MEE2 Unit 4 Terms and Practice PDF

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1 MEE2 Unit 4 Terms and Practice

1. A ratio is a comparison of two numbers. It can be expressed three ways. Ex 1a. There are 12 girls and 17 boys in a class. Write the ratio of girls to boys three ways. 12

12 to 17 12:17 17 Ex 1b. In the word, mathematics, what is the ratio of vowels to consonants? 4 4 vowels to 7 consonants 4:7 7 2. A proportion is an equation stating that two ratios are equal. 1∙ 10 = 2 ∙ 5 10 = 10.

1 2

5

= 10 is a proportion. Notice if you cross multiply,

Ex 2a.

Ex. 2b. Solve for x.

Ex 2c. Solve for x.

𝑥

−22

= 10 10x = – 110 x = −11

5

cross multiply divide

1

3 2 is to 7 as x is to 48 1

32 7

𝑥

= 48 1

7x = 3 2 ∙ 48

cross multiply

7x = 48 7x = 168 x = 24

change to improper fraction multiply divide

7 ∙ 2

2 Ex 2d. Terry baked 10 cookies with 2 scoops of flour. How many scoops of flour does Terry need in order to 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 45 10 write proportion in words bake 45 cookies? = 𝑥 = 2

𝑓𝑙𝑜𝑢𝑟

𝑓𝑙𝑜𝑢𝑟

10x = 90 x=9

cross multiply divide

1

Ex 2e. On a map, 5 in. represents 10 mi. If two cities are 18 in. apart on the map, what is the actual distance between them?

𝑖𝑛 𝑚𝑖

=

1 5

18 = 10 𝑥 1 x = 180 5 1 5 ∙ 5x = 5∙180

𝑖𝑛 𝑚𝑖

write proportion in words cross multiply multiply by reciprocal

x = 900 Ex 2f. If you can buy one can of pineapple chunks for $3 then how many can you buy with $12? 𝑥 1 𝑐𝑎𝑛𝑠 𝑐𝑎𝑛𝑠 write proportion in words = 12 = 3 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 3x = 12 cross multiply x=4 divide Ex 2g. One package of blueberries costs $3. How many packages of blueberries can you buy for $9? 1 3

𝑝𝑎𝑐𝑘𝑠 𝑝𝑎𝑐𝑘𝑠 = 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 𝑑𝑜𝑙𝑙𝑎𝑟𝑠

𝑥

=9 3x = 9 x=3

write proportion in words cross multiply divide

2

Ex 2h. If a certain recipe takes 25 cups of flour for 3 cups of sugar, how much sugar should be added if the cook only has 2 cup of flour?

𝑓𝑙𝑜𝑢𝑟 𝑠𝑢𝑔𝑎𝑟

𝑓𝑙𝑜𝑢𝑟

= 𝑠𝑢𝑔𝑎𝑟

2

2 5

3

=

2

𝑥 2 2 5x = 6 12 𝑥=6 5 5 5 12 ∙ x = ∙6 12 5 12 30 1 5 x= = = 22 2 12

write proportion in words cross multiply change to improper fraction multiply by reciprocal

Ex 2i. The money used in Jordan is called the Dinar. The exchange rate is $3 to 2 Dinars. Find how many dollars you would receive if you exchanged 32 Dinars. 𝑥 3 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 = = 𝐷𝑖𝑛𝑎𝑟𝑠 write proportion in words 2 𝐷𝑖𝑛𝑎𝑟𝑠 32 2x = 96 cross multiply x = 48 divide

3 Practice 1. In the word, proportion, what is the ratio of vowels to consonants? 6 4 4 C. B. 6 A. 10 4

𝑥 3

2. Solve for x. A.

=

5 12

12 15

B.

15 4

C.

3. Solve for x. A. 8

𝑥

4. Solve for x. A. 14

3 2 is to 8 as x is to 32 B. 28

4

=

12 5

−12 6

B. – 8

C. – 6

1

C. 7

1

5. On a map, 2 in. represents 10 mi. If two cities are 15 in. apart on the map, what is the actual distance between them? A. 30 B. 150 C. 300 6. One package of blueberries costs $5. How many packages of blueberries can you buy for $30? A. 6 B. 5 C. 10 3

7. If a certain recipe takes 24 cups of flour for 4 cups of sugar, how much sugar should be added if the cook only has 2 cup of flour? 10 3 11 C. 2 B. 1 8 A. 32 11

8. Jane was planning a trip to Western Samoa. Before going, she did some research and learned that the exchange rate is 6 Tala for $2. How many Tala would she get if she exchanged $54? A. 162 B. 18 C. 324

Answers 1-B 2-C

3-B

4-A

5-C

6-A

7-C

8-A...