Primary Mathematics/Percentages

Primary Mathematics Percentages Decimals Metric system Percentages Introduction Have you ever seen the symbol %? It’s called the percent symbol, and it expresses a part of a whole. The word percentage comes from two Latin words: per meaning "for each," and cent meaning "100." So, a percentage is a value (number) divided by 100. thumb|right|This grid has 100 squares. Since 25 are shaded, 25% of the grid is colored in. For example, 25% means 25 for each 100. We can write this as: A fraction: (which can be simplified to ) A decimal: A very common example is 50%. It means 50 out of 100, which is exactly half! Uses of Percentages We see percentages everywhere! They are a simple way to talk about parts of things, from a slice of pizza to the score on a test. For example: In stores: An item might be on sale for "20% off." At school: You might get a score of 95% on a spelling test. In sports: A basketball player might have a 75% free-throw shooting average. On batteries: Your phone battery might have 30% charge left. Finding the Base The base of a percentage change is the starting value. Many errors occur from using the wrong base in a percentage calculation. Example: A Store Discount and Tax Question: The store is having a 20% off sale, but you will also need to pay a 6% sales tax. What will be the final price if you want to buy a video game that costs $50? Solution Step 1: Calculate the discount. The discount is 20% of the original price. Our starting base is $50. So, the discount is $10. Step 2: Find the new sale price. We subtract the discount from the original price. The game now costs $40. Step 3: Calculate the sales tax. Here’s the important part! Do we calculate the tax on the original $50 or the sale price of $40? In most places, you pay tax on the price you actually pay at the register. So, our new base for the tax is now $40. The tax is $2.40. Step 4: Find the final price. We add the tax to the sale price. The final price you pay for the video game is $42.40. Solving chain can be written as: Original Price → Discount → Sale Price → Tax Addition → Final Price Notice that taking off 20% and adding 6% was not the same as just taking off 14% (20% - 6%). This is because the percentages were calculated on different bases ($50 and $40). Simple and Compound Interest Percentages can be used to calculate the amount of interest applied, whether it is simple or compounded. Simple Interest (SI) is when interest is calculated only on the original amount of money (the principal, P). Compound Interest (CI) is when you apply the same percentage interest rate repeatedly. For those familiar with powers and exponents, we can use the following formula to calculate the total: OR Simply, Where: P = Principal R = r = Interest rate n = Compounding frequency per period (t) nt = Time (usually in years) Question: Let's say you deposit $1,000 in a bank that pays 10% interest each year, compounded annually. Solutions Method 1: Manually After Year 1: You earn 10% of $1,000. Your new total is . After Year 2: You now earn 10% on your new total of $1,100. Your new total is . After Year 3: You earn 10% on your new total of $1,210. Your new total is . Method 2: Using the formula for compound interest As you can see, with compound interest, the added value grows faster each time. More complex interest calculations will be covered in later lessons. Primary Mathematics Percentages Decimals Metric system