Ok, maybe not that excited. ;) First, let's review what we learned last week...
Review
Fractions, decimals, and percentages are all PARTS of a WHOLE.
Different fractions can be used to describe the same amount of a whole. These are called equivalent fractions, and this is what they look like:
It's clear that there is half a pizza in each circle -- so the amount of the whole pizza that we have is equal (or equivalent) in all three examples, but the number of pieces we have changes. On the left, half of the pizza is represented as 1/2 -- which is one piece of two total pieces. In the center, the pizza is cut into four total pieces, so we have to take two of the four, if we want half. On the right, there are eight total pieces, and we need four of those eight to make half.
Fractions can be raised by multiplying or reduced by dividing. This is important for adding/subtracting fractions, because you can only add/subtract fractions with the same number of total pieces. For example, if I wanted to take 1/2 of my pizza and add 1/4 to it, I would have two pieces but they would be different sizes, so I couldn't say I have two halves-fourths, right? So what would I do? Well, I'd have to raise my 1/2 by multiplying my part and my whole by 2. Then I could add: 2/4 + 1/4 = 3/4 of the pizza.
Our number system is all based on groups of tens. Decimals are just fractions based on 10s, 100s, 1000s, etc. If you know place-value, then changing decimals to fractions is super easy. For example, if I know that 0.7 can be read as 7 tenths, then the fraction of this decimal is 7/10. The decimal 0.09 is read as 9 hundredths, which is 9/100 in fraction form.
To change a fraction into a decimal, divide! So for example, if I wanted to change the fraction 3/4 into decimal form, I would take 3 divided by 4 which equals 0.75. Three quarters is the same as seventy-five cents, right? This is why decimals and fractions can be used interchangeably. They look different from each other, but they are describing the same amount -- just like equivalent fractions look different but are describing the same amount.
Percentages
Percentages are fractions that are always based on 100 as the whole. The word per-cent means "out of 100". As decimals, percentages look like cents. So 65% looks like 65 cents (0.65); 8% looks like 8 cents (0.08), and so on.
All fractions can be changed to percents by raising the fractions up to pieces of 100. So for example if I had 5 $20-bills, and I gave you one of them, what fraction of my money would you have? You'd have one out of the five total, or 1/5. If I asked you what percent of my money you had, we'd have to raise 1/5 up to parts of 100. Now, if you're brilliant (which I'm sure you are), you've already realized my 5 $20-bills equal $100. So the one bill that you have is $20/$100 -- and if I have a fraction based on 100, it's a percent! So you would have 20% of my money.
Here's a playlist for learning percentages and how to work with them better:
That's probably enough math for now. Check back next week for applied percentages!
-Jc
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