Tutorials > Fractions
Introduction to Fractions
A fraction is a numerical quantity that is not whole. They are often encountered in weights and measurements. Examples include one-half (), a third (), and one-quarter ().
A fraction is made up of two values: a numerator and a denominator. The numerator is the top value of the fraction and indicates how many pieces of a whole you have. The denominator is the bottom value of the fraction and indicates how many pieces make up the whole.
In the case of one-half (), 2 pieces makes a whole (the denominator), and you have 1 piece (the numerator). In other words, you have 1 of 2 pieces, commonly referred to as one-half.
Simplifying Fractions
A fraction is simplified (or reduced) when there is no number that can be divided into both the numerator and denominator.
For example, in the fraction (two-quarters) the numerator and the denominator can both be divided by 2, making the simplified fraction (one-half).
In the example the top and the bottom values can both be divided by 5, making the simplified fraction .
Adding & Subtracting Fractions
To add or subtract fractions:
- First, find their least common denominator.
- Second, add (or subtract) the the numerator.
- Finally, simplify the answer.
In the example of + = , because the fractions and already have a common denominator (6), we simply add the numerators 1 and 2 together (making 3) and place the result over the common denominator (6), giving us . Finally, we simplify our answer of , giving us a final answer of .
In the example of + = , the denominators are different. So we must first find the least common denominator. We find the number 10 can be divided by both 5 and 2, so 10 is our least common denominator. Now we adjust the numerator in both fractions to their new common denominator. In the case of we know 5 goes into 10 2 times, so we multiply 2 by 2, giving us . In the case of we know 2 goes into 10 5 times, so we multiply 1 by 5, giving us . Now our problem becomes + . Both of these fractions have a common denominator of 10, so now we add the numerators 4 and 5 together (giving us 9) and place the answer over our common denominator of 10, giving us an answer of . Since there is no number that factors into both 9 and 10, we don't need to simplify our answer.
Multiplying Fractions
To multiply fractions:
- First, multiply the numerators together.
- Second, multiply the denominators together.
- Finally, simplify the answer.
For example: ⨯ = which simplifies to .
Dividing Fractions
To divide fractions:
- First, get the reciprocal of one of the fraction, by flipping it.
- Second, multiply the numerators together.
- Third, multiply the denominators together.
- Finally, simplify the answer.
For example: ÷ = ⨯ =