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The comparison by division of the pure numbers and the like denominate numbers are examples of ratios.
The comparison by division of two unlike denominate numbers, such as
are examples of rates.
Let's agree to represent two numbers (pure or denominate) with the letters and . This means that we're letting represent some number and represent some, perhaps different, number. With this agreement, we can write the ratio of the two numbers and as
or
The ratio is read as " to ."
The ratio is read as " to ."
Since a ratio or a rate can be expressed as a fraction, it may be reducible.
The ratio 30 to 2 can be expressed as . Reducing, we get .
The ratio 30 to 2 is equivalent to the ratio 15 to 1.
The rate "4 televisions to 12 people" can be expressed as . The meaning of this rate is that "for every 4 televisions, there are 12 people."
Reducing, we get . The meaning of this rate is that "for every 1 television, there are 3 people.”
Thus, the rate of "4 televisions to 12 people" is the same as the rate of "1 television to 3 people."
Write the following ratios and rates as fractions.
3 to 2
1 to 9
5 books to 4 people
120 miles to 2 hours
8 liters to 3 liters
Write the following ratios and rates in the form " to ." Reduce when necessary.
9 to 5
1 to 3
25 miles to 2 gallons
1 mechanic to 2 wrenches
5 to 6
For the following 9 problems, complete the statements.
Two numbers can be compared by subtraction if and only if
They are pure numbers or like denominate numbers.
A comparison, by division, of two pure numbers or two like denominate numbers is called a
A comparison, by division, of two unlike denominate numbers is called a
rate
is an example of a
is an example of a
ratio
is an example of a
is an example of a
rate
is an example of a
is an example of a
ratio
For the following 7 problems, write each ratio or rate as a verbal phrase.
two to five
29 mile per 2 gallons or miles per 1 gallon
5 to 2
For the following problems, write the simplified fractional form of each ratio or rate.
12 to 5
81 to 19
42 plants to 5 homes
8 books to 7 desks
16 pints to 1 quart
4 quarts to 1 gallon
2.54 cm to 1 in
80 tables to 18 tables
25 cars to 10 cars
37 wins to 16 losses
105 hits to 315 at bats
510 miles to 22 gallons
1,042 characters to 1 page
1,245 pages to 2 books
( [link] ) Convert to a mixed number.
( [link] ) of is what number?
( [link] ) Find the difference. .
( [link] ) Perform the division. If no repeating patterns seems to exist, round the quotient to three decimal places:
( [link] ) Find the value of
3.3875
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