Question

Explain how each of the following rates satisfies the definition of ratio. Given an example of how each is used.

A. 1580 people/square mile
B. 360 kilowatt-hour/4 months
C. 450 people/year
D. 355 calories/6 ounces

Answer 1

Explanation:

A ratio is defined as a comparison of two amounts by division.It is of the form of
`(p)/(q)` where p and q are the quantities.

A. 1580 people/square mile in division form

1580
`\frac{people}{\text{square mile}}`

This satisfies ratio definition as this compares two quantities People and Square mile and is of the form
`(p)/(q)`

Where,

p: People, q: Square mile

Example,

`(1580* people)/(1* squaremile)`

expresses that per 1 square mile there are 1580 people. Thus rate satisfies the ratio definition.

B. 360 kilowatt-hour/4 months

in division form
`\frac{\text{360 kilowatt-hour}}{\text{4months}}`

This satisfies ratio definition as this compares two quantities kilowatt-hour and months and is of the form
`(p)/(q)`

where, p: kilowatt-hour and q: people

Example,

`(\360* kilowatt-hour)/(4* months)`

expresses that per 4 months there are 360 kilowatt-hour. Thus, rate satisfies the ratio definition.

C. 450 people/year

In division form 450
`(people)/(year)`

This satisfies ratio definition as this compares two quantities people and year and is of the form
`(p)/(q)`

where, p: people and q: year

Example,

`\frac{450* people}{1*\text{year}}`

expresses that per year there are 450 people. Thus, rate satisfies the ratio definition.

D. 355 calories/6 ounces

In division form
`(355clories)/(6ounces)`

This satisfies ratio definition as this compares two quantities calories and ounces and is of the form
`(p)/(q)`

where p: calories and q: ounces

Example,

`\frac{355* calories}{6*\text{ounces}}`

expresses that per 6 ounces there are 355 calories. Thus, rate satisfies the ratio definition.