Business Math Day 4

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Business Math Day 4

• Percents

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6.1 Percent Equivalents

• Write a whole number, fraction or decimal as a
  percent.
• Write a percent as a whole number, fraction or
  decimal.
• 1100
• 0 . 8 80 4 / 5

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6.1.1 Write a whole number, fraction or decimal
as a percent.

• Percents are used to calculate markups,
  markdowns, discounts and many other business
  applications.
• Hundredths and percent have the same meaning
  per hundred.
• 100 percent is the same as 1 whole quantity. 100
  1
• When we multiply a number by 1, the product has
  the same value as the original number.

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Change to equivalent percents.

• N x 1 N
• So, if 1 100, then ½ x 100 50.
• Also, if 1 100, then 0.5 x 100 050.50
• In each case when we multiply by 1 in some form,
  the value of the product is equivalent to the
  value of the original number even though the
  product looks different.

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Write a number as its percent equivalent.

• Multiply the number by 1 in the form of 100,
• The product has a symbol.
• Example
• Write 0.3 as a percent.
• 0.3 0.3 x 100 030. 30
• The decimal point moves two places to the right

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Write the decimal or whole number as a percent.

• 0.98 0.98 x 100 098. 98
• 1.52 1.52 x 100 152. 152
• 0.04 0.04 x 100 004. 4
• 5 5.00 x 100 500. 500
• 0.003 0.003 x 100 000.3 0.3

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Try these examples.

• .76
• 76
• 2.46
• 246
• 0.0025
• 0.25

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Write a fraction as a percent.

• ¼ ¼ x 100/1 25 Reduce and multiply.
• For the following, change the mixed number to an
  improper fraction and multiply by 100.
• 3 ½ 3 ½ x 100/1 7/2 x 100/1 350
• ? ? x 100 / 1 200/3 66?

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Try these examples.

• ?
• 37.5
• ?
• 87.5
• ¾
• 75

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6.1.2 Write a percent as a whole number, fraction
or decimal.

• When a number is divided by 1, the quotient has
  the same value as the original number.
• N 1 N or N/1 N
• We can also use the fact that N 1 N to change
  percents to numerical equivalents.
• 50 100 50/100 50/100 ½
• 50/100 50/100 0.50 0.5

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Write the percent as a number.

• Divide by 1 in the form of 100 or multiply by
  1/100
• The quotient does not have the symbol.
• Examples
• 37 37 100 .37 0.37
• 127 127 100 1.27
• Divide by 100 mentally.
• Move the decimal point two places to the left.

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Write the percent as a fraction or mixed number.

• In multiplying fractions, we reduce or cancel
  common factors from a numerator to a denominator.
  Percent signs also cancel.
• Division is the same as multiplying by the
  reciprocal of the divisor.
• Similarly, 1
• Example
• 65 65 100 65/1 x 1/100 13/20

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Try these examples.

• 250
• 2 ½
• 12.5
• ?
• ¼
• 1/400

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6.2 Solving percentage problems

• Identify the rate, base and percentage in
  percentage problems.
• Use the percentage formula to find the unknown
  value when two values are known.
• P R x B

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6.2.1 Identify the rate, base and percentage in
percentage problems.

• In the formula P R x B
• B refers to the base which is the original
  number or one entire quantity.
• P refers to percentage and represents a portion
  of the base
• R refers to rate and is a percent that tells us
  how the base and percentage are related.

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6.2.1 Identify the rate, base and percentage in
percentage problems.
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Find the percentage.

• The original formula is P R x B
• To find the percentage, we multiply the rate by
  the base.
• If 80 people registered for this course and 20
  are Spanish-speaking, what number of students are
  Italian-speaking?
• Identify the base identify the rate.
• Use the solution plan to find the answer.

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Find the percentage.

• What are you looking for?
• The number of Spanish-speaking students
• 2. What do you know?
• The base is 80 (rate) and the rate is 20 or
  0.20.
• 3. Solution plan
• P 80 x 20 (or .2)
• 4. Solve
• P 16
• 5. Conclude
• 16 students are Spanish-speaking

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Try these problems.

• If 40 of the registered voters in a community of
  5,600 are Liberals, how many voters are Liberals?
• 2,240
• If 58 of the office workers prefer diet soda and
  there are 600 workers, how many prefer diet soda?
• 348

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Find the base.

• Refer to the original formula P R x B.
• To find B, we can change the formula so that it
  becomes B P/R
• To find the original number, we can divide the
  percentage by the rate.
• Example Forty percent, or 90 diners preferred
  outdoor seating at the new restaurant. How many
  diners were interviewed in all?
• Use the solution plan.

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Find the base.

• What are you looking for?
• The total number of diners surveyed.
• 2. What do you know?
• The percentage (90) and the rate (40).
• 3. Solution plan
• Base P/R Base 90/.40
• 4. Solve
• B 225
• 5. Conclude
• 225 diners were interviewed in all.

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Try these examples.

• 1700 dentists attending a convention last month
  prefer fluoride treatments for preschoolers.
  Thats 4 out of every 5 dentists. How many
  dentists attended in all?
• 2,125
• 80, or 560, of our current clients take
  advantage of our cash discount program for prompt
  payment. What is our current client base?
• 700

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Find the rate.

• Refer to the original formula P R x B.
• To find R, we can change the formula so that it
  becomes R P/B
• To find the rate, we can divide the percentage by
  the base.
• Example 55 insurance agents were able to meet
  with their clients to inform them of policy
  changes. If there are 220 agents in all, what
  percent does this represent?

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Use the solution plan.

• 1. What are you looking for?
• The percent or rate of agents who talked to
  their clients.
• 2. What do you know?
• The base or total number of agents and the
  percentage who
• talked to their clients.
• 3. Solution plan
• R P/B R 55/220
• 4. Solve
• R .25
• 5. Conclusion
• 25 of the agents talked to their clients.

