Review Sheet: Ratio, Proportion, Percent, Interest, and Percent of Change
Concept
Ratio: A ratio shows a relationship between two
numbers. Ratios can be written three different
ways.
5
5 to 3 or 5:3 or
3
Ratios are not fractions, but ratios can be reduced to
12 3
their lowest terms.
=
12:28 = 3:7 or 28 7
Sample Problem
Sally spends $200 of her $1,100 total monthly budget
on food. What is the ratio of her food expenses to her
total monthly expenses?
Proportion: A proportion is an equation that shows
that two ratios are equal. The cross products of a
true proportion are equal. That is, when you
multiply diagonally across the equals sign, the
products are equal. (Be sure the same units are
straight across from each other.)
3 ´
12 = 24
3 women 12 women
=
´
2
8 = 24
2 men
8 men
Proportion with Missing Number: If you know three
of the four numbers in a proportion, you can solve
for the missing number. The cross product
becomes the numerator and the remaining number
the denominator.
The directions on the hot chocolate mix say, “Add 3
teaspoons of mix to every 10 ounces of hot milk.” Bill,
Sam, and Fred mixed 9 teaspoons of mix with 30
ounces of hot milk. Did they make their hot chocolate
correctly?
Yes,
3 mix
9 mix
3´
9 = 90
=
they
10 milk 30 milk
10 ´
30 = 90
did.
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$200 to $1,100 = 2 to 11
or
2:11
or
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N = 33 ´ 30 = 110
9
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33 N
=
9 30
Change Percent to a Fraction: Write the percent over
100 and reduce.
Change Fraction to a Percent: Divide the numerator
by the denominator, move the decimal two places
to the right, and add a percent sign.
Change Percent to a Decimal: Drop the percent sign
and move the decimal two places to the left.
Change Decimal to a Percent: Move the decimal two
places to the right and add a percent sign.
Percent by Proportion: In any percent problem, there
are three elements: the Part, the Whole or Base,
and the Percentage Rate. These problems can be
solved with this proportion setup, using 100 as the
denominator
Part
% Rate
=
on the right.
Whole or Base
100
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Percent by Diagram: Percent problems can also be
solved using this
percent diagram.
Cover the element
you do not know.
Do the indicated
operation with the
other two elements.
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2
11
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A map scale says that 2 inches = 150 miles. What
actual distance would a map distance of 5 inches
represent?
N = 150 ´ 5 = 375 mi.
2
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2 in.
5 in.
=
150 mi. N mi.
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What fraction equals 80%?
80
8 4
=
=
100 10 5
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What percent equals
5
?
8
5 ÷ 8 = 0.625
0.625 = 62.5%
What decimal equals 22.5%?
22.5% = 0.225
What percent equals 3.75?
3.75 = 375%
The Mohamed’s pay 25% of their family’s total
monthly budget of $2,100 to rent their apartment. How
much is their monthly rent for their apartment?
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$N
25
=
$2,100 100
N = 2,100 ´ 25 = 52,500 = $525
100
100
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The Mohamed’s pay 25% of their family’s total
monthly budget of $2,100 to rent their apartment. How
much is the monthly rent for their apartment?
$2,100 x 25% = $525
Jerry gave his sister 30% of his Halloween candy. If
he gave her 12 pieces of candy, how many pieces of
candy did he start with?
12 ÷ 30% = 40
Simple Interest: The formula to calculate simple
interest is: Interest = Principal x Rate x Time.
Rate is a percentage and time must be in years.
Remember Interest + Principal = Total Payback.
Asher borrows $2,500 from his uncle for three years at
6% interest. What is the total amount he will he pay
back to his uncle for the loan.
Percent of Change: Percent is often used to describe
the amount of change over time. Calculate percent
of change in two steps:
1. Subtract the smaller number from the larger
number.
2. Divide this difference by the original number (the
number before the change).
A jacket is now on sale for $90. Last week the same
jacket was selling for $120. By what percent was the
price of the jacket reduced?
● $2,500 x 6% x 3 = $450 interest
● $2,500 + $450 = $2,950 total payback
● $120 - $90 = $30
● $30 ÷ 120 = 0.25 = 25%
The jacket’s price was reduced by 25%.