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Chapter 6 : Percents Section 1

Chapter 6 : Percents Section 1. Percents, Fractions, and Decimals. California Standards. Number Sense 1.0: Students solve problems involving fractions and percentages. Language of the Discipline. Percent: A RATIO that compares a number to 100 Fraction:

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Chapter 6 : Percents Section 1

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

  2. California Standards • Number Sense 1.0: Students solve problems involving fractions and percentages.

  3. 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.

  4. 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 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.

  5. 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 (%))

  6. 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 iswritten as a FRACTION or RATIO, you are beingtold 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.

  7. 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 (%))

  8. 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.

  9. 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 (%))

  10. 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.

  11. 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)

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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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