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Try these examples.

• The plant foreperson reported that 873 of the 900
  items tested met the quality control
  specifications for production. What is the rate
  of acceptable items?
• 97
• In the new product focus group, 6,700 of the
  8,375 customers rated the product as very good
  or superior. What was the rate?
• 80

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Identify what is missing.

• Sometimes, you will be asked to find one of the
  elements rate, base or percentage when you know
  the other two.
• Learn to read the problem to identify the
  missing element.
• Example 30 of 70 is what number?
• 30 is the rate.
• 70 is the base.
• You are looking for P or percentage.
• P R x B P 0.3 x 70 21

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Try these problems.

• Identify whats missing and then solve the
  problem using the correct formula.
• 60 is what percent of 80?
• R P/B R 75
• 35 of 350 is what?
• P R x B P 0.35 x 350 122.5
• 25 of what number is 125?
• B P/R B 125/.25 500

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6.3 Increases and Decreases

• Find the amount of increase or decrease in
  percent problems.
• Find the new amount directly in percent problems.
• Find the rate or the base in increase or decrease
  problems.

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6.3.1 Find the amount of increase or decrease in
percent problems.

• Examples of increases in business applications
  include
• Sales tax
• Raise in salary
• Markup on a wholesale price

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Decreases in percent problems

• Some examples of decreases include
• Payroll deductions
• Markdowns
• Discounts on sale items

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How to find the amount of increase

• To find the amount of increase amount of
  increase new amt beg. amt.
• Example Joes salary has been 400 a week.
  Beginning next month, it will be 450 a week. The
  amount of increase is 50 a week.

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How to find the amount of decrease

• To find the amount of decreaseAmount of
  decrease beg. amt - new amt.
• Example Roxannes new purse originally cost
  60, but it was on sale when she bought it on
  Saturday for 39.99. The amount of decrease (or
  markdown) is 20.01.

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Percent of change

• The amount of change is a percent of the original
  or beginning amount.
• Find the amount (increase or decrease) from a
  percent of change by
• Identifying the original or beginning amount and
  the percent or rate of change.
• Multiplying the decimal equivalent of the rate of
  change by the original or beginning amount.

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Heres an example

• Your company has announced a 1.5 cost of living
  raise for all employees next month. Your monthly
  salary is currently 2,300. Starting next month,
  what will your new salary be?
• You will need to find the amount of increase by
  multiplying the rate by the base.
• To find the new amount, add the amount of
  increase to the original amount.

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Find the new amount.

• Current salary 2,300 a month
• Rate of change 1.5
• Amount of raise
• Percent of change x original amount
• .015 x 2,300 34.50 a month
• Add 34.50 to the original amount of 2,300 to
  identify the new amount.
• New amount 2,334.50

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6.3.2 Find the new amount directly in percent
problems.

• Often in increase or decrease problems, we are
  more interested in the new amount than the amount
  of change.
• Find the new amount by adding or subtracting
  percents first.
• The original or beginning amount is always
  considered to be the base and is 100 of itself.

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Find the new amount directly in a percent problem.

• Find the rate of the new amount.
• For increase 100 rate of increase
• For decrease 100 - rate of decrease
• Find the new amount.
• P R x B
• New amount rate of new amt. x original amt.

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Heres an example.

• Medical assistants are to receive a 9 increase
  in wages per hour. If they were making 15.25,
  what is the new per hour salary to the nearest
  cent?
• Rate of new amount 100 rate of increase
• 100 9 109
• Rate of new amount 15.25 x 109
• Change 109 to its decimal equivalent 1.09
• 15.25 x 1.09 16.6225 16.62

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Heres another example.

• A new pair of jeans that costs 49.99 is
  advertised at 70 off. What is the sale price to
  the nearest cent of the jeans?
• Rate of new amount 100 - rate of decrease
• 100 - 70 30
• New amount rate of new amt. x original amt.
• New amount 30 x 49.99
• New amount 0.3 x 49.99 14.997
• New amount 15.00 (nearest cent)

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Try these examples.

• The property taxes at your business office will
  go up 5 next year. Currently, you pay 3,400.
  How much will you pay next year?
• 3,570
• A wholesaler is offering you a 20 discount if
  you purchase new inventory before the 15th of the
  month. If your normal invoice is 3,600, how
  much would you pay if you got the discount?
• 2,880

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6.3.3 Find the rate or the base in increase or
decrease problems.

• Identify or find the amount of increase or
  decrease.
• To find the rate of increase or decrease, use the
  percentage formula R P/B.
• Rate amount of change/original amount.
• To find the base or original amount, use the
  percentage formula B P/R.
• Base amount of change/rate of change.

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Heres an example.

• During the month of May, a graphic artist made a
  profit of 1,525. In June, she made a profit of
  1,708. What is the percent of increase in
  profit?
• Use the solution plan to figure out the answer.

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Solution plan

• What are you looking for?
• Percent of increase in profits.
• What do you know?
• Original amt. 1,525 New amt.1,708
• Solution plan
• Find amt. of increase Find percent of increase.
• Solution
• 1,708-1,525 183183/1,525 0.12 12
• Conclusion
• The rate of increase in profit is 12.

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Try these two examples.

• A popular detergent cost 5.99 last Saturday, but
  today the same detergent costs 7.50. What is the
  rate of increase?
• 25.2
• Sales in the East Region were 10,800 in January
  and dropped to 9,700 in February. What is the
  rate of decrease from January to February?
• 10.2

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Homework / Lab work

• Homework due at the end of the week
• Chapter 6 Exercises Set A
• Lab work Due Thursday, 500 pm
• Online Lab 3