Exemplar 4: MathematicsĀ 

Table of Contents
Page 43 (continued)

Let's look at our fraction problem again:

1 over 6 + 1 over 12 = ?

In this problem, one of the denominators is 6 and one is 12. What is the Greatest Common Factor that can go into both 6 and 12? 6 can go into 6 once and 6 can go into 12 twice. 6 is the largest number that can go into 12 evenly. So 6 is our GCF for this problem.

Remember, the GCF is the greatest, or largest, number that two denominators can be divided by. You might have seen that 3 can go into 6 twice and into 12 four times, but for this problem we will use 6 because it is the largest number that can go into both denominators.

Now that we know what the GCF is, let's use this information on our fraction problem. Multiply the denominators together and then use the GCF to divide them.

6 x 12 = 72 72 divided by 6 = 12

The answer is our Least Common Denominator. Now we know that 12 is the LCD in our fraction problem. Next, we need to add the LCD to our problem. The Least Common Denominator will replace the original denominators. Look at the original problem again:

1 over 6 + 1 over 12 = ?

To change

1 over 6
into an equivalent fraction with a denominator of 12, multiply by
2 over 2
.

1 over 6 x 2 over 2 = 2 over 12

Let's see what our problem looks like with these changes:

2 over 12 + 1 over 12 = ?

Now we need to compare the new fraction on the left with the second fraction in the problem. Since the denominators are the same now, the 12 in the second fraction does not need to be changed. 12 is already the LCD. The 2 in the second fraction does not need to be changed either because we did not change the denominator.

We're ready to solve our new fraction problem:

2 over 12 + 1 over 12 = ?

Now that the denominators are the same, we simply add the two numerators:

1 + 2 = 3

Our answer is:

3 over 12