebra

Solving Practical Problems Using Proportions. 1) Set-up the proportion using WORDS. 2) Set-up the proportion with known values. 3) Cross multiply. 4) Solve ...

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Name:____________________________________________________ Block:_____ Date:_______________________ MATH 6/7 NOTES & PRACTICE
Unit 9 Notes: Proportions
A proportion is an equation stating that two ratios (fractions) are equal.
๏‚ท If the cross products are equivalent, the two ratios form a proportion.
๏‚ท If the cross products are not equal, the ratios DO NOT form a proportion.
Examples:
Determine whether each pair of ratios forms a proportion.
A) 1
3,3
9 B) 1.2
4, 2
5
Independent Practice: Determine if each pair of ratios are equivalent.
1) 2
3,8
12
2) 4
2,18
7
3) 1.5
5,3
9
4) 2.1
3.5 ,3
7
5) 5.3
15.9 ,2.7
8.1
6) 18
2.4 ,15
2
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pf4
pf5

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Name:____________________________________________________ Block:_____ Date:_______________________ MATH 6/7 NOTES & PRACTICE

Unit 9 Notes: Proportions

A proportion is an equation stating that two ratios (fractions) are equal.

๏‚ท If the cross products are equivalent, the two ratios form a proportion.

๏‚ท If the cross products are not equal, the ratios DO NOT form a proportion.

Examples:

Determine whether each pair of ratios forms a proportion.

A)

1 3

3 9

B)

  1. 2 4

2 5

Independent Practice: Determine if each pair of ratios are equivalent.

2 3

8 12

4 2

18 7

  1. 5 5

3 9

  1. 1
  2. 5

3 7

  1. 3
  2. 9
  1. 7
  2. 1

18

  1. 4

15 2

If a proportion contains a variable, use cross multiplication and single-step algebra to find the missing

value.

Examples: Solve the proportion.

A)

๐‘Ž 25

52 100

B)

  1. 5 ๐‘š

15

  1. 5

Independent Practice: Solve each proportion.

๐‘˜ 35

3 7

3 ๐‘ก

18 24

10

  1. 4

5 ๐‘š

๐‘ 6

24 36

2 15

๐‘ 72

2

  1. 4
  1. 2 ๐‘ฃ

๐‘Ž

  1. 28

4

  1. 4

16 ๐‘ฅ+ 5

4 5

(distributive property)

Solving Proportions

  1. Write a proportion
  2. Cross Multiply
  3. Simplify
  4. Divide to isolate the variable ๏ƒผ The cross products of two ratios must be equal if the two ratios form a proportion
  1. If there are 3.28 feet in a meter, how many feet are in the 110 meter dash?
  2. A photograph is 3 inches wide by 5 inches long. If the photograph is enlarged so that the length is 7 inches, how wide is the enlarged photo?
  3. If 1 pint of paint is need to paint a square that is 5 feet on each side, how many pints are needed to paint a square that is 9 feet on each side?
  4. The world's largest baseball bat is 120 feet long. If there are 30.28 centimeters in a foot, find the length of the bat in centimeters.

Currency Exchange Rates

  1. Ming is planning a trip to Western Samoa. The exchange rate is 6 Tala for $2. How many Tala will she get if she exchanged $6?
  2. The money used in Jordan is called Dinar. The exchange rate is $3 to 2 Dinars. Find how many dollars you would receive if you exchanged 22 Dinars?
  3. Jenny is planning a trip to the United Arab Emirates. She learned that the exchange rate is 4 Dirhams for every dollar. How many Dirhams would she get if she exchanged $7?
  4. Asanji took a trip to Mexico. Upon returning to the US he converted his Pesos back to dollars. How much did he receive in dollars if he exchanged 42.7 Pesos at a rate of $5.30 = 11. Pesos? Round your answer to the nearest cent.
  1. The currency in Argentina is the Peso. The exchange rate is approximately $3 = 1 Peso. At this rate, how many Pesos would you get if you exchanged $121.10? Round your answer to the nearest tenth.
  2. The money in Peru is called the Nuevo Sole. The exchange rate is $8.80 for one Nuevo Sole. How many dollars would you receive if you exchanged 32.4 Nuevos Soles?
  3. The currency in Tajikistan is Somoni. The exchange rate is approximately 1 Somoni for every $9.70. At this rate, how many Somoni would you get if you exchanged $436.60? Round your answer to the nearest tenth.
  4. The money used in the Eastern Caribbean Islands is called the Eastern Caribbean Dollar. The exchange rate is $4 to one Eastern Caribbean Dollar. How many Eastern Caribbean Dollars would you receive if you exchanged $162.60?

Shapes

  1. Shawna reduced the size of a rectangle to a height of 2 inches. What is the new width if the original rectangle had a width of 24 inches and a height of 12 inches?
  2. Nicole reduced the size of a photo to a width of 4.6 inches. What is the new height if it was originally 9.4 inches tall and 9.2 inches wide?
  3. A triangle is 20 inches in height and has a base of 5 inches wide. If the base is reduced to a width of one inch, how tall will it be?
  4. A frame is 9 inches wide by 6 inches tall. If the width is reduced to 3 inches, what is the new length of the frame?