Let's learn with an example.
Jim needs to paint 4/5 of the wall today. So far, he's already painted 1/2 of it. How much more of the wall does Jim need to paint?
The problem is asking us to subtract fractions.
Their denominators are not the same.
Tip: Denominators are the bottom numbers in fractions.
Let's use a number line to help us solve this problem.
This is 4/5:
Our denominator is 5.Ā
So we divided the space between 0 and 1 into 5 equal parts.
This is 1/2:
We split 1 into two parts, because our denominator is 2.
Ā Ā Ā Ā Ā We can only subtract fractions when their denominators are the same.
If you look at the number lines, the number of equal parts between 0 and 1 is different for 4/5 and for 1/2.
So what should we do?
Fantastic. We need to find a common denominator for these fractions, and rewrite each as an equivalent fraction with this common denominator.
Finding a common denominator is like dividing both number lines into a common number of smaller parts.
The trick is to divide each part by the denominator of the other fraction.
Let's start working on 4/5.
The denominator of the other fraction, 1/2, is 2.
That means we further divide each part of 4/5 by 2 smaller parts.
How many equal parts are there between 0 and 1 now?
Correct, there are now 10 equal parts.
We can see that 4/5 is the same as 8/10.š
Tip: 4/5 and 8/10 are called equivalent fractions.Ā
Now, let's look at 1/2.
How should we further divide each part in the number line for 1/2?
We look at the denominator of 4/5, the other fraction.
It's 5.
That means, we further divide each part of 1/2 into 5 smaller parts.
We see that 1/2 is the same as 5/10.
Let's put our number lines together.
Now both have 10 equal parts between 0 and 1 on both number lines.
We found a common denominator, 10. š
Now, we're ready to subtract.
Ā Ā Ā Ā Ā When subtracting numbers on a number line, we move some steps backward.
8/10 minus 5/10 means we start from 8/10.
Then we subtract 5/10 from it. That means moving 5 steps backward.
On which part did we end up on?
Yes! On 3/10.
This is our final answer.
Great work learning how to subtract fractions with unlike denominators using number lines. š
Now, let's practice.