Chapter 6: Percents Section 3 Finding a Percent of a Number

California Standards  Number Sense 1.4: Calculate given percentages of quantities.  Mathematical Reasoning 3.2: Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

Language of the Discipline  Percent: A RATIO that compares a number to 100  Fraction: A mathematical term that describes a PART to WHOLE relationship. Here, the value on the top is the NUMERATOR and the value on the bottom is the DENOMINATOR.  Simplest Terms: A mathematical term that asks for FRACTIONS to be taken down to the SIMPLEST or LOWEST terms. Here, find a GCF of the two values and divide NUMERATOR and DENOMINATOR by the same value to get to the SIMPLEST TERM.  Decimal: The mathematical equivalent of a Fraction, Ratio, Percent that utilizes place value.  Expression: A mathematical problem or given situation.  Compatible Numbers: Compatible Numbers are used when estimating. Here, you find the closest values or fractions to make working with a problem easier.  Estimate: To round up or down, using place value. Here, goal is to find values that are easier to work with.

Finding a Percent of a Number  To find a Percent of a Number, it is actually a very straight-forward and easy function to carry out.  There are two suggested methods to solve.  Method #1: Write the PERCENT as a FRACTION.  Remember that PERCENTS can be written as FRACTIONS.  Use the FRACTION and MULTIPLY by the Number.  Here, you will be using CPP or EF to correctly solve.  Method #2: Write the PERCENT as a DECIMAL  Remember that PERCENTS can be written as DECIMALS.  Use the DECIMAL and MULTIPLY by the Number.  Here, simple multiplication will allow for you to solve correctly..

Examples of Finding A Percent of a Number  Example #1: Find 30% of 80.  Method #1: Percents as Fractions  30% = 30/100-Percent to Fraction Form  30/100 = 3/10-Fraction Simplified to Lowest Terms  (3/10)(80)-Fraction is Multiplied by the Number  (3/10)(80/1)-Whole Number is put over 1  240/10 = 24-Multiply across and then divide OR Use Cross Products to REDUCE then Multiply  Method #2: Percents as Decimals  30% = 0.30-Convert the Percent to a Decimal  (80)(0.30)-Decimal is Multiplied by the Number  (80)(0.30) = 24 -Resulting Product is the Answer  Note: BOTH Methods yield the SAME Answer. Use whichever Method you are most comfortable with OR use Method #1 to initially solve and Method #2 for your Double-Check.

Examples of Finding A Percent of a Number  Example #2: Find 60% of 700.  Method #1: Percents as Fractions  60% = 60/100-Percent to Fraction Form  60/100 = 3/5-Fraction Simplified to the Lowest Term  (3/5)(700)-Fraction is Multiplied by the Number  (3/5)(700/1)-Put the Whole Number over 1  2100/5 = 420 -Multiply across and then divide OR Use Cross Products to REDUCE then Multiply  Method #2: Percents as Decimals  60% = 0.60-Convert the Percent to a Decimal  (700)(0.60)-Decimal is Multiplied by the Number  (700)(0.60) = 420 -Resulting Product is the Answer

Examples of Finding A Percent of a Number  Example #3: Find 55% of 300.  Method #1: Percents as Fractions  55% = 55/100-Percent to Fraction Form  55/100 = 11/20-Fraction Simplified to the Lowest Term  (11/20)(300)-Fraction is Multiplied by the Number  (11/20)(300/1)-Put the Whole Number over 1  3300/20 = 165-Multiply across and then divide OR Use Cross Products to REDUCE then Multiply  Method #2: Percents as Decimals  55% = 0.55-Convert the Percent to a Decimal  (300)(0.55)-Decimal is Multiplied by the Number  (300)(0.55) = 165 -Resulting Product is the Answer

Examples of Finding A Percent of a Number  Example #4: Find 12.5% of 64.  Method #1: Percents as Fractions  12.5% = 12.5/100-Percent to Fraction Form  12.5/100 = 1/8-Fraction Simplified to the Lowest Term  (1/8)(64)-Fraction is Multiplied by the Number  (1/8)(64/1)-Put the Whole Number over 1  64/8 = 8 -Multiply across and then divide OR Use Cross Products to REDUCE then Multiply  Method #2: Percents as Decimals  12.5% = Convert the Percent to a Decimal  (64)(0.125)-Decimal is Multiplied by the Number  (64)(0.125) = 8 -Resulting Product is the Answer

Examples of Finding A Percent of a Number  Example #5: Find 52% of 200.  Method #1: Percents as Fractions  52% = 52/100-Percent to Fraction Form  52/100 = 13/25-Fraction Simplified to the Lowest Term  (13/25)(200)-Fraction is Multiplied by the Number  (13/25)(200/1)-Put the Whole Number over 1  2600/25 = 104 -Multiply across and then divide OR Use Cross Products to REDUCE then Multiply  Method #2: Percents as Decimals  52% = 0.52-Convert the Percent to a Decimal  (200)(0.52)-Decimal is Multiplied by the Number  (200)(0.52) = 104 -Resulting Product is the Answer

Quick Review  The Basis for Finding a Percent of a Number is MULTPLICATION!!!  Here there are 2 Methods.  Method #1: Using Percents as Fractions  Convert the Percent to a FRACTION in the Simplest Terms.  Use the Fraction and MULTIPLY by the Number.  Resulting PRODUCT will be your ANSWER.  Method #2: Using Percents as Decimals  Convert the Percent to a DECIMAL.  Use the Decimal and MULTIPLY by the Number.  Resulting PRODUCT will be your ANSWER.

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: -Find 90% of 240  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

C4U Question #2  Question #2: -Find 30% of 70.  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

C4U Question #3  Question #3: -Find 38% of 400.  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

C4U Question #4  Question #4: -Find 60% of 950.  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

C4U Question #5  Question #5: -Find 12% of 480.  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

C4U Question #6  Question #6: -Find 31% of 84.  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

Guided and Independent Practice  Complete #9-11’s – on pg.245 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 #’s on pg. 245