how do i add subtract multiply and divide fractions

Question

how do i add subtract multiply and divide fractions

Answer 1

fraction is added in this form

 

a/b  + c/d 

 

first find the l c m which is denominators from both fraction i.e  b*d = bd

 

so multiply each fraction by the lcm

 

so we have 

 

a (bd)/b  + c (bd)/d

 

= (ad  + cd) / bd

 

So for instance,

 

2/3  + 4/2

 

lcm = 3*2 = 6

 

= (6 (2/3)  + 6 (4/2)) / 6   [ 3 goes in 6 2 times, and 2 goes in 6 3 times]

 

((2)(2) + (3)(4))/ 6

 

(4 + 12) / 6 = 16/6 0r 2 4/6

 

 

Subtraction of fraction

 

 

3/4  - 4/8

 

l c m = 8 because both 4 and 8 goes in 8 unlike the previous example where 2 cannot go in 3 without a reminder.

 

((8*(3/4) - 8* (4/8)) / 8

 

((2)(3) - (1)(4))/ 8

 

(6 - 4) / 8 =  2/8 = 1/4

 

 

Multiplication of fraction 

 

5/2 * 1/3

 

simply multiply them out

 

(5*1)/ (2*3) = 5/6

 

Another example

 

2/4 * 3/6

 

you can do this in different ways:

 

2/4 * 3/6

 

= 1/2 * 1/2 = 1/4    or  (2*3)/ (4*6) = 6/24 = 1/4

 

 

 

Division of fraction 

 

3/4  divide by 6/2

 

We normally introduce reciprocal rule to this situation

 

by changing 6/2 into multiplication form as  1 divide by 6/2 = 2/6

 

now we have:

3/4 * 2/6

 

(3*2) / (4 * 6) =  6/24 = 1/4

 

I hope this helps.

 

Answer 2

Assuming no denominators are 0:

 

(a/b)*(c/d) = (a*c)/(b*d), where * means multiply.

 

To add/subtract we need same denominator:

 

(a/b)±(c/d) = (a/b)*(d/d)±(c/d)*(b/b)

= ((a*d)/(b*d))±((b*c)/(b*d))

= ((a*d)±(b*c))/(b*d)

 

To divide first fraction by 2nd fraction:

 

(a/b)/(c/d) = ((a/b)/(c/d))*((d/c)/(d/c))

= (((ad)/(bc))/((cd)/(cd))) = (ad)/(bc) = (a/b)*(d/c);

 

multiply first fraction by reciprocal of 2nd.