How do you add algebraic fractions?

Answer 1

Let me preface this with the statement that it is in fact difficult, and difficult for a reason. Adding fractions is NOT like adding integers. So expect to read this a few times, understanding a little bit more each time.

Start with an understanding of the relationship between fractions and division. 1 [divided by] 2 is not commutative; that is, 1 [divided by] 2 is NOT equal to 2 [divided by] 1. However, we can use the multiplicative inverse (the inverse relationship between multiplication and division) to turn division into multiplication:

1 [divided by] 2 = 1 x 1/2.

Now 1 x 1/2 is commutative, that is:

1 x 1/2 = 1/2 x 1.

Similarly, division is not associative, but multiplication of fractions is. This establishes an understanding of fractions as the multiplicative inverse form of division - a form of division that follows the rules (commutative, associative, distributive) of multiplication.

Note that when we multiply fractions, we are multiplying with multiplicative inverses, and can commute and associate to multiply numerators and multiply denominators:

2/3 x 3/4 = (2x3)/(3x4) (this step can be expanded if it aids understanding)

Next, when adding fractions, we have a multiplicative inverse embedded in the first fraction, followed by an explicit addition, followed by another multiplicative inverse embedded in the second fraction. What this means is that we effectively have mixed operations of both multiplication (in inverse form embedded in the fractions) and addition. We therefore MUST use a strategy related to the distributive property (which includes reverse distribution, known as factoring). The denominator (multiplicative inverse) is what needs to be factored, but it must be common to be factored so we have to take care of that first.

So how do we get a common denominator? To do this we need to also understand the multiplicative identity - the ONLY thing we can multiply something by without changing it's value (i.e. being wrong) is 1. But we can write 1 as a fraction with the same number in the numerator and denominator, such as 1 = 7/7. Now, adding fractions may look like this:

2/3 + 3/4 = 1x(2/3) + (3/4)x1 (multiply both sides by 1)

= (4/4)x(2/3) + (3/4)x(3/3) (write 1 as 4/4 on the left and 3/3 on the right)

At this point, either side of the '+' contains a multiplication of fractions, which we can multiply across numerators and multiply across denominators (as above), as long as we don't involve the '+' yet:

= (4x2)/(4x3) + (3x3)/(4x3)

=8/12 + 9/12

NOW we can factor the common denominator:

=(8 + 9)/12

=17/12

Unfortunately the font of the text interface is not conducive to math.

Answer 2

Okay, for example, if I were to try and add 3/8 and 2/4.

The first step I would do is make sure the denominators are the same, otherwise you'll have to make them the same.

You can multiply 2/4 by 2 so then it turns into 4/8.

Add 3/8 and 4/8 and you get 7/8.

Another example is that if you were to have 2/3 and 3/4. You would have to times both fractions by a number to make the denominators the same.

So I just have to times 2/3 by 4 and 3/4 by 3. That would equal 8/12 and 9/12. Add it together and you get 1 and 5 over 12.

Answer 3

In order to divide fractions there is a method called the "Kiss and Flip". Basically, two fractions divided by one another is the same thing as one fraction multiplied by the inverse of the second. We will use the fractions 1/5 and 1/4 as our examples...

A) 1/5 / 1/4(these are your two fractions)

B) 1/5 / 1/4 (the fractions "Kiss" a.k.a. come together in one equation)

C) 1/5 X 4/1 (and the second fraction "flips". When the second fraction flips the division sign becomes a multiplication sign)

D) 1/5 x 4/1 = 4/5 (at this point you multiply the numerators straight across and then the denominators. This is your answer!)

"When asked to multiply fractions don't ask why, just flip the second and multiply!"

Answer 4

1. Build each fraction so that both denominators are equal.

   Remember, when adding fractions, the denominators must be equal. So we must complete this step first. What this really means is that you must find what is called a Common Denominator. So you solve this by using what's called the Least Common Denominator (LCD). In either case you will build each fraction into an equivalent fraction.

2. Re-write each equivalent fraction using this new denominator

3. Now you can add the numerators, and keep the denominator of the equivalent fractions.

4. Re-write your answer as a simplified or reduced fraction, if needed.

I hope this helps!

Answer 5

First, you find the greatest common factor of the denominators.

Second, you multiply the top by what you had to multiply on the bottom.

Finally, you add the numerators together, NOT the denominators they stay the same, and then you would get your answer.

Answer 6

You have to make a common denominator like if your fractions were 1/4 + 3/8 you make it 2/8 (which is 1/4) = 3/8 which gives you 5/8.

Answer 7

with different denominators, just get their lcd and that will serve as they're denominator.

Answer 8

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