It’s Professor Dave, let’s work with fractions.
We’ve learned about addition and subtraction, and we’ve learned about fractions, so why
not learn how to add and subtract fractions?
Now that we know how to find the least common multiple of two numbers, this will be an easy
thing to do.
First let’s look at these two fractions, one eighth and three eighths.
Because these already have the same denominator, all we have to do is add the numerators.
One plus three is four, so we get four eighths.
It’s important to note that when adding fractions, we do not add the denominators.
Just like we would say one apple plus three apples equals four apples, the same logic
applies here.
We can imagine an eighth as a slice of pizza, and one slice plus three slices equals four
slices.
The denominator reports the magnitude of the fraction, so this won’t change as we add
and subtract.
Once we have the sum, we can reduce if applicable.
Four eighths reduces to one half, which makes sense as four slices is half a pizza, so that
will be our final answer.
What if the fractions do not have the same denominator?
In that case, we have to change them so that they do have the same denominator.
To do this, we have to find the least common multiple of the denominators.
Take one third and one fourth.
It’s not immediately obvious what this sum would be, but if we recognize that the least
common multiple of three and four is twelve, then we can make things easier for ourselves.
Multiplying by four over four, one third will become four twelfths, and multiplying by three
over three, one fourth will become three twelfths.
Now we just add them together, and four plus three is seven, so we get seven twelfths.
For subtraction, it’s essentially the same thing.
What if we had one third minus one fourth?
Then we would just change that to be four twelfths minus three twelfths, we just do
four minus three and we are left with one twelfth.
How about a trickier one, one fifth plus two elevenths?
Well the least common multiple of five and eleven is their product, fifty-five, so let’s
multiply by eleven over eleven and five over five, which will change these to eleven over
fifty five and ten over fifty five.
That gives us twenty-one over fifty-five, and that’s all there is to it.
Now try two sevenths minus three fifths.
The least common multiple is thirty-five, so this will become ten over thirty-five minus
twenty-one over thirty five, giving us negative eleven over thirty five.
You may want just a little more practice on your own, so let’s check comprehension.