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

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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.

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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.

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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..

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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.

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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

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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

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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

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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