Percenatge

House Rules

• Listen attentively.

• Ask question/s after the discussion.

Actively participate in the class.

Objectives:

• To learn the functions of a percent.

• Differentiate a percent from percentage.

• Apply the use of percent in the daily activities.

Game

• On your notebook, make one circle and one square.

• Then divide the circle into eight slices and ten slices for the square.

• Shade the slices one by one.

• Represent the slices into a fraction. Then convert it into decimal and percent.

Introduction

• Percent means “per centum”

• Latin word means centum “100”

• Example: Century means 100

Percent vs. Percentage

Percent (adverb, noun)• It accompanies an specific

number

• Ex: More than 95% of the participants who responded to the survey reported positive results.

Percentage (noun)• Is used without a number

• Part of a whole hundredths

• Ex: The percentage of the population exposed to rotavirus is between 70% and 75%.

Formulae

• Is/Of = %/100

• Part/ Whole = %/100

•Keynote: Remember to MULTIPLY

Exercises

• I. 25% of 200 is ____

•Of = 200

• Is = ?

•% = 25

•Cross multiply to find the missing number.

•F/ 200 = 25/100

•F(100) = 5,000

•Divide both sides with 100 to find F.

•F(100) = 5,000

• 100 = 100 ; So the 25% of 200 is 50

• II. What number is 2% of 50?

•Of = 50

• Is= ?

•%= 2

•Cross Multiply

•G/50 = 2/100

•G*100 = 100

•Divide both sides by 100 to get the value of G.

•G *100 = 100

•100 100

•So the value of G is 1 ; so the 2% of 50 is 1

• III. 24% of ___ is 36

• Is = 36

•Of= ?

•% = 24

•36/of = 24/100

•36/K = 24/100

•Cross multiply: 36* 100 = K *24

•3,600 = K*24

•Divide both sides by 24 to get the value of K.

•3,600 = K*24

•24 24 ; so the value that is missing is 150

• IV. Remember the number after “of” is always the whole.

•The number after “is” is always the part.

•25% of ___ is 60

•The proportion will be 60/ whole = 25/100

•Cross multiply: Use J as the variable for whole

•6,000 = J *25

•Divide both sides with 25

•6,000 = J * 25

•25 25

•So the value of J is 40; 25% of 240 is 60

•V. ___% of 45 is 9

•Whole = 45

•Part = 9

•% = ?

•S will be the variable used to find %

•9/45 = S/ 100

•Cross multiply: 900 = S*45

•Divide both sides by 45

•900 = S*45

•45 45

•The value of % is 20; 20% of 45 is 9

More exercises • 1. Chip bought something around $6.95 and the total bill is $7.61. Give the

tax rate.

• 2. An item is used to be sold for $0.75 then it has a marked up increase of $0.81. how much is the percent increase?

• 3. A computer software retailer used a marked up rate of 40%. Find the selling price of a computer game that cost the retailer 25%.

• 4. A golf shop pays its wholesaler $40 for a certain club, and then sells it to a golfer for $75. What is the markup rate?

• 5. A shoe store uses a 40% markup on cost. Find the cost of a pair of shoes that sells for $63.

• 6. An item originally priced at $55 is marked 25% off. What is the sale price?

• 7. An item that regularly sells for $425 is marked down to $318.75. What is the discount rate?

Answer key

• 1. The sales tax is a certain percentage of the price, so I first have to figure what the actual tax was. The tax was:

• 7.61 – 6.95 = 0.66

• Then (the sales tax) is (some percentage) of (the price), or, in mathematical terms:

• 0.66 = (x)(6.95)

• Solving for x, I get:

• 0.66 ÷ 6.95 = x = 0.094964028... = 9.4964028...%

• The sales tax rate is 9.5%

• 2. First, I have to find the absolute increase:   

• 81 – 75 = 6

• The price has gone up six cents. Now I can find the percentage increase over the original price.

• Note this language, "increase/decrease over the original", and use it to your advantage: it will remind you to put the increase or decrease over the original value, and then divide.

• This percentage increase is the relative change:

• 6/75 = 0.08

• ...or an 8% increase in price per pound.

• 3. The markup is 40% of the $25 cost, so the markup is:

• (0.40)(25) = 10

• Then the selling price, being the cost plus markup, is:

• 25 + 10 = 35

• The item sold for $35.

• 4. 75 – 40 = 35

Then I'll find the relative markup over the original price, or the markup rate: ($35) is (some percent) of ($40), or: Copyright © Elizabeth Stapel 1999-2011 All Rights Reserved

35 = (x)(40)

...so the relative markup over the original price is:

35 ÷ 40 = x = 0.875

Since x stands for a percentage, I need to remember to convert this decimal value to the corresponding percentage.

The markup rate is 87.5%.

• 5. This problem is somewhat backwards. They gave me the selling price, which is cost plus markup, and they gave me the markup rate, but they didn't tell me the actual cost or markup. So I have to be clever to solve this.

• I will let "x" be the cost. Then the markup, being 40% of the cost, is 0.40x. And the selling price of $63 is the sum of the cost and markup, so:

• 63 = x + 0.40x

• 63 = 1x + 0.40x

• 63 = 1.40x

• 63 ÷ 1.40 = x= 45

• The shoes cost the store $45.

• 6. First, I'll find the markdown. The markdown is 25% of the original price of $55, so:

• x = (0.25)(55) = 13.75

• By subtracting this markdown from the original price, I can find the sale price:

• 55 – 13.75 = 41.25

• The sale price is $41.25.

• 7. First, I'll find the amount of the markdown:

• 425 – 318.75 = 106.25

• Then I'll calculate "the markdown over the original price", or the markdown rate: ($106.25) is (some percent) of ($425), so:

• 106.25 = (x)(425)

• ...and the relative markdown over the original price is:

• x = 106.25 ÷ 425 = 0.25

• Since the "x" stands for a percentage, I need to remember to convert this decimal to percentage form.

• The markdown rate is 25%.

References

• http://www.basic-mathematics.com/formula-for-percentage.html

• http://www.biomedicaleditor.com/word-usage-percent.html

• http://www.mathsisfun.com/percentage.html

• http://www.purplemath.com/modules/percntof.htm