PERCENT

Prepared by:Regine Apple M. Lopez

PERCENT

• Definition

• Conversion

• Percentage, Rate and Base

• Percentage Problem

The term percent comes from the Latin phrase “per centum” meaning “by the hundreds.”

Percent means parts per hundred or for every hundred.

For instance, in a 100-item test a student got 88 correct answers. To indicate the items answered correctly, the example shows that 88/100 or 0.88 of the test items were answered correctly. A third way to express this idea is 88% of the test was answered correctly.

Hence, the 88 correct answers out of 100 items can be expressed in the following manner:

0.88 of the test; as a decimal

88 of the test; as a fraction 100

88% of the test; as a percent

Example:Of the 500 books in a library shelf,

20 books are mathematics books. Express the number of mathematics books as a : (a) common fraction; (b) decimal fraction; and (c) percent.

a. As a fraction : 20/500 = 1/25 b. As a decimal : 20/500 = 0.04 c. Thus, 20/500 = 4/100 = 4%

Therefore, 4% of the books are mathematics books.

Changing Percent to Decimalsremove the percent sign, then,

multiply the number by 1/100 or simply move the decimal point to the left since dividing by 100 implies moving the decimal point two places to the left.

Examples:1. Write 35% as a decimal

35% = 35 % = 0.35

2. Write 83.25% as a decimal

83.25% = 83. 25 % = 0.8325

3. Write 5 ½ % as a decimal

5 ½ % is also equal to 5.5%

5 ½ % = 05.5% = 0.055

Changing Percent to FractionTo change percent to fraction, remove the

percent sign, write the denominator 100 and reduce to lowest terms.

Examples:1. Write 76% as a fraction

76% = 76 100

= 19 25

2. Convert 12 ½ % as a fraction

12 ½ = 12 ½ / 100 convert 12 ½ to improper fraction

= 25/2 x 2 100 2= 25 or 1 100 8

Changing Decimal to PercentMultiply the decimals by 100 and affix the % sign.

This simply means, moving the decimal point two places to the right.

Examples:1. Change 0.21 to percent

0. 21 = 21 %

2. Convert 0. 9543 to percent

0.95 43 = 95.43 %

Changing Fraction to Percentconvert the fraction to decimal, and then convert

the obtained decimal to percent.

Examples:1. Change ¼ to percent

¼ = 0.25 , 0.25 = 25%

2. Convert 45/24 to percent45 = 1.875 (45÷24)24 = 187.5 %

Exercises: A. Write each percent as a Fraction.

1.) 85%2.) 10%3.) 5%

B. Write each decimal as a Percent.

1.) 0.102.) 0.053.) 0.20

Let’s Check! A. 1.) 85 B. 1.) 10%

100

2.) 10 2.) 5% 100

3.) 5 3.) 20% 100

Percentage – fractional part of the whole or part of the total.

Rate – the percent or the number of hundredth.

Base – the whole or standard basis of comparison.

Percentage problems can easily be solved using the proportion below:

r = p where r is the rate; b is a base; 100 b p is the percentage

or it can also be solved the formula: percentage = rate x base

p = r x b

Example:

1. In a class of 50 students, 10% are not present. How many students are absent?

Using the proportion: rate (r) = percentage (p) 100 base (b)

10 = p 100 50 100p = 500 p = 5

Using the formula:

p = r x bp = 10% x 50p = .10 x 50p = 5

Assignment:

Solve the following:

1.) Out of 200 first year college students, 130 are graduates from urban high schools. What percent came from urban high schools?

2.) The 320 members of the Mathematikos Club who attended the meeting represented 80% of the total member of club members. How many members were there in the club?

How does Percent relate to a business?

• Interest

• Commission

• Discount

Interest is the amount earned for the use of money.

In solving interest problems, use the following formula:

Interest = Principal x rate x timeI = Prt

Amount = Principal + interestA = P + PrtA = P ( 1 + rt )

Example:A man borrowed P40,000 from the bank at the

rate of 8% a year. What is the interest if it will paid after two years?

Solution : I = PrtI = P40,000 x 0.08 x 2 I = P6,400

Commission it is a fee or a percentage of the proceeds paid to a salesperson, broker, etc., either in addition to, or in lieu of, wages or salary. To find the amount of commission, change rate to decimal and multiply by sales.

Example:Mr. Carlos is a sales agent who gets a 15%

commission on all sales he makes for the month. In November, his total sales amounted to P35,000. What was his commission for the month of November?

The number sentence is:15% of 35 000 = n

Find the amount of commission.

15% = 0.15 x 35 000 = 5 250 Therefore, his commission for November was P5,250.

Discount is the amount deducted from the original price.

• To find the discount, multiply the price by the discount rate.• To find the discounted price, subtract the discount from the original price.

Example:

Mrs. Fernandez wants to buy a can of juice marked P78.00. How much will she save if she buys it during a sale offering 5% off on all prices?

Find the discount on P78.00 at 5%

Solution: Price x Rate = n P78.00 x 0.05 = 3.90

Mrs. Fernandez will save P3.90. Discounted price: P3.90 (P78.00 - P3.90 )

Let’s Apply!

1.) Mr. Garcia received P250,000 when he retired as a classroom teacher. He deposited this in a bank paying 5 ½ % interest rate per year. If he does not withdraw any money, what will be his total account after five years?

2.) Ed earns an 8% commission for selling appliances. If he sells a washing machine for P5,435 and a TV set for P7,500, how much will he get as commission?

3.) A department store offers a 25% discount on all items. How much will I pay for a single bed with a marked price of P8,500?