## Saturday, April 3, 2010

### Jamie's Fraction Growing Post

Part 1
In math, we were taught how to divide and multiply fractions with whole numbers.

This is my fraction quiz, and it will show you how I answered all the questions.

I will show you two ways to multiply a fraction with a whole number.

ex. 5 x 2/3

One way you can solve it, is by using pictures.
The second way to solve it, was by multiplying the whole number by the numerator of the fraction.
Now, I will show you how to divide a fraction by a whole number.

ex. 1/5 ÷ 2

To divide a fraction by a whole number, you have to draw the fraction first. You divide the whole into 5 parts, since the fraction is 1/5 as shown on the left in the picture. Then, to divide it by a whole number, you have to put a horizontal line across to show that you're dividing the fraction into 2.
Finally, I had to pick a word problem and show you how to solve it.

A pitcher of orange juice is 2/3 full. If four students equally share the juice, what fraction of the full pitcher does each student get?

To solve this problem, we have to divide a whole into thirds, and colour in 2 parts. Now, since the orange juice is equally shared with four people, you have to divide the 2/3 into 4 with horizontal lines, as showed in the picture.
Simple sentence answer: Each student gets 2/12 or 1/6 of the orange juice.

Part 2 - Multiplying

This part of the fraction growing post is about multiplying fractions with mixed numbers, and improper fractions.

First, I will show you how to multiply a fraction with a fraction.
To multiply fractions, all you have to do is multiply the numerators and the denominators to get your answer as shown in the picture below.

Now I will show you how to multiply a mixed fraction with a fraction.
All you need to do, is convert the mixed fraction into an improper fraction, which makes it easier to multiply. Now, since the number became 39/56, that is the answer. I cannot simplify the fraction, so you just have to leave it that way.

Lastly, this is how to multiply mixed numbers, with mixed numbers.
To multiply two mixed numbers, you have to convert them both to improper fractions. Then, Ms. U taught us a way to convert an improper fraction back to a mixed number.
Who goes in the house? The numerator does.
Who's knocking on the door? The denominator does.
Then, you have to find out how many times 16 (or who ever is 'knocking on the door') goes into 121 (the one that's in the house). Then that's the whole number you put on the top. Next, you have to multiply the number on the top which is 7, and the number knocking on the door which is 16. Now you have to subtract 112 from 121. Since that gives you 9, that is the numerator of the fraction that goes with the mixed fraction.

Part 3 - Dividing Fractions

Explain:

1 1/2 ÷ 3/4 = 2
The way I solved this, was I used cross multiplication, or whatever that's called. :P But first, I converted the mixed number into an improper fraction, to help me multiply the fractions faster. Then, now that I have the 2 fractions, I multiplied the denominator of the first fraction, and the numerator of the second number, which makes the denominator of the answer. Next, I multiplied the numerator of the first fraction, and the denominator of the second fraction, which makes the numerator of the answer. That's how I got 12/6. :D

3/4 ÷ 1/2 = 6/4 or 1 1/2
I did the same thing for this question, but I just didn't have to convert the mixed fraction into an improper because there is no mixed fraction. :)