ABSTRACT
A ratio is a comparison between two quantities using division. For example, we might say that a car “gets 30 miles per gallon.” This statement describes the relationship between gas consumption and miles traveled. The word “per” means “for every.” Similarly, the preparation of a cake might require 10 oz of chocolate. The relationship between the cake and the amount of chocolate required is a ratio. Other commonplace examples of ratios are “revolutions per minute” (RPM) and “cost per pound.” A ratio is expressed with a numerator and denominator, like a fraction. (However, a ratio is not a fraction. Fractions, for example, can be added together and ratios cannot.) Ratio examples: 30 miles 1 gallon or , it is also correct to say 1 gallon 30 miles https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429282744/4b1628fb-c55b-4b9d-9fff-6f5f91cdcb42/content/C006_equ_0001.tif"/> 1 cake 10 oz chocolate or 10 oz chocolate 1 cake https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429282744/4b1628fb-c55b-4b9d-9fff-6f5f91cdcb42/content/C006_equ_0002.tif"/>
Example Problem:
A laboratory solution contains 58.5 grams of NaCl per liter. Express this as a ratio.
Answer:
This relationship can be expressed either as:
58.5 g 1 L or 1 L 58.5 g https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429282744/4b1628fb-c55b-4b9d-9fff-6f5f91cdcb42/content/C006_equ_0003.tif"/>
Practice Problems
Express each of the following as ratios in a fraction form. Be sure to have units in the numerator and denominator. For example:
A car is traveling 55 mph. Answer: 5 5 m i l e s 1 h o u r https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429282744/4b1628fb-c55b-4b9d-9fff-6f5f91cdcb42/content/C006_equ_0004.tif"/>
It would also be correct to say: 1 h o u r 5 5 m i l e s https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429282744/4b1628fb-c55b-4b9d-9fff-6f5f91cdcb42/content/C006_equ_0005.tif"/>
A record is labeled “33 rpm.” ________
A laboratory centrifuge is spinning at 50,000 rpm. ________
A cake requires 8 oz of chocolate. ________
A jogger runs 3 miles in 38 minutes. ________
45% of the class is female. ________
The dosage for a drug is 38 mg for each kg of body weight . ________
A person will die if exposed to ≥ 57 mg of mercury per kg of body weight. ________
A laboratory solution requires 100 mg of NaCl for each liter of solution. ________
The cost of a CD is $15. ________
1 km = 1,000 m ________
1 pound = 454 g ________
1 mL = 1,000 µL ________
A biotechnology production process can produce 3 g of product in each liter of culture . ________
Answers
(The reciprocals are also correct. For example, for problem a, you might say 33 revolutions/1 minute or 1 minute/33 revolutions.)
33 revolutions/1 minute
50,000 revolutions/1 minute
8 oz of chocolate/1 cake
3 miles/38 minutes
45 females/100 students
38 mg drug/1 kg body weight of patient
57 mg of mercury/1 kg of body weight
100 mg NaCl/1 L total solution
$15/1 CD
1 km/1,000 m
1 pound/454 g
1 mL /1,000 µL
3 g/1 L
