414 Chapter 5 Ratio, Proportion, and Measurement
SECTION 5.1
Ratios
Objectives
1 Write ratios as fractions.2 Simplify ratios involving
decimals and mixed numbers.
3 Convert units to write ratios.4 Write rates as fractions.5 Find unit rates.6 Find the best buy based on unit
price.Ratiosare often used to describe important relationships between two quantities.
Here are three examples:Write ratios as fractions.
Ratios give us a way to compare two numbers or two quantities measured in the same
units.RatiosA ratiois the quotient of two numbers or the quotient of two quantities that
have the same units.There are three ways to write a ratio. The most comon way is as a fraction. Ratios
can also be written as two numbers separated by the word to,or as two numbers
separated by a colon. For example, the ratios described in the illustrations above can
be expressed as:- The fraction is read as “the ratio of 50 to 1.”
- 14 to10 is read as “the ratio of 14 to 10.”
- 2 3 is read as “the ratio of 2 to 3.”
Writing a Ratio as a FractionTo write a ratio as a fraction,write the first number (or quantity) mentioned as
the numerator and the second number (or quantity) mentioned as the
denominator. Then simplify the fraction, if possible.A colon separates the numbers
being compared.The word “to”separates the
numbers being compared.A fraction bar separates the
numbers being compared.50
1
50
1
, 14 to 10, and 2 : 3
1To prepare fuel for an outboard
marine engine, gasoline must
be mixed with oil in the
ratio of 50 to 1.To make 14-karat jewelry,
gold is combined with other
metals in the ratio of
14 to 10.In this drawing, the eyes-to-nose
distance and the nose-to-chin
distance are drawn using a
ratio of 2 to 3.23