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Breaking Down FractionsFractions are all around you. Bob ate half of a pizza. The store gave you a quarter for change. You have one can of a six-pack of soda left over. Fractions are there. But what is a fraction? It is a way of representing a number value that has been broken into equal parts. Is a fraction a division problem? Yes. Is a fraction a ratio? Yes. Is a fraction a decimal? It can be. Is a fraction a percentage? It can be after it is multiplied by one hundred. A fraction can become many numbers and any rational number can be written as a fraction. Does that help? Probably not.
Let's look at the basics of fractions. A fraction is made of two numbers (integers) and a line. The top number is called the numerator and the bottom number is called the denominator. The top number represents the number of pieces you have and the bottom number represents the number of equal pieces there could be. Sometimes you might have a big number to the left of the fraction. When you have those big numbers, the fraction is called a mixed number (a whole number and a fraction). For example:
You have one part.
There could be six equal parts.
You have four parts.
There could be nine equal parts.
3 4/9 (mixed number)
You have three whole objects.
You have four parts of a whole object.
There could be nine equal parts of a whole object.
Parts of a WholeFractions are numbers that represent a number of equal sized parts. If you are talking about halves, there you took an object and broke it into two equal parts. When you work with thirds, there are three equal parts. Any object or number can be broken into any number of equal parts. You might have to do a fraction problem with one thousand seventy-thirds. Don't forget about the mixed numbers that use whole numbers and fractions. A value such as 3 5/7 means you have three whole objects and five sevenths of a fourth object.
Finding Common FactorsMany functions with fractions will have you searching for common factors. You might need to simplify a fraction and turn 6/8 into 3/4. You need to know that 2 is a common factor for the numerator and denominator. You might use factors when you add or subtract fractions. Adding the fractions 3/5 and 7/10 is difficult. But if you change the first value by a factor of two you wind up with 6/10. Adding 6/10 to 7/10 is easy as pie (you get 13/10 or 1 3/10).
Factors are numbers that can evenly divide into both the numerator and denominator. A fraction such as 17/25 does not have any common factors and it cannot be reduced. A fraction such as 16/24 is much different. The numerator and denominator share the factors 2, 4, and 8. If you reduce the fraction, you get 2/3. You'll get used to common factors as you use them more.
Adding and SubtractingYou can add and subtract fractions just like any other number. Some addition and subtraction problems are easier than others. When you have that lowest common denominator, things go much easier. We'll cover the details in a bit, but here are some examples.
1/4 + 3/4 = 4/4
17/52 + 21/52 = 38/52 (could be simplified to 19/26)
5/6 - 4/6 = 1/6
91/143 - 22/143 = 69/143
Multiplying and DividingWhile multiplying and dividing fractions are a little more difficult than adding and subtracting, it still has a simple process. Multiplying has you multiplying numbers on top with each other and dividing has you do a little flip-flop with the second value. Again, we'll go into details in a bit. Here are some examples.
1/4 x 1/4 = 1/16 (see how the ones multiplied with each other and the fours multiplied each other?)
1/6 x 5/7 = 5/42 (Tops with tops and bottoms with bottoms.)
1/4 divided by 3/4 = 4/12 (We flipped the second value and then multiplied. It could also be simplified to 1/3.)
1/6 divided by 5/7 = 7/30 (Start with a flip. Multiply tops. Multiply bottoms.)
* Look at the difference between multiplying and dividing the same values. Make sure you understand that the values are much different. 5/42 is much different than 7/30. The flip in division makes all the difference.
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