### Fractions

Friday, April 10, 2009
This week, we began our new topic: fractions. During math skills, we were asked to compare fractions. There are two ways to compare; by using pictures and decimals. By comparing fractions with pictures, you are able to see the amount of pieces and which represents the numerator. When you compare fractions with decimals, you compare them by using the place values. For example, compare 2/3 and 4/6.

Decimal:
In order to get the decimal from the fraction, you divide the numerator by the denominator. If you divide 2 by 3, you will get 0.666667. If you divide 4 by 6, the answer will also be 0.666667. It's the same, so the fractions are equivalent.

Picture:

Clearly, 2/3 and 4/6 are equal. But they're not the same. For example, if you were to have 3 friends over at your house, and you wanted to eat pie. You cut the pie into sixths, and you take 4 pieces for you and your friends. Your mother comes into the kitchen and says, "2/3 of the pie is gone, who ate the pie?" You would've said, "No mom, my friends and I ate 4/6 of the pie." They're not the same because 4/6 would've been more precise.

Another example is 1/8 and 1/4; are they less than, greater than, or equal to? Let's find out.

Decimal:
Again, divide the numerator by the denominator. If you divide 1 by 8, you will get 0.125. If you divide 1 by 4, the answer will be 0.25. But which is more? Like I said in the beginning, you find out by comparing the place values.

As you can see, 1/8 is less than 1/4, because 1/4's tenth and hundredth places are bigger than 1/8's tenth and hundredth places. The extra 0's do not affect the decimal, it's there to be more precise.

Picture:

As you can see, 1/4 is obviously greater than 1/8. Both fractions have 1 as a numerator, which is very helpful when it comes to comparing fractions as well as ordering them. When 1 is the numerator, the fraction is called units. It's easier to compare and order them because the smaller the denominator is, the bigger the fraction. So, 4 being a denominator is bigger than 8 being a denominator.