Math 100 Class Notes
Writing Fractions in Order
One important application of the least common denominator is to use the LCD to help order or
compare fractions.
?
Insert < or > to form a true sentence.
The LCD for these fractions is 35.
Write each fraction as an equivalent fraction with a denominator of 35.
=
∙
∙
=
Compare the numerators of the equivalent fractions.
Since 21 > 20, then
>
Examples: Insert <, > or =
=
∙
∙
=
. Thus, > .
5.
6.
6.1 Ratio and Proportion
Writing Ratio as Fractions
A ratio is the quotient of two quantities.
For example, a percent can be thought of as a ratio, since it is the quotient of a number and 100.
53% =
or the ratio of 53 to 100.
The ratio of a number a to a number b is their quotient. Ways of writing ratios are:
a to b,
a : b, and
25
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R. Getso
Examples: Write the ratio in lowest terms.
1. 6 hours to 36 hours
2. 36 minutes to 3 hours
Solving Proportions
A proportion is a statement that two ratios are equal.
If
and
are ratios, then
=
is a proportion.
Example:
4. Is
=
a true proportion?
Examples: Solve each proportion.
5.
=
6.
=
3. 17¢ to $4
Math 100 Class Notes
7.
=
8. A 16-oz Cinnamon Mocha Iced Tea at a
local coffee shop has 80 calories. How many
calories are there in a 28-oz Cinnamon Mocha
Iced Tea?
Helpful Hint: When writing proportions to solve problems, write the proportions so that the
numerators have the same unit measures and the denominators have the same unit measures.
For example,
2 inches 7 inches
=
5 miles
miles
6.2 Percents, Decimals and Fractions
Understanding Percent
The word percent comes from the Latin phrase per centum, which means “per 100.”
Percent means per one hundred. The “%” symbol is used to denote percent.
1
1% =
= 0.01
100
Writing a Decimal as a Percent
Multiply by 1 in the form of 100%.
0.65 = 0.65(100%) = 65.% or 65%
Writing a Percent as a Decimal
Replace the percent symbol % with its decimal equivalent, 0.01; then multiply.
43% = 43(0.01) = 0.43
100% = 100(0.01) = 1.00 or 1
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