MP2 Section Four Notes on Percents and Probability
Fraction of a whole #
2/3 of 15 tuna cans – sample
*Think : Divide 15 into 3 equal sized groups. 5 in each
group
10= in 2 groups bc…… xxxxx xxxxx xxxxx
2/3 of 15= 10
1. Take the WHOLE number and divide it by the
denominator
2. that answer will give you how many are in each
group
3. Then multiply that number by the numerator
Ex: 2/3 of 36
1. 36 divided by 3= 12
2. 12 x 2 = 24
OR
2/5 of 20
1. re write the fraction as 2/5 x 20/1 (20/1 is same as
just the #20)
2. multiply across (after you cross reduce)
3. Solve and simplify the fraction
Understanding Percents


percent means “per hundred” or “of 100”
% is the percent sign
Fraction = 25/100
Decimal = .25
Percent = 25%
*When going from a decimal to a percent: multiply by 100 or move decimal two times
to the right
Ex= .62 x 100= 62%
*When going from fraction to percent= make equivalent fractions with 100
Ex: 3/10 -- x10 on top and bottom -- 30/100 === 30%
4/25----x 4 = 16/100==== 16%
Definition: A percent is a ratio whose second term is 100. Percent means parts
per hundred. The word comes from the Latin phrase per centum, which
means per hundred. In mathematics, we use the symbol % for percent.
Let's look at our comparison table again. This time the table includes percents.
Comparing Shaded Boxes to Total Boxes
Grid
Ratio
Fraction
Percent
1
96 to 100
96%
2
9 to 100
9%
3
77 to 100
77%
Writing Fractions
as Percents
Problem: Last marking period, Ms. Jones gave an A grade to 15 out of
every 100 students and Mr. McNeil gave an A grade to 3 out of
every 20 students. What percent of each teacher's students
received an A?
Solution
Teacher
Ratio
Fraction
Percent
Ms. Jones
15 to 100
15%
Mr. McNeil
3 to 20
15%
Solution: Both teachers gave 15% of their students an A last marking period.
In the problem above, the fraction for Ms. Jones was easily converted to a percent. This is
because It is easy to convert a fraction to a percent when the denominator is 100. If a
fraction does not have a denominator of 100, you can convert it to an equivalent fraction with
a denominator of 100, and then write the equivalent fraction as a percent. This is what was
done in the problem above for Mr. McNeil. Let's look at some problems in which we use
equivalent fractions to help us convert a fraction to a percent.
Example 1: Write each fraction as a percent:
Solution
Fraction
Equivalent
Fraction
Percent
50%
90%
80%
Example 2: One team won 19 out of every 20 games played, and a second team
won 7 out of every 8 games played. Which team has a higher
percentage of wins?
Solution
Team
Solution:
Fraction
Equivalent
Fraction
Percent
1
95%
2
87.5%
The first team has a higher percentage of wins.
In Examples 1 and 2, we used equivalent fractions to help us convert each fraction to a
percent. Another way to do this is to convert each fraction to a decimal, and then convert
each decimal to a percent. To convert a fraction to a decimal, divide its numerator by its
denominator. Look at Example 3 below to see how this is done.
Example 3: Write each fraction as a percent:
Solution
Fraction
Decimal
Percent
87.5%
95%
1.5%
Now that you are familiar with writing fractions as percents, do you see a pattern in the
problem below?
Problem: If 165% equals
, and 16.5% equals
, then what fraction is equal to 1.65%?
Solution
Percent
Fraction
165%
16.5%
1.65%
Summary: To write a fraction as a percent, we can convert it to an equivalent
fraction with a denominator of 100. Another way to write a fraction as a
percent is to divide its numerator by its denominator, then convert the
resulting decimal to a percent.
Converting a Fraction to a Percent
Do the following steps to convert a fraction to a percent:
For example: Convert 4/5 to a percent.




Divide the numerator of the fraction by the denominator
(e.g. 4 ÷ 5=0.80)
Multiply by 100 (Move the decimal point two places to the
right) (e.g. 0.80*100 = 80)
Round the answer to the desired precision.
Follow the answer with the % sign (e.g. 80%)
Converting a Percent to a Fraction
Do the following steps to convert a percent to a fraction:
For example: Convert 83% to a fraction.



