Praxis Core Prep: Reasoning with Quantities
The Praxis Core exam tends to involve questions on the math section about quantities and how they are related. Various categories of quantities exist, and two major systems are used for measuring them.
The two major systems of measurement
The two mainstream systems of measurement in the United States are the English system and the metric system. Here are the basic units of measurement for each system.
Form of Measurement  English System  Metric System 

Distance  Inch, foot, yard, mile  Meter 
Volume  Cup, pint, quart, gallon  Liter 
Weight  Ounce, pound, ton  Gram 
The metric system has fewer units because each category of measurement uses the same base unit. However, you can add prefixes to the unit that give you morespecific information about the size of the measurement. For example, 1,000 grams is the same as 1 kilogram. All the prefix meanings in the metric system are multiples of 10 or multiples of 1/10.
Metric Prefix  Meaning 

Milli  1/1,000 
Centi  1/100 
Deci  1/10 
Main unit (meter, liter, gram)  1 
Deca  10 
Hecto  100 
Kilo  1,000 
The English system doesn’t have consistent base units for categories of measurement. The English units for each type of measurement are based on each other, but not in ways that mere suffixes are sufficient for changing terminology with varying levels. Here’s how the different units of measurement relate within each form:

Distance: 12 inches make up a foot, 3 feet make a yard, and 5,280 feet compose a mile.

Volume: 2 cups form a pint, 2 pints make a quart, and 4 quarts make up a gallon.

Weight: 16 ounces make a pound, and a ton is 2,000 pounds.
Converting units of measurement
Problems on the Praxis Core exam may involve converting one unit of measurement to another. For example, you may need to determine that 5 feet is the same as 60 inches or figure out how many deciliters are in 3 hectoliters.
To make such conversions, use the more basic unit to multiply if the answer involves the bigger unit and divide if the answer involves the smaller unit. For example, say you want to know how many inches of twine are in 4 yards. You have to convert yards to feet to inches:

Convert yards to feet.
4 yards = 4(3 feet) = 12 feet

Convert feet to inches.
(12 feet)(12 inches) = 144 inches
Therefore, 4 yards is equal to 144 inches.
To convert from greater to lesser units, divide instead of multiply. The same applies to metric units, but the conversions are easier because you can simply multiply by multiples of 10 or 1/10.
How many kilograms are in 7 centigrams?

(A) 0.00007

(B) 7,000

(C) 700

(D) 70

(E) 7
The answer is Choice (A). Moving from kilograms to centigrams, the number gets smaller, so multiply 7 by 1/10 for every space the prefixes are apart on the table
Choice (B) falsely involves the result of multiplying 7 by 10^{5} instead of by 1/10 as a factor that many times. Choices (C) and (D) involve too few factors and multiplying in the wrong direction. Choice (E) falsely implies that a kilogram is the same as a centigram.
Basic word problems
Conversions with units can be involved in answering word problems, but often they also require performing other operations. You need to memorize the meanings of the units and prefixes for the Praxis Core exam because they won’t be provided. You also need to understand how words used in each system for each type of measurement are connected to each other.
If a cook pours 5 quarts of water out of a 3gallon container and then another cook takes his place and adds 2 pints of water, how many cups of water are in the container?

(A) 8

(B) 16

(C) 72

(D) 32

(E) 64
The correct answer is Choice (D). The best way to determine the answer is to convert all the measurements to numbers of cups and then calculate the number of cups remaining.
You could also convert the measures to numbers of pints and convert to cups on the last step. 5 quarts is equal to 5(4) cups; 3 gallons is the same as 3(16) cups; and 2 pints is a measure equal to 2(2) cups. 48 – 20 + 4 = 32, so the answer is 32.
Choice (A) is the number of quarts that result, and Choice (B) is the equivalent measure in pints. Choice (C) is the number of quarts that would result if all of the mentioned quantities were added, and Choice (E) could be the correct answer if there were 4 cups in a pint instead of 2.