Rakiya A.

asked • 04/02/14# how do i add subtract multiply and divide fractions

how do i add subtract multiply and divide fractions

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## 2 Answers By Expert Tutors

IBRAHIM A. answered • 04/02/14

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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.

Steve S. answered • 04/02/14

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Tutoring in Precalculus, Trig, and Differential Calculus

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.

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Philip P.

04/02/14