Percent Notes

Tape Diagrams are a way to represent percent problems.
Draw a long rectangle and label the percents below and the values above.
If you know 100%, then find what 50% (divide 100% in half)would be and draw a line in the middle of the rectangle and label it. You can then find 10% (divide 100% by 10) and label the rectangle. From there you can find any multiple of ten and add that on the diagram or half 10% to find what 5% would be.
tape diagram

Finding Percents

1.  To find the percent one number is of another:  use part divided by whole times 100.
For example: 15 is what percent of 40?
You put 15/40, divide and get 0.375, then multiply by 100, so the answer is 37.5%.

2. To find the tax for an item you convert the percent (tax rate) to a decimal and multiply the price, round to nearest hundredth if needed. That will give you the tax and you add it to the price to find the total cost.
For example: If you buy a $15 shirt and the tax is 7% what will the total cost be?
You change 7% to 0.07 and multiply by 15, so 0.07x15=$1.05
Then at the tax to the price, $15 + 1.05= $16.05

Also if you only need to know the final cost not the exact amount of the tax you can simply add one to the percent as a decimal and multiply.
You would change 7% to 0.07 add 1 to get 1.07 then multiply by 15.
1.07x15=$16.05

3. To find the tip for a meal, you convert the percent (tip rate) to a decimal and multiply the price, round to nearest hundredth if needed. That will give you the tip and you add it to the price to find the total cost.
For example, if you want to tip 15% on a $34 meal, you convert 15
5 to 0.15 and multiply by 34.  0.15x34= $5.10

Also if you only need to know the final amount to pay not the exact amount of the tip you can simply add one to the percent as a decimal and multiply. so for the situation mentioned above you would multiply 34 by 1.15 and get the same tip.  34 x 1.15= $5.10.

4. To find the discount of an item you convert the percent off to a decimal and multiply the price by the decimal. To find the sale price subtract the discounted amount from the original price.
For example, if you by a video game for $56 and have a 30% discount coupon the discount would be convert 30% to 0.30 then multiply by 56, so 0.30 x 56= $16.80. To find the sale price $56 - 16.80= $39.20.

5. If you are given the percent of a number and asked for the original number you divide the value by the percent converted to a decimal. If ask What is the number if 40% is 38? 
You would convert 40% to .40 then divide 38 by .40. So 38/.40=95.
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