How to add and subtract fractions

Fractions are often forgotten almost as soon as their learned in school, however their use is essential as adults for cooking, teaching children, measuring, and much, much more. When adding and subtracting fractions, the key is to find a least common denominator, once you have that it's as easy as, well, pie!

Instructions

Difficulty: Easy

Things You’ll Need:

• Paper
• Pencil
• Fractions to play with

1. Adding & subtracting fractions is as easy as pie! The key to adding and subtracting fractions is understanding how they work. The number sat above the line in a fraction is called the numerator. The number beneath is labelled the denominator.
   
   The best way to illustrate this is to imagine a pie. Your numerator is the number of slices you have on your plate. Your denominator is the total number of slices that are in the pie. So if you remove 1 slice out of 4, you have had 1/4 of the pie.
2. If your denominators are the same, it's simple When adding or subtracting, if your denominators are the same, your job is much easier. At the end of the equation, your solution's denominator will be the same. The numerators are your only focus, so add or subtract them as required. So 1/5 + 2/5 = 3/5 or 2/5 -1/5 = 1/5.
   
   In some cases, your numerator will exceed your denominator, so you will need to reduce your fraction into whole numbers. So if your answer was 6/5 you would change that to 1 1/5 or if 10/5 your answer would be 2.
3. Not all fractions are so simple, so in some cases you will need to re-work your denominators before you attempt adding or subtracting. The least common denominator (LCD) of 2 or more denominators is the smallest whole number that is divisible by each of the denominators.
4. To find the LCD, list multiples of each denominator by multiplying by 2,3,4 etc to find the smallest common number that appears in each list.
   
   Example: Suppose we wanted to add: 1/2 + 1/3 + 1/4 + 1/6. We would find the least common denominator as follows...
   
   First list the multiples of each denominator.
   
   Multiples of 2 are 2, 4, 6, 8, 10, 12
   Multiples of 3 are 3, 6, 9, 12, 15, 18, 21...
   Multiples of 4 are 4, 8, 12, 16, 20, 24...
   Multiples of 6 are 6, 12, 18
   
   When you look at the list of multiples, you can see that 12 is the smallest number that appears in each list.
   
   Therefore, the least common denominator of 1/2, 1/3, 1/4 and 1/6 is 12.
5. Adding fractions with larger numbers in the denominators can get pretty complicated, so another method for finding the lowest common denominator is:
   
   Work out the number of times each prime number appears when you factor numbers, so...
   
   2 is a prime number, so 2
   3 is a prime number, so 3
   4 is 2 x 2, so 2, 2
   6 is 3 x 2, so 3, 2
   
   Count the number of times each prime number appears in each of the factorizations...
   
   The count of primes in 2 is one 2
   The count of primes in 3 is one 3
   The count of primes in 4 is two 2s
   The count of primes in 6 is one 2 and one 3
   
   Since we now know the count of each prime number, simply write down that prime number as many times as you counted for it above. So, we have: the largest count of 2's is 2 and the largest count of 3's is one.
   
   The least common denominator is the product of all the prime numbers written down. So 2 x 2 x 3 = 12.
6. Once you have your LCD, you will need to re-work out your numerators to suit your new LCD. Re-write a fraction as an equivalent fraction using the least common denominator by:
   
   Divide your least common denominator by the denominator of the fraction.
   
   For 1/2, you would work out 12 divided by 2 = 6
   For 1/3, you would work out 12 divided by 3 = 4
   For 1/4, you would work out 12 divided by 4 = 3
   For 1/6, you would work out 12 divided by 6 = 2
   
   Multiple the answer times the numerator of the fraction.
   
   1/2 = 6/12
   1/3 = 4/12
   1/4 = 3/12
   1/6 = 2/12
7. Now, you can pull it all together! So it looks like:
   
   6/12 + 4/12 + 3/12 + 2/12 = 15/12 which needs reducing to 1 3/12. Your 3/12 can be reduced to 1/4, so your final answer is 1 1/4.