Slide 2 Chapter 6: Percents Section 1 Percents, Fractions, and
Decimals Slide 3 California Standards Number Sense 1.0: Students
solve problems involving fractions and percentages. Slide 4
Language of the Discipline Percent: A RATIO that compares a number
to 100 Fraction: A part to whole numeric structure. The value on
the top is known as the NUMERATOR and the value on the bottom is
known as the DENOMINATOR. A mathematical relationship that
indicates the quotient of two quantities, such as 1/5. Decimal: A
numeric value that relies on PLACE VALUE. Here, decimals show
smaller and smaller parts of the whole. Example: 0.25 is called out
as Twenty-Five Hundredths. Rational Numbers: A number that can be
written in the form a/b where b CANNOT equal ZERO (0). EQUIVALENT:
EQUAL in value. Rounding: Mathematical process where one uses place
value to take a number up or down to the nearest whole. Slide 5
Writing Decimals as Percents Lets begin the lesson with DECIMALS
first. DECIMALS are friendly and easy to work with. DECIMALS are
helpful because you have set PLACE VALUES to help you convert
easily from one form to another. As you move from the WHOLE Units
and focus on the values behind the DECIMAL, you have TENTHS,
HUNDREDTHS, and THOUSANDTHS. Here, you use the DECIMAL form itself
to help you convert to PERCENTS. Example: 0.45 is called out as
FORTY-FIVE HUNDREDTHS. Note the word HUNDREDTHS. This tells you
that you multiple by 100 to convert from DECIMAL to PERCENT. Lets
convert 0.45. If we multiply the decimal by 100: (0.45)(100) = 45%
Quick Trick: You can also do a quick and easy shift of 2 place
values to the RIGHT to make a PERCENT. Slide 6 Examples of
Converting Decimals to Percents Example #1: Write 0.34 as a percent
Here, the decimal value is called out as THIRTY-FOUR HUNDREDTHS.
Once you hear the word HUNDREDTHS that tells you to MULTIPLY by 100
OR shift the decimal place over 2 place values to the RIGHT.
(0.34)(100) = 34% (Here, we MULTIPLIED by 100 and added the
percentage symbol (%)) 0.34 = 34% (Here, we shifted 2 place values
to the RIGHT and added in the Percentage Symbol (%)) Example #2:
Write 0.07 as a percent Here, the value is called out as SEVEN
HUNDREDTHS. Again, you hear the word HUNDREDTHS and that tells you
to MULTIPLY by 100 OR shift the decimal place over 2 place values
to the RIGHT. (0.07)(100) = 7% (Here, we multiplied by 100 and
added the percentage symbol (%)) 0.07 = 7% (Here, we shifted 2
place values and added in the Percentage Symbol (%)) Slide 7
Writing Percents as Decimals Lets look at PERCENTS. PERCENTS are
fun and easy to work with since PERCENTS are a part of 100.
Example: 75% is the same as 75 of 100 or 75/100 To convert from a
PERCENT to a DECIMAL, all you have to do is DIVIDE by 100. Quick
and easy. Write 78% as a DECIMAL. Here, 78% can be thought of as
78/100. Note: When the PERCENT is written as a FRACTION or RATIO,
you are being told to DIVIDE by 100. 78% = 78/100 = 0.78 Quick
Trick: You can also do a quick and easy shift of 2 place values to
the LEFT to make a DECIMAL. Remember that the decimal is found
BEHIND the whole number. Slide 8 Examples of Converting Percents to
Decimals Example #1: Write 45% as a Decimal. Here, we have 45%.
This means 45% = 45/100 45 100 = 0.45 (Here, we DIVIDED by 100 and
the resulting quotient is in DECIMAL form.) 45% = 0.45 (Here, we
shifted 2 place values to the LEFT and dropped the Percentage
Symbol.) Example #2: Write 37.5% as a Decimal. Here, we have 37.5%.
This means we have 37.5/100 37.5 100 = 0.375 (Here, we DIVIDED by
100 and the resulting quotient is in DECIMAL form) This example is
interesting because 37.5% is Thirty-Seven and a Half Percent. It is
still stacked over the standard percent value of 100. 37.5% = 0.375
(Here, we shifted 2 place values to the LEFT and dropped the
Percentage Symbol (%)) Slide 9 Writing Fractions as Percents
FRACTIONS are very straightforward and easy to work with. Remember
that FRACTIONS are values that represent Part to Whole
relationship. To convert from a FRACTION to a PERCENT, you begin
with the FRACTION and DIVIDE the NUMERATOR by the DENOMINATOR. Then
once a DECIMAL is found, you rewrite it as a PERCENT. Here, this
means you will shift the DECIMAL to the RIGHT 2 place values. Here,
your FRACTIONS are set up to be solved and changed into PERCENTS.
