Equivalent Fractions
Essentially we use fractions to describe how many parts something is divided into, as well as some number of pieces of the whole.
The number of pieces of the whole thing that we have (top number = numerator)
½
The number of parts that the thing is divided into (bottom number = denominator)
Given that fractions represent parts of a set, different fractions can be used to represent the same fraction:
1/2 3/6 4/8 5/10
As we can see, although the fractions above are different, they all represent the same amount. Therefore they are equivalent.
As equivalent fractions represent the same amount, they will all appear at the same point on a number line.
To form equivalent fractions, multiply or divide the numerator and denominator of the fraction by the same number (but not zero).
Generally, we want to express fractions in lowest terms, or simplest form. To do this simply keep dividing the numerator and denominator by numbers that divide evenly into both numbers until the only number that will divide evenly into both is 1.
Therefore, four twelfths and one third are equivalent fractions, with one third being the fraction expressed in lowest terms.