## Thursday, April 1, 2010

### Mary Jane's Fraction Growing Post

In our past few math classes, we learned how to multiply and divide fractions.

Here is a video showing what I did correctly on the fraction quiz and what I did wrong. I will show you the correct work for the questions I got wrong.

I will now show you how to multiply a fraction by a whole number using one of the questions on page 202 of our Math Links textbook.

I chose to do my example on the question
5 x 2/3.

- you could add 2/3 5 times, like this:

- you could have 5/1 x 2/3 and
multiply the numerator and denominator of each fraction like this:

Next, I will show you how to divide a fraction by a whole number using one of the questions on page 208 of our Math Links textbook.

The question I chose as my example is 1/3 ÷ 3.

- use a diagram showing a fraction strip divided into 1/3 then you divide that 1/3 into 3 portions using horizontal lines, as shown in this picture:

Lastly, I will chose a word problem to solve from page 208 of our Math Links textbook.

Problem: 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?

What you have to do to solve it:
- find the key words in the question that will help you solve the problem
The key words in this question is 2/3, four students, and what fraction of the full pitcher does each student get.

- you now have to make a simple sentence answer
Each student gets ___ of the full pitcher of orange juice.

- you can now solve the problem
To solve the problem, I drew a fraction strip and divided that into 2/3, then I divided that 2/3 into 4 portions using horizontal lines. Since our numerator is 2, you then have to shade in 2 rectangles in the new fraction strip that contains 12 rectangles.

Each student gets 2/12 or 1/6 of the full pitcher of orange juice.

Part 2:

For part 2 of my fraction growing post, I will be showing you how to multiply fractions.

1) Multiplying a fraction by a fraction

To multiply a fraction by a fraction, you will have to multiply the 2 numerators and the 2 denominators. When you have done that you will then have to put the fraction into its simplest terms if possible.

2) Multiplying a fraction by a mixed number

To multiply a fraction by a mixed number you will have to convert the mixed number into an improper fraction. To do that you will have to multiply the whole number by the denominator and then add the numerator. Once you have done that you will have to multiply the numerators and the denominators. If the product you get is an improper fraction you will have to convert it to a mixed number in lowest terms. If the product you get is a proper fraction, all you have to do is put it in its simplest terms.

3) Multiplying a mixed number by a mixed number

To multiply a mixed number by a mixed number you will have to convert both mixed numbers into an improper fraction. You will again have to multiply the whole number by the denominator and add the numerator. Once you get the improper fraction you will have to multiply the numerators and the denominators. When you get the product as an improper fraction you will have to convert it back to a mixed number. To do that you will have to find how many times the denominator goes into the numerator. After converting, you will have to put it in its simplest terms.

Part 3:

For today's class we wrote some notes on dividing fractions in our foldable. We were also asked to do 2 questions and show how we got our answer.

One of the questions were: 1 1/2 ÷ 3/4 = 2

How many 3/4 are there in 1 1/2 ?

What I did was I drew 2 fraction strips and divided each into 4 portions. I divided it into 4 because you have to find how many 3/4s are in 1 1/2. I then colored all 4 portions in one strip to represent 1 in 1 1/2 then I shaded 2 portions in the other to represent 1/2 in 1 1/2. Now I found how many 3/4s are in 1 1/2 and I got 2 3/4s in 1 1/2.

Here is a picture to show what I did:

The other question was : 3/4 ÷ 1/2 = 6

How many 1/2s are in 3/4?

To find the answer I drew a fraction strip and divided that into 4's. After that, I divided the strip into a half to represent 1/2. I came up with 8 little squares in my fraction strip. I now colored in 6 little squares altogether because if you looked at the strip without the half it looks like you colored 3/4. Since you technically colored 6 little squares in, that becomes your answer.

Here is a picture to show what I did: