How To Find Common Denominator Fractions

How to Find Common Denominators

If you are trying to
add or subtract fractions with unlike denominators, yous've come to the
right place! In order to add or decrease fractions, we accept to have common denominators.
Sometimes, though, you lot're given a problem that looks similar this:

Those are definitely non common denominators! In order to get the denominators the
same, follow these steps:

1. List multiples of both numbers. Start by listing 4 multiples for each number.

4: iv, eight, 12, xvi
2: 2, 4, half-dozen, 8

2. Expect at the lists you've made. Underline whatsoever numbers that are on both lists.

iv: 4, viii, 12, 16
2: 2, iv, half dozen, 8

three. Look for the smallest underlined number (known as the least common multiple,
or LCM). This is your common denominator.

Common denominator: four

4. Multiply the numerator and denominator by the factor that information technology would accept to become
to your common denominator…like this:

and this:

For this multiplication, the first number you use is the fraction y'all are irresolute,
and the 2d number comes from the respond to this question: "what number would
I multiply the denominator by to get to the common denominator?" For the beginning fraction,
your denominator is already your mutual denominator, and so yous but multiply it by
i/1. Nosotros multiply by i (or a fraction equaling ane) considering this does not modify
the amount of the fraction, it just changes the name of the fraction. For the second
fraction, you would multiply by 2/2 because your denominator (2) needs to be multiplied
by 2 to reach the common denominator of 4.

Now that y'all accept mutual denominators, you lot tin can but add the fractions together.
Remember, when you lot add together fractions, the numerators (top numbers) add and the denominators
(bottom numbers) stay the aforementioned!

Your new problem would look like this:

In one case you lot add them, y'all should get v/4

If yous know how to simplify this (by changing it into a mixed number), please do
and so. If not, please review how to deal with
improper fractions.

Desire i more practice trouble with finding mutual denominators? This time, nosotros'll
practice a subtraction problem. Hither information technology is:

Follow the same steps. They are:

1. Listing the multiples for each number.

iii: 3, 6, 9, 12
4: 4, eight, 12, 16

two. Expect at the lists you've made. Underline any numbers that appear on both lists.

3: 3, half-dozen, nine, 12
4: four, 8, 12, 16

3. Expect for the smallest underlined number (least common multiple, or LCM). This
is your common denominator.

Common denominator: 12.

4. Multiply the numerator and denominator of each fraction by the cistron that it
would take to get to your common denominator. Recall about it like this:

What do yous multiply by three to become to 12? Well, nosotros know that 3 x iv = 12, so we know
we need to multiply by four:

Now, we exercise the same thing with 1/4 to get:

What exercise you multiply 4 past to get to 12? Well, we know that 4 x 3 = 12, so we know
nosotros're going to multiply by 3. That looks like this:

Now we have both of our fractions with common denominators, so we tin can subtract!
Call back, in a subtraction problem, the numerators subtract only the denominators
stay the same. Information technology looks similar this: