Fractions
FRACTION ADDITION

Adding fractions with a common denominator
Adding mixed fractions with a common denominator
Adding fractions that do not have a common denominator
Addition word problem
Go to the Fraction home page
contact me

Note: Click on any of the word(s) in red type to see a definition.


ADDITION

You're creating a cold cut platter. You bought 3 1/6 lb. corned beef, 4 1/4 lb. roast beef, and 1 1/3 lb. turkey. How much cold cuts do you actually have? (No, the correct answer in not "enough").

In order to do this calculation, we first have to be able to add fractions. Unfortunately when adding fractions, like the three fractions above, that pesky denominator comes into play. In order to add fractions, they must have the same denominator.

We'll start off with fractions that have a common denominator, then we'll see what to do when they have different denominators.

When you do have a common denominator, your job is easy. All you have to do is add the numerators together.

So if I had to add 3/8 and 1/8 together, all I would have to do is add 3 and 1 together. I could write this as: 3/8+1/8=(3+1)/8=4/8.
However, I'm not quite finished. 4/8 is not in lowest terms. The GCF of 4 and 8 is 4. So:
3/8+1/8=4/8=(1*4)/(2*4)=1/2.
How about if I was assigned 7/10 + 9/10?
7/10+9/10=16/10.
but 16/10 is an improper fraction, and we know from studying how to change improper fractions into mixed fractions that 16/10=1 6/10.
Thus 7/10+9/10=16/10=1 6/10. But, I'm still not finished. Why? Because 6/10 is not in lowest terms. 6/10=3/5. (if you want to review reducing fractions click here.)
Thus 7/10+9/10=16/10=1 6/10=1 3/5.
I'll take a break here for you to try out your new expertese at adding fractions with common denominators. Then we'll turn our attention to adding mixed fractions with a common denominator.
Exercise 1
2/5 + 4/5
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 2
1/10 + 3/10
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 3
8/25 + 22/25
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 4
2/15 + 8/15
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 5
3/8 + 7/8
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next section.

Go to the top of this page
Go to the Fraction home page
Go to the next section

Okay, you can add regular fractions provided they have a common denominator.
Now I'm going to extend your knowledge to include mixed fractions..

All you have to do here is add the two whole number parts together, and add the fraction parts together.
So if example1 above were 1 2/5 + 3 4/5 then add the 1 and 3 together to get 4, and the 2/5 and 4/5 together to get 6/5.
1 2/5 + 3 4/5 = 4 6/5. But 6/5 is an improper fraction equal to 1 1/5. What do we do now?
Well 4 6/5 =4 + 6/5 =4 + 1 + 1/5=5 1/5.
1 2/5 + 3 4/5 = 4 6/5 = 5 1/5.
Okay that's fine but what if I have one mixed fraction and one regular one. We'll see that situation in this next example
1 4/9 + 2/9
Now it's assumed when we write 2/9 that there is no whole number part to this fraction, thus the whole number part of our sum is 0 (the whole number part from 2/9 is zero) plus 1 (the whole number part from 1 4/9).
The whole number part of the sum is 1+0=1
Adding the fraction parts 4/9 + 2/9 = 6/9. However 6/9 is not in lowest terms. 6/9=2/3
4/9 + 2/9 = 6/9 = 2/3
Putting it all together
1 4/9 + 2/9 = 1 2/3
Here's another set of examples for you to practice on. Then we'll get to the real meat of the matter when we confront fractions with different denominators.
Exercise 1
1 5/12 + 11/12
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 2
2 1/10 + 5 7/10
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 3
1 8/17 + 2 12/17
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next section.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 4
5 1/7 + 2 3/7
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 5
2 4/5 + 8 3/5
Step 1: Add the fractions
Step 2:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 3
Step 3:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go to the next section

Now at last, the hard stuff!
What do you do when you have to add fractions with different denominators, other than scream and yell for help?
The answer is to force the fractions to have the same denominator, and not just any denominator, but the smallest number that the original denominators would divide.
The term for this is The Lowest Common Denominator (LCD), and in the next paragraph we'll see how to arrive at the LCD, and how to change our fractions into ones with the LCD

Rather than explain the LCD, and then give an example, this will be more clear if I do the oppisite.

