Ratio
Pronunciation: /ˈreɪ.ʃoʊ/ Explain
A ratio is used to compare two quantities, or to give a
number that can be used to convert one unit of measure to a different, related unit of
measure. For example, in 2010, there are about 307,000,000
people in the United States. Of these, about 3,000,000
live in Mississippi. The ratio of the number of people in Mississippi to the number of
people in the United states is 3,000,000:307,000,000 ≈
3:307 ≈ 1:101. This means that about 1 out of
every 100 people in the United States lives in Mississippi.
When comparing a part to a whole, a ratio is sometimes called a
proportion.
You can also compare different things using a ratio. For example, extrapolating
from existing data, there are about 120 million cats in
the United States. The ratio of cats to humans is 120,000,000
to 307,000,000. 120,000,000:307,000,000 ≈ 120:307 ≈
1:2.6. There is about one cat for every 2.6 people in
the United States.
Ratios are often expressed as percentages. A
percentage
is a portion out of 100. 1
out of 100 is 1 percent.
A ratio can also be expressed as a real number, also called a
rate. For example, if 1 gallon
of gas costs $4.50, the ratio of dollars to gallons is
$4.50:1. This is called the price per gallon. In this
case, the price per gallon is written as $4.50/gal rather
than as a ratio.
Ratios are used through math. Some of the ratios that are used are:
- Numbers
- Rational Numbers
- A real number that can be expressed exactly as the ratio of two integers.
- Algebra
- Variation:
- In variation, one variable differs from another by a constant ratio. The ratio
is called the constant of variation.
- Geometric series
- In a geometric series, each term is multiplied by a constant ratio to get
the next term.
- Conversion factor - A conversion factor is a
ratio used to convert one unit of measure to a related unit of measure.
- Rational expression
- A rational expression is an expression that contains one or more ratios of
polynomials.
- Ratio test - A test for convergences of series that uses the ratio of a
term to the term before it.
- Geometry
- Trigonometric ratio - A trigonometric ratio is a ratio of the lengths
of two sides of a right triangle.
- Golden Section
- A golden section is the ratio that divides a line segment into two parts such
that the ratio of the length of the whole to the length of the larger segment
is the same as the ratio of the length of the larger segment to the smaller
segment.
- Pi π
- Pi is the constant ratio of the circumference of a circle to the diameter of
the circle.
- Similarity ratio - The ratio of corresponding sides of similar
geometric figures is constant.
- Dilation ratio
- A dilation ratio tells how much bigger or smaller a dilation transformation
will make an object.
- Cartography (maps)
- Map scale - A map scale is the ratio of a unit of measure on the map
to the same unit of measure for the thing being mapped.
- Shopping
- Price - All prices are ratios. Usually a price tells how much for
1 unit. Sometimes a price is how much for a pound
or a kilogram. Sometimes a price is something like
'3 for $5'.
Converting a word problem to a ratio
Some of the keys to solving ratio word problems are:
- Make sure quantities are the same units.
- Write all ratios as fractions
The steps to solving ratio word problems are:
- Assign variables to unknown quantities
- Write one or more equations using fractions for ratios.
- Solve the equation(s).
- Convert the answer into words.
Example 1: A box of chocolates contains raspberry
cremes and strawberry cremes in a ratio of 2:3. There are 10 raspberry cremes. How
many strawberry cremes are in the box?
- Assign variables - The unknown is the number of strawberry cremes. Let
x be the number of strawberry cremes in
a box.
- Write an equation - .
- Solve the equation
- Cross multiply: .
- Simplify multiplication: .
- Divide both sides by 2: .
- Convert the answer into words - There are 15 strawberry cremes in a box.
Example 2: The ratio of boys to girls in a class is
5:6. There are 33 students in the class. How many are girls?
- Assign variables - The unknowns are the number of boys and the number
of girls. Let b be the number of boys and g be the number of girls.
- Write equations - ,
.
- Solve the equations
- Cross multiply: .
- Solve for g by dividing both sides of the equation by 5: .
- Substitute for g
in the second equation:
- Change the b to the common denominator of 5: .
- Combine the like fractions: .
- Clear the fraction by multiplying both sides of the equation by 5: .
- Divide both sides of the equation by 11: .
- Substitue 15 for b in the second equation: .
- Subtract 15 from both sides of the equation: .
- Convert the answer into words: There are 18 girls in the class.
References
- McAdams, David E.. All Math Words Dictionary, ratio. 2nd Classroom edition 20150108-4799968. pg 150. Life is a Story Problem LLC. January 8, 2015. Buy the book
Cite this article as:
McAdams, David E. Ratio. 4/30/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/ratio.html.
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Revision History
4/30/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/4/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
1/5/2011: Initial version. (
McAdams, David E.)