Math Page 1

Math Page 1
Fractions: What are they?
1/4 is a fraction. It tells us that we are using 1 of 4 parts in a whole unit. Like taking 1/4 of the proverbial pie. The bottom number tells us how many units it takes to make up a whole pie. The top number tells us how many of the units we are taking at this time. So 1/4 is telling us that the pie is cut into 4 equal parts and that we are taking one of the 4 parts. If we took two pieces then we would be taking 2/4 of the pie, 3 pieces and we would be taking 3/4 of the pie and if 4 pieces we would be taking 4/4 of the pie or the entire pie. What happens if we take 5 pieces pie? We would then be taking 5/4's of pie, but each pie only has 4 pieces so we must have found another pie. We take all of one pie and 1 of 4 equal pieces of the other pie. What else does 1/4's represent. It is also an indicator of a decimal value or a percentage value. If we divide 1 by 4, we get .25 or 25%, If we divide 2 by 4, we get .50 or 50%, If we divide 3 by 4, we get .75 or 75%, and If we divide 4 by 4, we get 1 or 100%. Notice the similiarities here. We had .25 as a decimal and then as 25% and we had .50 and it is also 50%. We go from the decimal value to the percentage value by shifting the decimal point 2 places to the right. From .25 to 25.% or 25% and .50 to 50.% or 50%. Here is something we use all the time .25 is a quarter and .50 is fify cents. They are also known as a quarter and a half dollar. They are called this because it take 4 quarters to make a dollar and it takes 2 fifty cent pieces to make a dollar. So how does 2/4 end up being 1/2? We simply look at the top and bottom number and see that they can both be divided evenly by 2. So we divide 2 into 2 and get 1, and then we divide 2 into 4 and get 2. We now have 1/2 or one-half. This is called the lowest common denominator.

If 2 bits is a quarter and 6 bits is seventy-five cents then what is a bit worth? It takes 4 quarters to make a dollar and there are 2 bits to a quarter, then a bit must be worth 1/8 of a dollar or 12 and 1/2 cents (1/2 of a quarter). We get this by taking 1/2 of the value of a quarter, because it takes 2 bits to make a quarter. 1/2 of 1/4 just happens to be 1/8. To check back it would be 2/8 equals 1/4. If we divide 2 by 2 we get 1 and if we divide 8 by 2 we get 4, and we come back to 1/4. We could just multiply 1/2 times 1/4 and we get the same thing. 1 times 1 is 1 and 2 times 4 is 8 or 1/8. This is top times top and bottom times bottom.
Add-On and Mark-up Pricing. What is the difference between add-on and Mark-up pricing? You must remember to factor in the total cost of your item. This should include an amount for any shipping and handling costs to get the product to your store. Or you could just adjust your profit percentages to cover the extra costs associated with a product. Add-On Pricing is simply taking your cost and multiplying it by a given percentage and then adding it to the cost of an item. We could also just multiply the cost by 100% plus the add-on percentage. If we wish to use a 30% add-on profit, we would multiply the cost by 130% and would arrive at our retail price. If an item cost $10.00 and we wish to use an add-on profit of 30% we would multiply the $10.00 my 30% or .30 and arrive at $3.00 as our add-on amount and then our retail price would be $13.00 or we could multiply the cost of $10.00 by 130% or 1.30 and arrive at $13.00. Mark-up or Margin Pricing is using the cost of an item as a given percentage of the retail price. This method is used when you are trying to keep tabs of your Cost of Purchases using the Financial Statement percentages. In other words, where you see your Sales as 100%, your Cost of Goods as 70% and your Net Sales as 30%. To find the retail price of an item using the Mark-up method you simply divide the cost by 1 minus the mark-up percentage. This is done because the cost represents 100% of the retail price minus the profit margin. If we wish to have the profit margin percentage as 30% we would divide the cost by 70% and would arrive at the retail price. In this case if we have an item costing $10.00, we would divide the $10.00 cost by 70% or .70 and arrive at a retail value of $14.29. We can check this number by multiplying the computed retail price by 70% and coming back to the cost price of $10.00.

So which is the best to use. For dealing with the Tax Boards and the IRS it is usually best to use the Mark-up or Margin Pricing because it makes it easier to keep track of your margin without doing extra calculations. You just check your net purchases as a percentage of your sales and you should arrive at a number near the the profit margin. This is the ballpark method that tax agencies tend to use to keep tabs on your business. If you had $25,000 in sales and the industry average cost on sales for your business is 70% then your cost of goods should be around $17,500. Any major variance from this number could increase your possibility of an audit by about 10 to 20 times. Just being in business increases your possibility of an audit by about 10.
A CAUTION: You should always keep very good records of items sold at marked down prices, such as items on sale or close-outs. These types of items tend to knock the percentages out of kilter and the tax boards especially want to know why your margin is off. Without the required backup documentation you may end up paying the tax board a lot more than you owe them plus the applicable interest and penalties.
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