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: 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.

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.

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 (%))

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.

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 (%))

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.

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 0.65 is the resulting DECIMAL. 0.65 = 65% (Here, we shifted 2 place values to the RIGHT and added the Percentage Symbol (%))

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.

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)

Quick Review Writing Decimals as Percents Writing Percents as Decimals 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.

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.

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.

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.

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.

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.

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