Adding and subtracting fractions is a multi-step operation. First, you have to make the denominators of the fractions the same by multiplying the top and bottom of each fraction by the opposite fraction’s denominator. Next, add the numerators and simplify the result. This video explains that process, then walks students through an example problem.

The numerator is the number on top,

Denominator is down down low.

When you add fractions you need to stop,

Make sure the denominators are good to go.

We need to make the denominators the same,

Otherwise adding them would be insane.

So we multiply each fraction, top and bottom,

By the denominator of his buddy.

We do it to the top and the bottom,

So the value doesn’t change, yeah you got 'em.

Yeah, we do that to both of these guys,

Multiply by the bottom of the buddy, alright?

Our denominators are now the same,

And when we add fractions, they don’t change.

Add numerators like 10 + 16,

But keep the denominator the same thing.

Multiply the bottom and the top by the opposite denominator,

Keep the bottom the same, but add the tops,

We aim steady, a-a-adding, if you're ready or not. (x2)

Let’s try it on, see if it fits,

Let’s add

^{1}⁄

_{4}+

^{2}⁄

_{5}.

First we take the 5 and multiply

Both the top and the bottom on the other side.

Hmm, we get

^{5}⁄

_{20},

That’s equal to

^{1}⁄

_{4}, yeah, you get me.

Then we take the 4 from before,

Multiply the other side, yeah for sure.

We get

^{8}⁄

_{20},

That’s still equal to

^{2}⁄

_{5}, but get ready.

Now we keep the 20 the same,

But we add 8 + 5, OK?

^{13}⁄

_{20}, yeah, that’s the truth,

Now we make sure that it’s reduced

And simplified, so our fraction is nice,

We’re adding fractions and we're doing it right!

Multiply the bottom and the top by the opposite denominator,

Keep the bottom the same, but add the tops,

We aim steady, a-a-adding, if you're ready or not. (x2)

*And when you're subtracting, it’s the same thing! Just follow all the steps, but subtract the numerators. You got it? Yeah. You got it.*

The numerator is the top number in a fraction. The denominator is the bottom number.

In order to add or subtract fractions, the denominators have to be the same. This song will show you how to make that happen.

Adding fractions requires denominators to be the same. Why? Try to add fractions without making the denominators the same and see if it makes sense?
^{
1
}
⁄
_{
2
}
+
^{
1
}
⁄
_{
4
}
. If we don't make the denominators the same first, we'd get
^{
2
}
⁄
_{
6
}
, and we know that
^{
2
}
⁄
_{
6
}
=
^{
1
}
⁄
_{
3
}
. That is less than
^{
1
}
⁄
_{
2
}
. But how could I start with
^{
1
}
⁄
_{
2
}
and then add
^{
1
}
⁄
_{
4
}
to it, and still get
^{
1
}
⁄
_{
3
}
? It doesn't make any sense. The problem is that we didn't make our denominators the same.

How do we make the denominators the same? To do this, multiply the top and bottom of the first fraction by the second fraction's denominator, then multiply the top and bottom of the second fraction by the first fraction's denominator.

In order to add
^{
1
}
⁄
_{
4
}
and
^{
2
}
⁄
_{
5
}
, the denominators have to be the same. This means multiplying both the numerator and denominator of each fraction by the opposite fraction's denominator.

^{
1
}
⁄
_{
4
}
+
^{
2
}
⁄
_{
5
}

(
^{
1
}
⁄
_{
4
}
×
^{
5
}
⁄
_{
5
}
) + (
^{
2
}
⁄
_{
5
}
×
^{
4
}
⁄
_{
4
}
)

(1 × 5)/(4 × 5) + (2 × 4)/(5 × 4)

^{
5
}
⁄
_{
20
}
+
^{
8
}
⁄
_{
20
}
=
^{
13
}
⁄
_{
20
}

If we're trying the make the denominators the same, how come we have to multiply the numerator too?

This is a little tricky to understand, but once you get it, it will "click." We don't actually want to change the fraction's value (that wouldn't make any sense). We just want to rewrite it in a way that looks easier to add. So if we want the value to stay the same, we can't multiply it by 4 or 5 or
^{
1
}
⁄
_{
3
}
or any other number. We can only multiply it by 1. But there are lots of fractions that equal 1. In fact any number over itself equals 1. So
^{
2
}
⁄
_{
2
}
, or
^{
5
}
⁄
_{
5
}
, or
^{
99
}
⁄
_{
99
}
all equal 1.

So when we multiply
^{
1
}
⁄
_{
4
}
×
^{
5
}
⁄
_{
5
}
, we are actually multiplying
^{
1
}
⁄
_{
4
}
× 1, the value doesn't change. We can see that too. Because
^{
1
}
⁄
_{
4
}
=
^{
5
}
⁄
_{
20
}

Let's try again with
^{
1
}
⁄
_{
3
}
and
^{
3
}
⁄
_{
8
}
.

^{
1
}
⁄
_{
3
}
+
^{
3
}
⁄
_{
8
}

(
^{
1
}
⁄
_{
3
}
×
^{
8
}
⁄
_{
8
}
) + (
^{
3
}
⁄
_{
8
}
×
^{
3
}
⁄
_{
3
}
)

(1 × 8)/(3 × 8) + (3 × 3)/(8 × 3)

^{
8
}
⁄
_{
24
}
+
^{
9
}
⁄
_{
24
}
=
^{
17
}
⁄
_{
24
}

This process also works for subtraction! Use exactly the same steps, but subtract the numerators at the end instead of adding them.

^{
5
}
⁄
_{
6
}
–
^{
1
}
⁄
_{
2
}

(
^{
5
}
⁄
_{
6
}
×
^{
2
}
⁄
_{
2
}
) – (
^{
1
}
⁄
_{
2
}
×
^{
6
}
⁄
_{
6
}
)

(5 × 2)/(6 × 2) – (1 × 6)/(2 × 6)

^{
10
}
⁄
_{
12
}
–
^{
6
}
⁄
_{
12
}
=
^{
4
}
⁄
_{
12
}
=
^{
1
}
⁄
_{
3
}