## Monday, March 12, 2007

### SUBTRACTING FRACTIONS .

When you want to subtract fractions that are a mixed number you should convert the mixed number into an improper fraction, then subtract them as fractions.Heres an example 5 1/8 - 2/3 = ? .. convert the mixed number into an improper fraction. which is 41/8 find the most common denominator and that is 24. your fraction now is 123/24. SINCE 8 x 3 = 24 and 41 x 3 = 123. The other fraction is 16/24 because 8 x 2 = 16 and 8 x 3 = 24. Then subtract 123 from 16 and that equals 107/24.. if you want to convert it back to a mixed number you have to see how much 24 goes into 107 . which is 4 times, then how much remains and that would be 11. mixed fraction is 4 11/24...
If the fractions aren't in a mixed number.. heres the way to do it.
2/3 - 3/5 = 10/15 = 9/15 = 1/15 .. multiply the denominators by each other ( 5 x 3 =15) .. then cross multiply 2 x 5 = 10 and 3 x 3 = 9 .. fraction is now 10/15 and 9/15 then subtract 10 from 9 and that gives you 1/15 ..
If the fractions have different denominators
1) Find the least common denominator.
2) Find the equivalent fraction using this denominator.
3) Subtract the fractions, if you could reduce then you should.

### There are 3 Simple Steps to add fractions:

Step 1: Make sure the bottom numbers (the denominators) are the same

Step 2: Add the top numbers (the numerators). Put the answer over the the same denominator as in step 1

Step 3: Simplify the fraction.

### Example 1:

 1 + 1 4 4

Step 1. The bottom numbers are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

 1 + 1 = 1 + 1 = 2 4 4 4 4

Step 3. Simplify the fraction:

 2 = 1 4 2

(If you are unsure of the last step see the equivalent fractions page)

### Example 2:

 1 + 1 3 6

Step 1. The bottom numbers are now different. We need to make them the same:

 1 = 2 3 6

Step 2. Add the top numbers and put them over the same denominator:

 2 + 1 = 2 + 1 = 3 6 6 6 6

Step 3. Simplify the fraction:

 3 = 1 6 2

## Adding Fractions with Different Denominators

To Add Fractions with different denominators:

• Find the Lowest Common Denominator (LCD) of the fractions
• Add in the new numbers to the fractions to have the LCD
• Add the numerators of the fractions
• Simplify the Fraction

Example: Find the Sum of 2/9 and 3/12

• Determine the Greatest Common Factor of 9 and 12 which is 3
• Either multiply the denominators and divide by the GCF (9*12=108, 108/3=36)
• OR - Divide one of the denominators by the GCF and multiply the answer by the other denominator (9/3=3, 3*12=36)
• Rename the fractions to use the Least Common Denominator(2/9=8/36, 3/12=9/36)
• The result is 8/36 + 9/36
• Add the numerators and put the sum over the LCD = 17/36
• Simplify the fraction if possible. In this case it is not possible

@ pictures from various sites

### Equivalent Fractions

Equivalent Fractions are fractions that are equal or have the same value. They both represent the same pieces.

They are either a multiple or a divisor.

-This is like a multiple, you have a pie. Your sharing it with your best friend. So, each of you get 1/2 of the pie. The 2 pieces of the pie are too big for you two to eat. So, you went and cut the 2 pieces into half. Now you both have 2/4.
-To find a multiple of a fraction, you multiply both the numerator and the denominator by the same number.
-Example: 2/4 x 5/5 = 10/20

-This is a divisor, you have a pie. It was cut into 4 pieces. You and your friend are going to share it. So, you get 2/4 and he gets 2/4. You put your 2 pieces together and realize you have 1/2 of the whole pie.
-To find a divisor of a fraction, divide both the numerator and denominator by the same number.
-Example: 50/60 divide by 10/10 = 5/6

### Improper fraction

Definition: A fraction with a numerator larger than the denominator

How to convert a improper fraction to mixed
Step one: check how much the denominator can go into the numerator. Then put the whole number for the mixed as how many times the denominator can go into the numerator.
Step two:The remaining numbers are the numerator and the denominator stays the same.

Picture:

## Saturday, March 10, 2007

### Proper Fractions

Proper Fractions
Definition : A proper fraction is a fraction with a smaller numerator then denominator.

Names used in fractions:
numerator - is the number to the left of the line. In the fraction 7/8 the numerator is 7.
denominator - is the number to the right of the line. In the fraction 7/8 the denominator is 8.

Proportional Fractions - At the beginning of this page we defined the word fraction as a portion of the whole. We have shown that there is more than one way to write the portion that is half of the pizza. One half can be written as 4/8, 2/4 or 1/2. We say that these equivalent fractions are proportional fractions because they are the same portion of the pizza. Here are some different examples of proportional fractions using the integer bars. All of them are equivalent.

Thanks to for helping me finish this post: