LESSON 3 PERCENT

Learning Outcomes By the end of this lesson, students should be able to: Convert decimal to percent Convert fractions to percent Convert percent to decimal Convert percent to fraction Convert fractional percent to decimal Find Part Find Base Find Rate Find a value after an increase or decrease

List of Topics Converting decimal to percent 3.2 Converting fractions to percent 3.3 Converting percent to decimal 3.4 Converting percent to fraction 3.5 Converting fractional percent to decimal 3.6 Finding Part 3.7 Finding Base 3.8 Finding Rate 3.9 Finding a value after an increase and decrease

Converting decimal to percent The percent sign (%) has the mathematical value of one hundredth (0.01 or 1/100 ). 30% represent 30 parts of 100 and can be expressed in decimal fraction form as 0.30 or in common fraction as 3/100. Percents are commonly use, but to use them in arithmetic application, one must convert them into decimal or common fraction. Conversions are crucial in solving a large variety of problems. To convert a decimal as a percent, move the decimal point two places to the right and attach a percent sign (%).

Example Decimals Percent 0.45 45% 0.6 60% 2.6 260% 0.0012 0.12% 0.325 32.5%

Converting fractions to percents To convert a fraction to a percent, divide the numerator by the denominator, move the decimal point two places to the right, and add the percent sign. Example of conversion of fractions to percent

Fraction Decimal Percents 1/8 .0125 12.5% 2/5 0.4 40% 3/4 0.75 75% 11/20 0.55 55%

Converting percent to decimal To convert a percent to a decimal, move the decimal point two places to the left and remove the percent sign. Example of conversion of percents to decimals.

Example Percents Decimal 20% 0.2 65% 0.65 125% 1.25 0.25% 0.0025

Converting percent to fraction To convert a percent to a fraction, first change the percent to a decimal, and then write the decimal as a fraction in lowest terms.

Example Percents Decimal Fraction 20% 0.20 2/100 = 1/50 55% 0.55 55/100 =11/20 21% 0.21 21/100 6% 0.06 6/100 =3/50

Converting fractional percent to decimal To convert a fractional percent to a decimal, it first requires changing the fraction to a decimal, leaving the percent sign in tact. For example, first write ½% as 0.5%. Then write 0.5% as a decimal by moving the decimal point two places to the left and dropping the percent sign.

Example

Example Fractional Percents Decimal with percent Decimal % 0.20% 0.002 0.625% 0.00625 0.444% 0.0044 0.06% 0.0006

The whole or total, the starting point. Rate: Finding Part Each percentage problem will have three components of a percent problem. Usually, two of these components are given, and the third component must be found. The three key components in a percent problem are as follows. Base: The whole or total, the starting point. Rate: A number followed by percent (%) that represents the relationship between the percentage and the base. Rate must be changed to a decimal or fraction before being used in the formula. Part: Result of multiplying the base and the rate Formula: Part = Base x Rate

Example A shop gives a 12% discount on all shoes. Find the discount of as shoe that cost RM 150. Solution: Rate = 12% discount (0.12 in decimal) Base = RM 150 Part = 0.12 x RM 150 = RM 18.00 discount

Finding the base With the part and rate known, the base can be calculated using the following formula: B = P/R Example If the sales tax rate is 4%, find the amount of sales when the sales tax is RM 16. Solution: Rate = 4%, or 0.04, Part = RM 16 B = 16/0.04 =400

Finding the rate Rates (or percent) are tools for showing the relationship between a percentage and a base. Rate can be calculated using the following formula: R =P/B Example Production rose from 4220 units to 6280 units. Find the percent of increase. Solution: Part = 6,280 – 4,220 = 2,060 change in production Base = 4,220 units of production R = 2,060/4220 = 0.488 = 48.8%

Finding a value after an increase or decreases To examine the outcome of increase or decrease in transaction, we need to understand the basic calculations involved. Increase problems are indicated by phrases such as after “an increase of”, “more than” or “greater than”. Decrease problems are indicated by phrases such as “after a decrease of”, “less than” or “after a reduction of”. The original value (base) is always the original amount, (100%) before any increase or decrease takes place.

Original + increase = New value This year’s sales are RM 151,555 which is 10% more than last year’s sales. Find last year’s sales. Solution: Original + increase = New value 100% + 10% = 110% (New rate) B = RM 151, 555/110% = 151, 5550/1.1 =137,777.28

Lesson Summary Understanding the percentage signs and the ability to convert it to decimals or fractions are crucial to enhance the problem solving skills of the students.