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UNIT 15

- RATIO AND PROPORTION

RATIOS

- A ratio is the comparison of two like quantities
- The terms of a ratio must be compared in the

order in which they are given - The first term is the numerator of a fraction,

and the second term is the denominator - A ratio should be expressed in lowest fractional

terms - Express 3 feet to 18 inches as a ratio in lowest

terms - Change the quantities to a common unit
- We will change the 3 feet to 36 inches
- Then write the ratio as a fraction and reduce

PROPORTIONS

- A proportion is an expression that states the

equality of two ratios - The product of the means equals the product of

the extremes - Solve the proportion below for A

1.2A (14.8)(2.4) Cross Multiply

Divide both sides by 1.2

A 29.6 Ans

DIRECT PROPORTIONS

- Two quantities are directly proportional if a

change in one produces a change in the other in

the same direction - When setting up a direct proportion in fractional

form, numerator of first ratio must correspond to

numerator of second ratio. Denominator of first

ratio must correspond to denominator of second

ratio

DIRECT PROPORTION EXAMPLE

- If reducing calorie intake by 2,000 calories

results in a weight loss of one pound, how many

pounds would a person lose if he/she ate 14,500

less calories? - Since an increase in calorie reduction will

result in an increase in weight loss, the

proportion is direct - Set calories as the numerator and pounds as the

denominator in both ratios - Solve by cross multiplication

x 7.25 pounds Ans

INVERSE PROPORTIONS

- Two quantities are inversely or indirectly

proportional if a change in one produces a change

in the other in the opposite direction - If an increase in one produces a decrease in the

other, or if a decrease in one produces an

increase in the other, the two quantities are

inversely proportional - When inverse proportion is set up in fractional

form, numerator of first ratio must correspond to

denomi-nator of the second ratio. Denominator of

first ratio must correspond to numerator of

second ratio

INVERSE PROPORTION EXAMPLE

- It takes 3.5 hours for the 12 workers at Bettys

Bakery to prepare the baked goods sold each day.

How many hours would it take 15 workers to

produce the same goods? - Since more workers would require less time to

bake the goods, this problem is an inverse

proportion - Set numerator of first ratio equal to 3.5 hours

and set corresponding 12 workers equal to

denominator of second ratio. Denominator of first

ratio will be the variable (x hours) and

numerator of second ratio will be the

corresponding 15 workers

Now, solving by cross multiplication

x 2.8 hours Ans

PRACTICE PROBLEMS

- Express the following ratios in lowest terms
- 1. 1628
- 2. 2/5 to 1/3
- 3. 20 min to 1 hour
- Solve the following proportions

PRACTICE PROBLEMS

- 7. The fifteen workers in the Fly-By-Night

Machine Shop produce 1200 widgets daily. How many

widgets would twenty workers produce daily? - 8. The scale on a given map is 1 inch 32

miles. How many miles would there be between two

cities that are 3 inches apart on the map? - 9. Two gears are in mesh. The driver gear has

30 teeth and revolves at 250 revolutions per

minute. Determine the number of revolutions per

minute of a driven gear with 12 teeth. - 10. If six identical machines can produce 1000

parts in 7 hours, how many hours will it take

four of these machines to produce the same 1000

parts?

PROBLEM ANSWER KEY

- 1. 4/7
- 2. 6/5
- 3. 1/3
- 4. 5.6
- 5. 277.55
- 6. 20
- 7. 1600 widgets
- 8. 112 miles
- 9. 625 rpm
- 10. 10.5 hours

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