Adding and Subtracting Fractions

By: Mansi & Keshav

Here are ways you can add and subtract fractions using different methods such as the basic fractions, improper fractions, and mixed fractions. Also make sure to check out the videos for further help!

Subtraction

Basic Fractions


5/8 - 1/4( 8 / 4 = 2)

5/8 - 2/8 (5 - 2 = 3)

3/8


You first have to find the common denominator however you already know that 2 goes into 8. This leaves you with 5/8 - 2/8 so now you have to subtract the numerators which equals to 3 so the final answer is 3/8.


Mixed Fractions


2 9/8 - 5/3 ( 8 x 3 = 24 )

25/8 - 5/3

75/24 - 40/24 (75 - 40 = 35)

35/24 = 1 11/24


First you must convert the mixed fractions to improper fractions and to do that you have to multiply the denominator by the whole number and then add the numerator so you have 25/8 - 5/3. Now you have to find the common denominator by multiplying the two denominators which leaves you with 24. You do the same thing to the top as you did to the bottom meaning however many times the denominator goes to the common denominator you multiply that number with the numerator. Now you are left with 75/24 - 40/24 and you have to subtract the numerators which is 75 - 40 = 35 so the fraction is 35/24. Now you have to convert it back to a mixed number which is 1 11/24 because 34 divided by 24 is 1 with the remainder of 11.


Improper fractions


56/7 - 256/6 (6 x 7 = 42)

336/42 - 256/42 (336 - 256 = 80)

80/42 = 2 2/42

2 2/21


First thing you do is find the common denominator which is 6 x 7 = 42. Now you do the same thing to the top as you did to the bottom meaning however many times the denominator goes to the common denominator you multiply that number with the numerator leaving you with 336/42 - 256/42. Now you have to subtract the numerators which is 336 - 256 = 80. The fraction 80/42 can be simplified to 2 2/42 because 42 goes in 80 twice with a remainder of 2. However 2/42 both can be divided by 2 so the final answer is 2 2/21.

Addition

Basic Fraction


To add a basic fraction (¼+⅓) you first have to make a common denominator. That should be the LCM of both denominators (3/12+4/12). Remember that whatever you do to one number you do to the other number. Finally add the two numerators together. If you can simplify then simplify.


Mixed Fraction


To add a mixed fraction (1 ½ + 2 ¼) you first have to make a common denominator. Next do what you did to the denominator to the the numerator. Add the 2 together (1 2/4 + 2 1/4 =3 3/4) Add the fractions first, then add the whole numbers. If the sum is an improper fraction then convert it to a mixed fraction (2 7/5 -> 3 2/5). Simplify if you can.


Improper Fraction


To add an improper fraction (7/4+3/2) There are two different ways. The first way is to do it like a basic fraction. The second way is to convert it into a mixed fraction by seeing how many times