Percentages

=**Percentages (%), decimals and fractions**=

When you say "Percent" you are really saying "out of 100"
(50% of this box is green) ||  || And **25%** means 25 per 100 (25% of this box is green) || ||
 * [[image:http://www.mathsisfun.com/numbers/images/percent-grid-50.gif width="134" height="134" caption="50%"]] || So **50%** means 50 per 100

Using Percent
Because "Percent" means "per 100" you should think "this should always be divided by 100" So **75%** really means 75/100 And **100%** is 100/100, or exactly **1** (100% of any number is just the number, unchanged)

The following power point will give you a simply overview on the basics of percentages.



To work out the percentage of this shape that is shaded, you must first work out what each part represents. There are 20 equal parts, so each part represents 5%.

=**100% (the whole) ÷ 20 = 5%**=

6 of the parts are shaded, so 30% of the total shape is shaded. 6 x 5% = **30%**

=Converting between percentages and decimals.= A percentage is an amount of a 100. ie 20% is 20/100. It is now a fraction. To convert this fraction to a decimal we write 20 and place a decimal point 2 spaces to the left. Two spaces for 2 zeros. The decimal of 20% is 0.20.


 * To change a percentage to a decimal,** **divide by 100**.

Change 48% to a decimal: 48 ÷ 100 = 0.48
 * To change a decimal to a percentage,** **multiply by 100**.

Change 0.67 to a percentage: 0.67 x 100 = 67% =REMEMBER: To convert from a Percent to Decimal=

To [|convert from percent to decimal]: (you can click on this link for more information) divide by 100, and remove the "%" sign. The easiest way to divide by 100 is to **move the decimal point 2 places to the left**. So:
 * From Percent || To Decimal ||  ||
 * [[image:http://www.mathsisfun.com/images/percent-to-decimal.gif width="337" height="58"]] || move the decimalan point **2 places to the left**, and remove the "%" sign. ||

=From Decimal to Percent=

To [|convert from decimal to percent]: multiply by 100, and add a "%" sign. The easiest way to multiply by 100 is to **move the decimal point 2 places to the right**. So: You can watch the following powerpoint for further explanations.
 * From Decimal || To Percent ||  ||
 * [[image:http://www.mathsisfun.com/images/decimal-to-percent.gif width="337" height="59"]] || move the decimal point **2 places to the right**, and add the "%" sign. ||

A **Percent** can also be expressed as a **//Decimal//** or a **//Fraction//**
=Decimals, Fractions and Percentages=
 * [[image:http://www.mathsisfun.com/images/fractions/pie-1-2.jpg width="120" height="120"]] ||  || **A Half** can be written... ||
 * As a percentage: || 50% ||
 * As a decimal: || 0.5 ||
 * As a fraction: || 1/2  ||
 * As a fraction: || 1/2  ||
 * Decimals, Fractions and Percentages are just different ways of showing the same value:**


 * [[image:http://www.mathsisfun.com/images/fractions/pie-1-4.jpg width="120" height="120"]] ||  |||| **A Quarter** can be written... ||
 * As a fraction: || 1/4  ||
 * As a decimal: || 0.25 ||
 * As a percentage: || 25% ||  ||
 * As a percentage: || 25% ||  ||

=HARDER EQUATIONS USING PERCENTAGES; FRACTIONS AND DECIMALS= = = =Converting a Fraction to a Decimal= The easiest way to [|convert a fraction to a decimal] is to divide the top number by the bottom number (divide the numerator by the denominator in mathematical language)

Example: Convert 2/5 to a decimal
Divide 2 by 5: 2 ÷ 5 = 0.4
 * Answer: 2/5 = 0.4**

media type="youtube" key="LXIS-7rQc74" height="315" width="420"
 * The following video explains how to convert fractions to a decimal and then into percentages.**

=Converting a Decimal to a Fraction= To [|convert a decimal to a fraction] needs a little more work.

Example: To convert 0.75 to a fraction

 * ~ Steps ||~ Example ||
 * First, write down the decimal "over" the number 1 || 0.75 / 1 ||
 * Then multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc) || 0.75 × 100 / 1 × 100 ||
 * (This makes it a correctly formed fraction) || = 75 / 100 ||
 * Then [|Simplify] the fraction || 3 / 4 ||
 * Then [|Simplify] the fraction || 3 / 4 ||

=Converting a Fraction to a Percentage= The easiest way to [|convert a fraction to a percentage] is to divide the top number by the bottom number. then multiply the result by 100, and add the "%" sign.

Example: Convert 3/8 to a percentage
First divide 3 by 8: 3 ÷ 8 = 0.375,

Then multiply by 100: 0.375 x 100 = 37.5

Add the "%" sign: 37.5%
 * Answer: 3/8 = 37.5%**

=Converting a Percentage to a Fraction= To [|convert a percentage to a fraction], first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

Example: To convert 80% to a fraction
Write the percentage as a fraction over 100 and then simplify:
 * ~ Steps ||~ Example ||
 * Convert 80% to a decimal (=80/100): || 0.8 ||
 * Write down the decimal "over" the number 1 || 0.8 / 1 ||
 * Then multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc) || 0.8 × 10 / 1 × 10 ||
 * (This makes it a correctly formed fraction) || = 8 / 10 ||
 * Then [|Simplify] the fraction || 4 / 5 ||
 * Then [|Simplify] the fraction || 4 / 5 ||

=Percentage of a number=

Step 2: then multiply the decimal by 30. 0.2 x 30 = 6
 * Example:**
 * Method One:** To find 20% of 30. Step 1: convert the 20% to a decimal. 20% = 0.2

This is the best method as it always works.


 * Method Two:** Another way to find 20% of 30 is to first find 10% of 30 and then multiply by 2. ie:10% of 30 is 30 ÷ 10 = 3

then 2 x 3 = 6


 * Method Three:** Or a third way would be to recognise that 20% is equivalent to one fifth, and so just divide 30 by 5. ie: 30 ÷ 5 = 6

=Some Worked Examples=

**Example: Calculate 25% of 80**
25% = 25/100

( 25/100 ) × 80 = 20 So 25% of 80 is **20**

**Example: A Skateboard is reduced 25% in price in a sale. The old price was $120. Find the new price**
First, find 25% of $120: 25% = 25/100 ( 25/100 ) × $120 = $30 25% of $120 is $30 So the **reduction** is $30

Take the reduction from the original price $120 - $30 = $90. The Price of the Skateboard in the sale is **$90**


 * We use these methods in life everyday. Watch the Following video showing how.**

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