Adding fractions and subtracting fractions
Introduction to adding and subtracting fractions
It may seem difficult learning how to add fractions and how to subtract fractions at first, but once you get the hang of it, you will be amazed at how easy it is. Firstly you must know that a fraction is made up of a numerator and a denominator. The numerator tells the amount of parts used or remaining out of the whole, and the denominator tells the amount of equal parts an object is divided into.
There are three types of fractions:
- proper fractions - These are fractions where the numerator is smaller than the denominator. Eg 1/3.
- improper fractions - These are fractions whose numerators are larger than denominators. Eg 10/5
- mixed fractions or mixed numbers - These fractions/numbers consist of a whole number accompanied by a fraction.
Adding fractions and subtracting fractions
Just like comparing fractions, adding fractions or subtracting fractions, the denominators must always be the same. Fifths can be subtracted from fiths and tenths can be subtracted from tenths, but fifths cannot be added or subtracted from tenths without doing some former calculations. The denominators must be changed first.
If the fractions to be addded or subtracted have the same denominator, then work with the numerators only. When I say work with the numerators only I mean add or subtract the numerator only.
E.g:5/11 + 2/11
Add the 5 to 2 and put the result 7 as the numerator, therefore 5/11 + 2/11 = 7/11.
E.g: 6/12 - 1/12
Subtract 1 from 6 and put the result 5 as the numerator, the answer 5/12.
Adding three fractions
How to add fractions with different denominator
With add fractions with different denominators, you must change the denominators to make them the same. To do so, you find something called, 'the lowest common multiple' of the denominators. To do this, you list about the first 10- 20 multiples of the denominators and then pick out the lowest common one. Multiples are the results you get when you multiply a given number by any other number. For example, the multiples of 2 are 2, 4, 6, 8, 10, etc. You get the multiples by multiplying 2 by 1, 2 by 2, 2 by 3, 2 by 4 and 2 by 5 respectively. After picking the lowest common multiply, this is the common denominator which you would use. Now you have to change the fractions to fractions which have denominators of the lowest common multiple you got, by dividing the lowest common multiple by the old denominator and then multiply the old numerator by the result you got.
Step 1: List the multiples of the denominators
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 etc
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 etc
Step 2: Find the lowest common.
Step 3: Change the fractions into ones with denominators of 15.
To change 1/5 to a fraction with a denomiator of 15. Divide 15 by 5. Then multiply 1 by the result, which is 3. 1/5 = 3/15. To change 2/3 to a fraction with a denominator of 15. Divide 15 by 3 = 5, then multiply by 2, the old denomiator.
Now add 3/15 and 10/15 = 13/15
Subtracting fraction with different denomination
Follow the same process to subtract fractions with different, first change the fractions to fractions with common denomiators then subtract. Its as easy as that.
For example if asked to subtract 3/4 form 10/12
Step 1- List the multiples of the denominators, this would be multiples of 4 and multiples of 12.
Multiples of 4 - 4, 8, 12, 16, 18
Multiples of 12- 12, 24, 36, 48, 60
Step 2- Pick out the lowest common multiple
This would be 12.
Step 3- Change the fractions into fractions with the denominator of 12
To change 3/4 to a fraction with a denominator of 12. Devide 12 by 4 = 3. Then mutiply 3 from the 3/4 by 3 (result from dividing 12 by 3). The other fraction already has a denominator of 12. There you can do your calculation.So the final answer would be 10/12 -9/12 = 1/12.
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Adding mixed fractions and subtracting mixed fraction
Okay, to add mixed fractions (mixed numbers) you separate the addition of the whole numbers from the addition of the fraction. Add the whole number together first and then add the fractions.
For example: 1 1/3 + 2 1/3
The result is 3 2/3.
Do the samething to subtact mixed fractions. Subtract the whole numbers first then the fractions after.