About Fractions And Addition And Subtraction

A fraction is a number that can represent part of a whole

. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (, , , etc.).

Source Wikipedia.

Addition and Subtraction:

The following examples show algebra variables fractions for addition and subtraction.

Addition of Variables Fractions:

The formula to find the fractions for addition is a/b+c/d = (ad+bc)/(bd) .

Solve the algebra fractions: (xy)/3+(xy)/12

Solution:

Cross multiply the numerator and multiply denominators

= (xy xx 12+3 xx xy)/(3 xx 12)

Add the numerator

= (12xy+3xy)/36

= (15xy)/36

By reducing this fraction we get the answers (5xy)/12 .

Solve the algebra fractions: (10z^2)/2+(5y)/(2x)

Solution:

Cross multiply the numerator and multiply denominators

= (10z^2 xx 2x+2 xx 5y)/(2 xx 2x)

Add the numerator

= (20xz^2+10y)/(4x)

= (30xyz^2)/(4x)

By reducing this fraction we get the answers (15yz^2)/2 .

Subtraction of Variables Fractions:

The formula to find the subtraction of fraction is a/b - c/d = (ad-bc)/(bd) .

Solve the algebra fractions: (zy)/3-(2yz)/12

Solution:

Cross multiply the numerator and multiply denominators

= (zy xx 12-3 xx 2yz)/(3 xx 12)

Subtract the numerator

= (12yz-6yz)/36

= (6yz)/36

By reducing this fraction we get the answers (yz)/6 .

Solve the algebra fractions: (10x^2)/2-(5x^2)/2

Solution:

Cross multiply the numerator and multiply denominators

= (10x^2 xx 2-2 xx 5x^2)/(2 xx 2)

Subtract the numerator

= (20x^2-10x^2)/4

= (10x^2)/4

By reducing this fraction we get the answers (5x^2)/2 .

Multiplication and Division:

The following examples show algebra variables fractions for multiplication and division.

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Multiplication of Variables Fractions:

The formula to find the fractions for multiplying is a/b xx c/d = (ac)/(bd) .

Solve the algebra fractions: (2xy)/(8z) xx (xy)/9

Solution:

Multiply the numerator and denominators

= (2xy xx xy)/(8z xx 9)

= (2x^2y^2)/(72z)

By reducing this fraction we get the answers (x^2y^2)/(36z) .

Solve the algebra fractions: (6a)/2 xx (7b)/2

Solution:

Multiply the numerator and denominators

= (6a xx 7b)/(2 xx 2)

= (42ab)/4

By reducing this fraction we get the answers (21ab)/2 .

Division of Variables Fractions:

The formula to find the fractions for dividing is a/b c/d = (ad)/(bc) .

Solve the algebra fractions: (3y)/(5y) / (8x)/(2x)

Solution:

Take the reciprocal of the second term and to do the multiplication process

= (3y)/(5y) xx (2x)/(8x)

= (3y xx 2x)/(5y xx 8x)

= (6xy)/(40xy)

By reducing this fraction we get the answers 3/20 .

Solve the algebra fractions: (4a)/(6b) / (7c)/(3d)

Solution:

Take the reciprocal of the second term and to do the multiplication process

= (4a)/(6b) xx (3d)/(7c)

= (4a xx 3d)/(6b xx 7c)

= (12ad)/(42bc)

By reducing this fraction we get the answers (6ad)/(21bc) .

by: mathqa

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