## Introduction: Subtracting Fractions

First Prize in the

Burning Questions Round 6.5

Subtracting fractions can be tricky for some, and can take a bit of work to learn at first. Here I will be breaking down the steps as clearly as possible.

## Step 1: Find the LCD (lowest Common Denominator)

A **denominator** is the bottom number of a fraction.

When you have two fractions, we need to find a multiple of the two denominators that are equal. We do this by comparing the multiples of both denominators until we find the first instance where both denominators are the same number.In this example our denominators are 3 and 5.

For help with the art of multiplication, see Kitemans instructable on multiplication

## Step 2: LCD Part 2

After comparing the two tables, we notice that the first instance of a matching number comes when both multiples equal 15. This is called a **least common multiple**.

## Step 3: LCD Part 3

A* Least Common Multiple* that is our *Denominator* is naturally called a **Least Common Denominator**, which is what we were looking for.

Armed with this information, we can find our **multipliers**. In other words, what did we multiply each number by to get our LCD of 15?

## Step 4: Multiplying the Fraction Parts

We found out in step 2 that 15 is our LCD for the two fractions, and in step 3 we found our multipliers. We now must multiply our **numerators** by this same number as we used for the denominators.

After the multiplication we end up with the fractions of 5/15 and 6/15

## Step 5: Subtraction

Now we must subtract the numerators from eachother. In this case we end up with a negative number, as 5-6 = -1.

When we write negative fractions, the negative number does not 'belong' to the numerator itself, but to the entire fraction. The negative number is written to the left of the fraction itself.

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