Adding fractions


This article explores adding fractions. We shall explore what a numerator is and what a denominator is, and lastly look at some examples of adding fractions. When working with fractions you must know what a numerator and denominator is. Before reading this article it maybe useful to have some basic knowledge of fractions. Click here if you want to learn more about fractions

Numerator

A numerator is a number that is used to represent part of a whole. The number can be found above the line or on top in a fraction which shows how many parts are indicated by the denominator are taken. For example: 3 in 3/6 as shown in the diagram above.

Numerator

Denominator

The denominator is the figure below the numerator in a fraction. Very simply the number at the bottom in any fraction.

Denominator

Adding fractions

Addition of fractions is very simple and straight forward. You just have to learn a few simple rules or steps.

When adding like fractions such as the one below, fractions which have the same denominator you simply add the top numerators and then write the fractions with the numerators addition over the denominator of the two fractions.

When a similar denominators are involved. You don't add the denominator you simply add the numerators only.
Example:Work out the following addition;
3/5 + 3/5
Answer:
3/5 + 3/5 = 3 + 3/5 = 6/5
Explanation: This is very basic to work out. We can see that both fractions in the addition have a common or the same denominator. We only need to add the numerator, adding the numerator...
3 + 3 = 6
...therefore...
3/5 + 3/5 = 3 + 3/5 = 6/5

Fractions which have different denominators have to be treated differently. We first have to find the lowest common multiple of the denominators of the fraction. Then use that as the denominator in the final answer. We can see this in the following example.

Example: Work out the following addition;
1/2 + 1/3
Answer:
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Explanation:

The denominators for this example are different. In this example we have to convert the all the fractions in the equation so that they have the same denominators. The numerators will be affected as well since the denominators are end up being affected or change.

The LCM of 2 and 3 is a six, therefore;.

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Notice that the numerators have been affected as well. For each fraction you had to multiply the denominator by the LCM to get the new denominator that is common in both fractions. We must multiply this number as well with the numerator to keep the fraction constant.

1 × 3 / 2 × 3 = 3/6

You do the same for the second fraction. You had to multiply the denominator 2 by 3 to get a 6. Since you multiplied the bottom you had to do the same to the top. The same for;

1 × 2/3 × 2 = 2/6
Notice we multiplied both the bottom and the top by the same number.
Example: Work out the following addition.
3/5 + 2/10
Answer:
3/5 + 2/10 = 6/10 + 2/10 = 6 + 2/10 = 8/10
Explanation: We have method that we used above. We will first find the lowest common multiple (LCM) of 5 and 10. The lowest common multiple of 5 and 10 is 10. Therefore;
3/5 + 2/10 = 6/10 + 2/10 = 6 + 2/10 = 8/10
Note here that;
8/10 = 4/5
Notice also that we had to increase the numerator and denominator of the first fraction which made sure that the fraction was still equivalent to the first fraction i.e;
3 × 2/5 × 2 = 6/10
;
//Comments
This article explores adding fractions. We shall explore what a numerator is and what a denominator is, and lastly look at some examples of adding fractions. When working with fractions you must know what a numerator and denominator is. Before reading this article it maybe useful to have some basic knowledge of fractions. Click here if you want to learn more about fractions

Numerator

A numerator is a number that is used to represent part of a whole. The number can be found above the line or on top in a fraction which shows how many parts are indicated by the denominator are taken. For example: 3 in 3/6 as shown in the diagram above.

Numerator

Denominator

The denominator is the figure below the numerator in a fraction. Very simply the number at the bottom in any fraction.

Denominator

Adding fractions

Addition of fractions is very simple and straight forward. You just have to learn a few simple rules or steps.

When adding like fractions such as the one below, fractions which have the same denominator you simply add the top numerators and then write the fractions with the numerators addition over the denominator of the two fractions.

When a similar denominators are involved. You don't add the denominator you simply add the numerators only.
Example:Work out the following addition;
3/5 + 3/5
Answer:
3/5 + 3/5 = 3 + 3/5 = 6/5
Explanation: This is very basic to work out. We can see that both fractions in the addition have a common or the same denominator. We only need to add the numerator, adding the numerator...
3 + 3 = 6
...therefore...
3/5 + 3/5 = 3 + 3/5 = 6/5

Fractions which have different denominators have to be treated differently. We first have to find the lowest common multiple of the denominators of the fraction. Then use that as the denominator in the final answer. We can see this in the following example.

Example: Work out the following addition;
1/2 + 1/3
Answer:
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Explanation:

The denominators for this example are different. In this example we have to convert the all the fractions in the equation so that they have the same denominators. The numerators will be affected as well since the denominators are end up being affected or change.

The LCM of 2 and 3 is a six, therefore;.

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Notice that the numerators have been affected as well. For each fraction you had to multiply the denominator by the LCM to get the new denominator that is common in both fractions. We must multiply this number as well with the numerator to keep the fraction constant.

1 × 3 / 2 × 3 = 3/6

You do the same for the second fraction. You had to multiply the denominator 2 by 3 to get a 6. Since you multiplied the bottom you had to do the same to the top. The same for;

1 × 2/3 × 2 = 2/6
Notice we multiplied both the bottom and the top by the same number.
Example: Work out the following addition.
3/5 + 2/10
Answer:
3/5 + 2/10 = 6/10 + 2/10 = 6 + 2/10 = 8/10
Explanation: We have method that we used above. We will first find the lowest common multiple (LCM) of 5 and 10. The lowest common multiple of 5 and 10 is 10. Therefore;
3/5 + 2/10 = 6/10 + 2/10 = 6 + 2/10 = 8/10
Note here that;
8/10 = 4/5
Notice also that we had to increase the numerator and denominator of the first fraction which made sure that the fraction was still equivalent to the first fraction i.e;
3 × 2/5 × 2 = 6/10
;
© 2015 All rights reserved.