Fractions are split into parts. The top number is the "numerator", the bottom number is the denominator and the line between is essentially a division symbol.
There are different kinds of fractions. Proper fractions, such as one third, have a smaller numerator than denominator. An improper fraction has a larger number on top (numerator) and can be changed into a mixed number.
Fractions have their own place on the number line, just like whole numbers.
Fractions have many equivalents, there is more than one way to name a fractional part, even though it is the same amount.
When working with fractions it is important to understand that there are multiple ways to express the same value.
You also must understand that there is a value that is less than one but greater than zero.
Addition and Subtraction of Fractions
Fractions, proper or improper and mixed numbers can be added and subtracted just like whole numbers. The first step in this process is to find Common Denominators. A common denominator is just what it sounds like, a common (same) denominator (number on the bottom). Mixed numbers must be first turned into improper fractions before the common denominator is determined. Common denominators are found by determining the least common multiple of the two denominators and what number that denominator is multiplied by to get to that multiple. The numerator must also be multiplied by that number and that gives you a fraction equivalent that can be added or subtracted. It is important that the fractions be transformed into fractions with common denominators because when adding or subtracting the denominator does not change. Only the numerators are added to or subtracted from each other. This entire process is nicely illustrated in the following video.
Adding and subtrating fractions can be a bit confusing at first but once
you get this system down, it can also be quite fun, the following sites
have games that will help build your abitiliy, confidence, and
enjoyment of fractions.
Once the common denominators have been determined, the numerators also changed, and an equivalent fraction created it is time to add or subtract! Like I said above, only the numerators are used in this step, the denominator stays the same. For example, 18 twenty-fourths added to 22 twenty-fourths equals 40 twenty-fourths, the twenty-fourths DO NOT get added together.
Once we have our answer, in this case 40 twenty-fourths we are not done. It is most common to give the answer in Lowest Terms. Lowest terms means the fraction's numerator and denominator have no lower common factors (not including 1). Lowest terms are determined by fining the greatest common factor of the numerator and the denominator and dividing each by that number, you are reducing the fraction to it's lowest equivalent fraction. Web Math gives us a handy online calculator, along with explanation of the reduction. This resource would be great for checking work!
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