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Fractions Addition: Simple Fractions, Least Common Denominator

On this page and the next two pages, we will add fractions that, at the start, do not have a common denominator.

To add two fractions, we:
1) Make sure that each fraction has the same denominator: the least common denominator.
2) Add only the numerator of each fraction.
3) After adding, write the answer over the denominator.

Our first example is 1/2 + 1/4:

1) The denominators are not the same.

To find the least common denominator, we use what we learned in the Fractions Fundamentals unit to find the least common multiple of 2 and 4:

4: 4, 8, 16
2: 2, 4

The least common multiple of the number 2 the number 4 is 4. The denominator of each fraction must be 4.

So, we must convert 1/2 to a fraction that has a denominator of 4.

We learned in Basic Multiplication that multiplying any number by 1 still gives us the number. We learned in Fractions Introduction that a number written over itself as a fraction is 1 (2/2, 3/3/ 4/4, and so on). Multiplying the numerator of a fraction by a number and the denominator by the same number gives us a fraction that looks different but is the same.

1/2 is the same as 2/4:

1
2
2

×

=

2
2
4

1 / 2
=
2 / 4
=
 plus     White Box   White Box   White Box  equals     White Box   White Box   White Box

We have changed 1/2 + 1/4 to 2/4 + 1/4.

Now that each fraction has the same denominator, all we do is add the numerators and get our answer:

2) 2 + 1 = 3

3) 3 over 4 is 3/4.

2 / 4
+
1 / 4
=
3 / 4
+
=
 plus     White Box   White Box   White Box  equals     White Box   White Box   White Box

The next example is 1/3 + 4/9:
1) The denominators are not the same.

To find the least common denominator, we use what we learned in the Fractions Fundamentals unit to find the least common multiple of 3 and 9:
9: 9, 18, 27
3: 3, 6, 9

The least common multiple of the number 3 the number 9 is 9. The denominator of each fraction must be 9.

So, we must convert 1/3 to a fraction that has a denominator of 9.

We learned in Basic Multiplication that multiplying any number by 1 still gives us the number. We learned in Fractions Introduction that a number written over itself as a fraction is 1 (2/2, 3/3/ 4/4, and so on). Multiplying the numerator of a fraction by a number and the denominator by the same number gives us a fraction that looks different but is the same.

1/3 is the same as 3/9:

1
3
3

×

=

3
3
9

1 / 3
=
3 / 9
=
 plus     White Box   White Box  equals     White Box   White Box   White Box   White Box   White Box   White Box   White Box   White Box

We have changed 1/3 + 4/9 to 3/9 + 4/9.

Now that each fraction has the same denominator, all we do is add the numerators and get our answer:
2) 3 + 4 = 7
3) 7 over 9 is 7/9.

3 / 9
+
4 / 9
=
7 / 9
+
=
 plus     White Box   White Box   White Box   White Box   White Box   White Box   White Box   White Box  equals     White Box   White Box   White Box   White Box   White Box   White Box   White Box   White Box

Sometimes you will get an answer (sum) that's 1 or greater than 1. An example is 3/5 + 7/10:
1) The denominators are not the same.

To find the least common denominator, we use what we learned in the Fractions Fundamentals unit to find the least common multiple of 5 and 10:
10: 10, 20, 30
5: 5, 10

The least common multiple of the number 5 the number 10 is 10. The denominator of each fraction must be 10.

So, we must convert 3/5 to a fraction that has a denominator of 10.

We learned in Basic Multiplication that multiplying any number by 1 still gives us the number. We learned in Fractions Introduction that a number written over itself as a fraction is 1 (2/2, 3/3/ 4/4, and so on). Multiplying the numerator of a fraction by a number and the denominator by the same number gives us a fraction that looks different but is the same.

3/5 is the same as 6/10:

3
2
6

×

=

5
2
10

3 / 5
=
6 / 10
=
 plus     White Box   White Box   White Box   White Box  equals     White Box   White Box   White Box   White Box   White Box   White Box   White Box   White Box   White Box

We have changed 3/5 + 7/10 to 6/10 + 7/10.

Now that each fraction has the same denominator, all we do is add the numerators and get our answer:
2) 6 + 7 = 13
3) 13 over 10 is 13/10.

Because you are just starting to learn how to add fractions, FoxyMath will accept 13/10 as the correct answer. However, you should be able to use what you learned in Fractions Introduction to convert this improper fraction to the mixed fraction 1 3/10. If you don't understand this then please review Fractions Introduction.

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