Changing Form: Mixed Fractions to Improper Fractions
Before we start, let's review a few definitions. A mixed fraction is one that has both a whole and a fractional part, such as 3 1/2. An improper fraction is one where the numerator (the top part) is larger than the denominator (the bottom part), such as 7/2. Both of these examples represent the same number (3.5); it's just written differently.
Changing fractions from mixed to improper form is pretty easy; you don't even need to find a least common denominator, like you would if you were comparing or subtracting fractions.
Let's look at what a whole number represents. Suppose that 3.5 above represents how many pizzas we have left over from a party; we have 3 whole pizzas, plus half of a pizza. We can write that at 3 1/2 (three and one half) or 7/2 (seven halves, which form three wholes plus one more half).
Recall that anything divided by itself equals one: 2/2 = 1, 3/3 = 1, etc. To convert from mixed to improper form, start by changing the whole number part into a fraction. Continuing with our example, we multiply 3 by 2 to get 6/2; 6/2 is the same as three. We now have two fractions with like denominators, so we can add: 6/2 + 1/2 = 7/2. Another way of saying this is to multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.