Example: Write 4/5 as a Percent. Divide the NUMERATOR 4 by the
DENOMINATOR 5. 4 5 = 0.80 4/5 = 0.80 The DECIMAL is found. We
convert to a PERCENT by shifting over 2 place values. 0.80 = 80%
Quick Trick: Divide. Determine the Decimal. Shift. Slide 10
Examples of Converting Fractions to Percents Example #1: Write 7/8
as a Percent. Here, we have the FRACTION 7/8. 7 8 = 0.875 (Here,
the NUMERATOR gets DIVIDED by the DENOMINATOR) 0.875 is the
resulting DECIMAL. 0.875 = 87.5% (Here, we shifted 2 place values
to the RIGHT and added the Percentage Symbol.) Example #2: Write
13/20 as a Percent. Here, we have the FRACTION 13/20 13 20 = 0.65
(Here, the NUMERATOR gets DIVIDED by the DENOMINATOR) 0.65 is the
resulting DECIMAL. 0.65 = 65% (Here, we shifted 2 place values to
the RIGHT and added the Percentage Symbol (%)) Slide 11 Writing
Percents as Fractions PERCENTS, like FRACTIONS are very
straightforward and easy to work with. Remember that PERCENTS are
values that represent a PART of a 100. To convert from a PERCENT to
a FRACTION, you begin with the PERCENT, re-write it as a FRACTION
over 100. Then simplify the FRACTION down to the LOWEST FRACTION.
Here, your PERCENTS are set up to be solved and changed into
FRACTIONS. Example: Write 75% as a Fraction. 75% = 75/100 75/100
can be simplified by DIVIDING Numerator and Denominator by 25. 75
25/100 25 = 3/4 Therefore 75% = 3/4 Quick Trick: Convert Percent
into a Fraction. Simplify to the Lowest Terms. Slide 12 Examples of
Converting Percents to Fractions Example #1: Write 55% as a
Fraction. Here, we have the Percent 55%. 55% = 55/100 55 and 100
can be divided both by 5 55 5/100 5 = 11/2055% = 11/20 (Here, we
re-write the Percent as a Fraction over 100. Find the GCD and
simplify down.) Example #2: Write 24% as a Fraction. Here, we have
the Percent 24% 24% = 24/100 24 and 100 can be divided both by 4 24
4/100 4 = 6/25 24% = 6/25 (Here, we re-write the Percent as a
Fraction over 100. Find the GCD and simplify down) Slide 13 Quick
Review Writing Decimals as Percents To write a decimal as a
percent, MULTIPLY by 100. Writing Percents as Decimals To write a
Percent as a decimal, DIVIDE by a 100. Writing Fractions as
Percents To write a Fraction as a Percent, you DIVIDE the NUMERATOR
by the DENOMINOR. Get a resulting decimal and then convert the
decimal into a Percent by shifting the decimal over 2 place values.
Writing Percents as Fractions To write a Percent as a Fraction, you
write your Percent as a fRaction over 100. Find the GCD and
simplify down. Slide 14 Check for Understanding Please determine
the BEST answer for the following expression. Carry out ALL work
and calculations in your NOTES for later reference Please write
your answer on your wipe boards and wait for the teachers signal.
On the count of 3, hold up your wipe boards. Slide 15 C4U Question
#1 Question #1: -Write 0.32 as a Percent Please work out the
problem within your notes Write the correct answer on your white
board. Wait for Teachers Signal. Slide 16 C4U Question #2 Question
#2: -Write 68% as a Decimal Please work out the problem within your
notes Write the correct answer on your white board. Wait for
Teachers Signal. Slide 17 C4U Question #3 Question #3: -Write 17/25
as a Percent Please work out the problem within your notes Write
the correct answer on your white board. Wait for Teachers Signal.
Slide 18 C4U Question #4 Question #4: -Write 38% as a Fraction.
Please work out the problem within your notes Write the correct
answer on your white board. Wait for Teachers Signal. Slide 19
Guided and Independent Practice Complete #s 8-10 on pg.237 in your
math textbook. Work carefully, show your problem solving process,
and double check all calculations. Use scratch paper to carry out
your work. Once you have completed the assigned problems, please
raise your pencil and wait to be stamped by Ms. Graham. If you
receive and R go to the back table. After being stamped move onto
Independent Practice in your textbook on pg.237 #s 18-20