I have to add the fractions 5/6 and 3/8. The denominators are 6 and 8. Now I need to find the smallest number that both 6 and 8 divide.
Well let's look at the higher of the two numbers, 8.
Now, obviously 8 divides itself, but 6 does not divide 8. Therefore 8 won't work as our LCD.
Okay, let's multiply 8 by 2 and try again. 8*2=16. Now, 8 divides 16, but 6 does not divide 16. Therefore 16 won't work as our LCD.
Okay, let's multiply 8 by 3 and try again. 8*3=24. Now, 8 divides 24, and 6 divides 24 as well. Therefore 24 is the LCD in this example.
Now in the section on changing a fraction's denominator we examined how to increase a denominator to a multiple of itself.
Using this information and the LCD we could conclude that:
24/6=4 thus 5/6=5/6 * 4/4 = (5*4)/24 = 20/24
and
24/8=3 thus 3/8=3/8 * 3/3 = (3*3)/24 = 9/24
thus 5/6 + 3/8 = 20/24 + 9/24 = 29/24.
Now, 29/24 = 1 5/24, which is already in lowest terms.
Conclusion: 5/6 + 3/8 = 20/24 + 9/24 = 29/24 = 1 5/24.
Now that wasn't too bad, was it? That's all there is to it. Take the highest denominator and keep increasing it, until you have a number all of the denominators can divide. Then using the technique we used in the "changing a fraction's denominator" section, you can change the fractions to ones with a common denominator. If you're still in the dark, pay attention, because I'll show this to you one more time, then you can show me what you learned.
1 2/3 + 2/15
The denominators are now 3 and 15, the hightest of which is 15
15 obviously divides itself, and 3 divides 15, thus 15 is the LCD
15/3=5 so 2/3 = 2/3 * 5/5 = (2*5)/15 = 10/15
1 2/3 = 1 10/15
2/15 = 2/15
1 2/3 + 2/15 = 1 10/15 + 2/15 = 1 12/15
However 12/15 is not in lowest terms. 12/15 = 4/5
1 2/3 + 2/15 = 1 10/15 + 2/15 = 1 12/15 = 1 4/5
1 2/3 + 2/15 = 1 4/5
Now here are ten exercises for you to try. Then we'll answer the cold cut platter question posed at the beginning of this section
Exercise 1
3 1/14 + 2 2/7
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
3 1/14 = 2 2/7 =
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 2
7/20 + 5/6
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
7/20= 5/6=
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 3
1 2/45 + 7/15
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
7/15 = 1 2/45 =
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 4
1 4/11 + 2/3
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
1 4/11 = 2/3 =
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 5
4 5/7 + 8/21
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
4 5/7 = 8/21=
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 6
5 1/8 + 3/4
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
5 1/8 = 3/4 =
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 7
2 1/18 + 3/4
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
2 1/18 = 3/4=
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 8
2 1/3 + 2 5/9
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
2 1/3 = 2 5/9 =
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 9
8 1/14 + 3 2/7
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
8 1/14 = 3 2/7=
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go on to the next problem.
Go to the next section

Exercise 10
4 1/10 + 2/3
Step 1: Find the LCD
Step 2: Change both fractions to ones with the LCD
4 1/10 = 2/3 =
Step 3: Add the fractions
Step 4:If this is an improper fraction, change it to a mixed fraction. If your answer was not an improper fraction skip this step and go directly to step 5
Step 5:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

Go to the top of this page
Go to the Fraction home page
Go to the next section

Now back to the cold cut problem.

You're creating a cold cut platter. You bought 3 1/6 lb. corned beef, 4 1/4 lb. roast beef, and 1 1/3 lb. turkey. How much cold cuts do you actually have?

To solve this, we have to add 3 1/6, 4 1/4, and 1 1/3.
3 1/6 + 4 1/4 + 1 1/3.
the three denominators are 6, 4, and 3 ; So we need to find a LCD. the largest of the three denominators is 6.
6 divides 6, 3 divides 6, but 4 does not divide 6, so let's go on
6*2=12. 6 divides 12, 3 divides 12, and 4 divides 12. 12 is the LCD
12/6=2 so 3 1/6 = 3 2/12
12/4=3 so 4 1/4 = 4 3/12
12/3=4 so 1 1/3 = 1 4/12
3 1/4 + 4 1/8 + 1 1/3= 3 2/12 + 4 3/12 + 1 4/12= 8 9/12 = 8 3/4.
The total amount of meat bought is 8 3/4 lbs.

Go to the top of this page
Go to the Fraction home page
Go to the next section