Remove the Percent sign
Make a fraction with the percent as the numerator and
100 as the denominator (e.g. 83/100)
Reduce the fraction if needed
Converting a Decimal to a Percent
Do the following steps to convert a decimal to a percent:
For example: Convert 0.83 to a percent.


Multiply the decimal by 100 (e.g. 0.83 * 100 = 83)
Add a percent sign after the answer (e.g. 83%)
Converting a Percent to a Decimal
How to convert a percent to a decimal:
For example: Convert 83% to a decimal.
Divide the percent by 100 (e.g. 83 ÷ 100 = 0.83)
Finding the Percent of a Number
To determine the percent of a number do the following steps:



Multiply the number by the percent (e.g. 87 * 68 = 5916)
Divide the answer by 100 (Move decimal point two places
to the left) (e.g. 5916/100 = 59.16)
Round to the desired precision (e.g. 59.16 rounded to the
nearest whole number = 59)
Determining Percentage
Example: 68 is what percent of 87?


Divide the first number by the second (e.g. 68 ÷ 87 =
0.7816)
Multiply the answer by 100 (Move decimal point two
places to the right) (e.g. 0.7816*100 = 78.16)


Round to the desired precision (e.g. 78.16 rounded to the
nearest whole number = 78)
Follow the answer with the % sign (e.g. 68 is 78% of 87)
% to a fraction (example)
1. Take percent and place # over 100
2. Reduce
Fraction to a percent
1. First way you make equivalent to 100
2. second way= divide the numerator by the denominator
a. then multiply by 100
Percents of a number
Ex 60% 0f 80
Two ways8
First way
1. Place percent as a fraction over 100
2. Reduce fraction
3. Place whole number over 1
4. Multiply across to get answer and reduce till number
over 1
5. “of “ means to multiply
6. Or you can cross reduce your fraction to make it
smaller then multiply across
60/100 x 80/1
60/100= 3/5 x 80/1
3/5 x 80/1====the 80 and the 5 can both go into
five. Therefore cross reduce them
5/5= 1 and 80/5 = 16
New fractions are : 3/1 x 16/1 = when multiplied
across it b/cms 48/1 or the number 48.!
Second way
1. Take 100% of the percent number ..60/100 60 divided by 100
= .60
2. multiply that by the whole number
3. if any extra in the percent add it to the number
ex: 60% of 80
100% of 60% = .6
.6x 80= 48
% of dealing with MONEY!!
Regular and Sale price-transparency of notes
- also goes along with problem of the day worksheet
- teaching lesson
PROBABILITY
2 types : theoretical and experimental
1. use spinner
2. use dice for examples (1/6-16.7% is theory, but experiment is class results)
3. notes form transparency from math coach on probability
Notes from Harcourt!!!- on probability- both types and examples 
** probability lessons- YOU BET and TILES IN A BAG
Probability Concepts
About Probability
When we talk about probability we are assigning some measure of
chance to an experiment. An experiment is an activity that has two or more
clearly discernible results or outcomes. The collection of all outcomes is
referred to as the sample space.
An event is any subset of the sample space. In performing an
experiment, the probability is:
P = number of occurrences of the event
total number of trials
When all possible outcomes of a simple experiment are equally likely,
the theoretical probability of an event is:
P = number of outcomes in the event
total number of possible outcomes
Example:
If you toss a coin, the theoretical probability of the coin landing with
heads up is ½, because there is only one acceptable outcome (heads) out of
two possible outcomes.
If you actually performed the experiment 100 times, you might find
that the actual results were 45 heads and 55 tails. Experimental probability
does not always match theoretical probability, which is based on logical
analysis.
In an experiment, we are more confident that experimental
probability approaches actual (theoretical) probability with a very large
number of trials.
Implications for Instruction
There are several reasons why it is important to perform experiments and
examine outcomes in the classroom. An experimental approach has these
advantages:
1. It is significantly more intuitive and conceptual. Results begin to
make sense and do not result from some abstract rule.
2. It eliminates guessing at probabilities and wondering, “Did I get it
right?” Trying to determine the number of elements in a sample space
can be difficult without some intuitive background knowledge.
3. It provides an experimental background for examining the theoretical
model.
4. It helps students see that experimental probability approaches
theoretical probability after a large number of trials.
5. It develops an appreciation for a simulation approach to solving
problems. Many real world problems are actually solved by conducting
experiments or simulations.
6. It is a lot more fun and interesting.