Download 6.1

Math 64
6.1 "Ratios and Rates"
Bibiana Lopez
Riverside City College
July 2010
(RCC)
6.1
July 2010
1 / 14
Objectives:
* Write ratios and rates as fractions.
* Find unit rates and unit prices.
(RCC)
6.1
July 2010
2 / 14
Writing Ratios as Fractions
A ratio is the quotient of two quantities. A ratio, in fact, is no
di¤erent from a fraction, except that a ratio is sometimes written
using notation other than fractional notation. For example, the ratio
of 2 to 3 can be written as
1 to 2 or 12 (fractional notation) or 1 : 2 (colon notation)
(RCC)
6.1
July 2010
3 / 14
Writing Ratios as Fractions
A ratio is the quotient of two quantities. A ratio, in fact, is no
di¤erent from a fraction, except that a ratio is sometimes written
using notation other than fractional notation. For example, the ratio
of 2 to 3 can be written as
1 to 2 or 12 (fractional notation) or 1 : 2 (colon notation)
In this section, we write ratios using fractional notation. If the
fraction happens to be an improper fraction, do not write the fraction
as a mixed number. Why?
The mixed number form is not a ratio or quotient of two quantities.
(RCC)
6.1
July 2010
3 / 14
Writing Ratios as Fractions
A ratio is the quotient of two quantities. A ratio, in fact, is no
di¤erent from a fraction, except that a ratio is sometimes written
using notation other than fractional notation. For example, the ratio
of 2 to 3 can be written as
1 to 2 or 12 (fractional notation) or 1 : 2 (colon notation)
In this section, we write ratios using fractional notation. If the
fraction happens to be an improper fraction, do not write the fraction
as a mixed number. Why?
The mixed number form is not a ratio or quotient of two quantities.
If a ratio contains decimal numbers or mixed numbers, we simplify by
writing the ratio as a ratio of whole numbers.
(RCC)
6.1
July 2010
3 / 14
Writing Ratios as Fractions
Writing a Ratio as a Fraction:
The order of the quantities is important when writing ratios.
To write a ratio as a fraction, write the …rst number of the
ratio as the numerator of the fraction and the second
number as the denominator.
(RCC)
6.1
July 2010
4 / 14
Writing Ratios as Fractions
Example 1: (Writing ratios as fractions)
Write each ratio as a ratio of whole numbers using fractional notation.
Write the fraction in simplest form.
a) 4.63 to 8.21
b) 8.1 to 10
(RCC)
6.1
July 2010
5 / 14
Writing Ratios as Fractions
d) 3 13 days to 4 16 days
c) 120 miles to 80 miles
(RCC)
6.1
July 2010
6 / 14
Writing Ratios as Fractions
Example 2: (Application)
Find the ratio of the length to the width of a regulation size basketball
court.
(RCC)
6.1
July 2010
7 / 14
Writing Ratios as Fractions
Example 3: (Application)
Find the ratio of the longest side to the perimeter of the right-triangularshaped billboard.
(RCC)
6.1
July 2010
8 / 14
Writing Rates as Fractions
A special type of ratio is a rate. Rates are used to compare di¤erent
kinds of quantities. For example,
3 miles
1 mile
=
(In simplest form)
33 minutes
11 minutes
(RCC)
6.1
July 2010
9 / 14
Writing Ratios as Fractions
Example 4: (Writing rates as fractions)
Write each rate as a fraction in simplest form.
a) 4 inches of rain in 18 hours
b) 295 miles on 15 gallons of gasoline
(RCC)
6.1
July 2010
10 / 14
Finding Unit Rates
A unit rate is a rate with a denominator of 1.
Writing a Rate as a Unit Rate:
To write a rate as a unit rate, divide the numerator
of the rate by the denominator.
(RCC)
6.1
July 2010
11 / 14
Finding Unit Rates
Example 5: (Finding unit rates)
Write each rate as a unit rate.
a) A hummingbird moves its wings at a rate of 5400 wingbeats a minute.
Write this rate in wingbeats per second.
b) 400,000 library books for 8000 students.
(RCC)
6.1
July 2010
12 / 14
Finding Unit Prices
Rate are used extensively in sports, business, medicine, and science.
One of the most common uses of rates is in consumer economics. When a
unit rate is "money per item," it is also called a unit price.
unit price =
(RCC)
price
number of units
6.1
July 2010
13 / 14
Finding Unit Prices
Example 6: (Finding unit price)
Find each unit price.
a) $57.50 for 5 compact disks
(RCC)
b) $0.87 for 3 apples
6.1
July 2010
14 / 14