Fractions Subtraction: Simple Fractions, Least Common Denominator

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

To subtract two fractions, we:
1) Make sure that each fraction has the same denominator: the least common denominator.
2) Subtract only the numerator of each fraction.
3) After subtracting, 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 subtract the numerators and get our answer:

2) 2 - 1 = 1

3) 1 over 4 is 1/4.

2 / 4
-

1 / 4
=

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

The next example is 7/9 - 1/3:
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 7/9 - 1/3 to 7/9 - 3/9.

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

7 / 9
-
3 / 9
=
4 / 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