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Chapter 6: Percents Section 1 Percents, Fractions, and Decimals.

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Presentation on theme: "Chapter 6: Percents Section 1 Percents, Fractions, and Decimals."— Presentation transcript:

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2 Chapter 6: Percents Section 1 Percents, Fractions, and Decimals

3 California Standards  Number Sense 1.0: Students solve problems involving fractions and percentages.

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.

5 Writing Decimals as Percents  Let’s 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.  Let’s convert 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.

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 (%))

7 Writing Percents as Decimals  Let’s 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.

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 =  (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% =  (Here, we shifted 2 place values to the LEFT and dropped the Percentage Symbol (%))

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.

10 Examples of Converting Fractions to Percents  Example #1: Write 7/8 as a Percent.  Here, we have the FRACTION 7/8.  7 ÷ 8 =  (Here, the NUMERATOR gets DIVIDED by the DENOMINATOR)  is the resulting DECIMAL.  = 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 (%))

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.

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)

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.

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 teacher’s signal.  On the count of 3, hold up your wipe boards.

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 Teacher’s Signal.

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 Teacher’s Signal.

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 Teacher’s Signal.

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 Teacher’s Signal.

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


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