5.1INTRODUCTION TO PERCENTS

Objective A - Writing a Percent as a Fraction or a Decimal

  • Percentmeans,“Parts of 100”.
  • There are 100 cents in a dollar.
  • There are 100 years in acentury.
  • 30 of the 100 parts are shaded; therefore 30% of the figure is shaded.
  • Percents are just another way of writing fractions when the denominator equals100.
  • In most applied problems with percents, it is necessary to rewrite the percent as a fraction or a decimal (or vice versa).
  • To change a percent to a fraction, you drop the percent symbol and either:
  1. Write the number over 100.
  2. Alternatively, multiply by. (Both accomplish the same purpose)

Ex.Write 73% as a fraction.(Note: What is 0.73 written as a fraction?)

  • Conclusion - decimals with two places (Hundredths) are another name for percents.
  • Meaning,either write thepercent as a fraction (always simplify to lowest terms).
  • Alternatively, write thepercent as a decimal number.
  • To change a percent to a decimal:
  • Move the decimal point two places to the LEFT, and then remove the % sign.
  • Remember that a percent is a fraction with a denominator of 100,
  • Therefore, you are dividing by 100!
  • Recall what wasdone in Chapter#4 when dividing by 100.

Write the following as both a fraction (reduced, if possible) and as a decimal.

Ex. 58%Ex. 34%Ex. 110%

Write the following as a fraction. (With mixed number percents, multiplyingby 1/100 is the easier process)

Ex. Ex.

Write the following as a decimal.

Ex. 89.5%Ex. 0.65%Ex. 2.19%

Objective B - Writing a Fraction or a Decimal as a Percent

  • A fraction or decimal can be written as a percent by multiplying by 100%.
  • Process:
  1. Move the decimalpointtwo places to the RIGHT, and then add the % sign.
  2. Multiply thefraction (or decimal)by 100%.
  1. That is multiply the fraction (or decimal) by 100.
  2. Leaving the percent symbol in the result.

Ex. Write 0.35 as a percent.Ex. Write 2.05 as a percent.

Ex. Writeas a percent.Ex. Writeas a percent.(Remainder in fractional form)

Ex. Write as a percent.(Round to nearest tenth)Ex. Write as a percent.(Round to nearest tenth)

5.2 - 5.4 PERCENT EQUATIONS

  • You will need to remember this basic formula: Percent •Base = Amount
  • When using this formula, and are given a percent value:
  • Convertpercents to decimals before multiplying by the Base!
  • Remember, that the word OF means to MULTIPLY.
  • The word IS translates to an EQUALS SIGN.
  • These problems are similar to the translation problems in Chapter#11.

5.2 PERCENT EQUATIONS: PART 1

Objective A - Finding the Amount When You Are Given the Base and Percent

  • Whenever you encounter the word “what,” translate it into the variable n in the equation.
  • For example, 7% of 50 is what?
  • 7%of50 iswhat?

(percent)•(base) =(n = amount)

  • Answer:(0.07) • (50) = n→n = 3.5

Ex.16% of 50 is what?(Alternatively, Find 16% of 50?)Ex.What is 0.06% of 250?

5.3 PERCENT EQUATIONS: PART II

Objective A - Finding the Percent When You Are Given the Base and the Amount

  • Once again, you will translate “English” words into an equation.
  • Whenever you run into the word “what,” translate that as the variable n in the equation.
  • When you find the value for n, it will be a decimal number – you will need to change the decimal to a percent for the answer.
  • For example, What percent of 80 is 25?
  • What %of80 is25?

(n = percent)•(base) =(amount)

  • Answer:n • (80) = (25)→n = 0.3125→n = 31.25%(percentage)

Ex. 24 is what percent of 60?Ex. What percent of 400 is 12?

5.4 PERCENT EQUATIONS: PART III

Objective A - Finding the Base When You Are Given the Percent and the Amount

  • One more time, translate “English” words into an equation.
  • Remember: whenever you encounter the word “what,” translate itinto the variable n in the equation.
  • For example, 10% of what is 20?
  • 10%ofwhat is20?

(percent)•(n = base) =(amount)

  • Answer:(0.10) • (n) = (20)→n = 200

Ex. 54 is 90% of what?Ex. 87.5 is 50% of what?

5.5 PERCENT PROBLEMS: PROPORTION METHOD

  • It is possible to solve any of these percent problems using a proportion.
  • Use the same basic(percent • Base = Amount) equation, but restructure the basic equation into two ratios equaling each other:
  • First, divide both sides of this equation by Base on both sides, such that = 1 on the left side of the equation, and results on the right side of the equation.
  • Then, write the percent as a fraction so that forms a proportion.
  • Therefore, these two ratios for the proportion →
  • The first ratio is the percent ratio, written as
  • The second ratio is the Amount-to-Base ratio written as
  • Sometimes, it is easier to remember this method using the equation
  • Redoing any of the previous problems using this form of the equation produces the same correct solutions!

Ex. What is 28% of 950?

Ex. 48 is what percent of 160?

Ex. 90% of what is 63?

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