## Saturday, April 3, 2010

### Fractions By: Laura

Hi everybody! Happy Easter! Hope everyone had an awesome spring break!

Here is my fractions video :)
http://www.ustream.tv/recorded/5703295

Sorry...Brianna and I were very hyper that day. But we got the message across. Now let's do some more questions!
Determine the product using 2 different methods:
4 x 1/2

The simplest way to solve this (in my opinion) is to change the whole number into a fraction and then just multiply. To change any whole number into a fraction all you have to do is put 1 as your denominator.

Our new equation:
4/1 x 1/2

Now we multiply the numerators by each other, and the denominators by each other.
4 x 1 =4
1 x 2= 2

Our product is now 4/2. To simplify you divide the numerator by the denominator.

4 divided by 2=2
The final product is 2.

Another way to solve this problem is by using diagrams/pictures.

We started out by representing 4 1/2s because that is what the equation is. Then, by adding them together we get the finished product of 4/2 -or- 2.

Now that we have covered multiplication, let's move on to division!

1/4 divided by 2:

As you can see, we started with 1/4. Then, we divided the entire rectangle in two. Now, we pick one to finish the division. That gives us 1/8.

Now, let's try out what we have learned with a word problem. :)

The ares of Manitoba, Saskatchewan, and Alberta are the same. The sum of their areas is 1/5 the area of Canada. Express the area of these provinces as a fraction of the area of Canada.

In order to figure this out, we have to divide 1/5 of the area of Canada by 3 provinces. -OR- 1/5 divided by 3.

Each province is 1/15 of the area of Canada.

PART 2:

A fraction multiplied by a fraction:

You multiply the numerators to get the numerator and the denominators to get the denominator. Pretty simple.

A fraction multiplied by a mixed number:

First you have to change the mixed number into a fraction by multiplying the whole number by the denominator, then adding the numerator to that number. Then that number becomes your numerator and you keep the same denominator. Then you multiply those fractions and you get your answer.

A mixed number multiplied by a mixed number:

OK, so you already know how to change a mixed number into an improper fraction. (WN x d + n) So that's the same method you use for determining the product of a mixed number by a mixed number. You change them both into improper fractions and then multiply. Then, from there you change the improper fraction into a mixed number by dividing the numerator by the denominator and using the remainder as your fraction.

1 3/7 x 3 2/5

1 x 7 = 7

7 + 3 = 10

Improper fraction = 10/ 7

3 x 5 =15

15 + 2 = 17

Improper fraction = 17/ 5

New question:

10/7 x 17/5

10 x 17 = 170

7 x 5 = 35

PRODUCT: 170/35

170 divided by 35 = 4 6/7

PART 3:

Explain:

1 1/2 divided by 3/4

First we have to find a COMMON DENOMINATOR for each fraction. In other words, we have to find a number that 2 and 4 go into evenly, preferably the SMALLEST COMMON DENOMINATOR. The smallest common denominator of 1 1/2 and 3/4 is 4. This means that we change 1 1/2 to 1 2/4 and keep 3/4 the same. Now we divide by figuring out how many times 3/4 goes into 1 2/4.

3/4 divided by 1/2.

Again, we have to find the LOWEST COMMON DENOMINATOR, which we already know is 4. Therefore we turn 1/2 into 2/4 and leave 3/4 the same. Now our job is to find out how many times 2/4 goes into 3/4.

Our answer is 1 1/2. Our denominator changed because when we started to divide, our whole changed from quarters to halves.

~Laura Kathleen~

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