We have two options here. We can manipulate the answers to work backwards and find a common denominator. This involves simply subtracting or adding two fractions. We can also try to rewrite the numerator by adding and subtracting the value . This serves the purpose of creating a sum in the numerator than can be split into  and . This gives us one of the factors in the denominator in each numerator. When we separate or decompose the fraction, we can divide out by the common factor to re-express this as the difference of two rational expressions. 

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number.

3/727

Reciprocal 727/3

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number).  The opposite reciprocal takes the negative of that number.

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number).  The negative reciprocal takes the negative of that number.

Reciprocal 

Negative Reciprocal 

First, we must solve the equation for y to determine the slope:  y = (2/4)x + 7/4

By looking at the coefficient in front of x, we know that the slope of this line has a value of 1/2. To find the slope of any line perpendicular to this one, we take the negative reciprocal of it:

slope = m , perpendicular slope = –1/m

slope = 1/2 , perpendicular slope = –2

The reciprocal is defined such that a faction times its recprocal is 1. For you this just means turn the fraction upside down, ie the numerator is the denominator and vice versa. 

The reciprocal of a fraction is simply exchanging the denominator and numerator of a fraction.

You can double check that it works by making sure the product of a fraction and its reciprocal is 1. 

LCM = least common multiple = 2 x 2 x 3 x 5 = 60

GCF = greatest common factor = 3

Prime factor each number

3 = 3 x 1

12 = 3 x 4 = 3 x 2 x 2

30 = 5 x 6 = 5 x 2 x 3

LCM – GCF = 60 – 3 = 57

  In order to find the least common denominator, you must find the least common multiple of all three numbers.  For this problem, the least common multiple of all three numbers is 16 (divisible by 2, 4, 8 , 1, and 16). 

The lowest common denominator looks at the denominator (bottom number) of all of the fractions and finds the smallest number that all of the numbers divide into.

Of those numbers the largest is 18.  First check to see if all the numbers divide into 18.  3 and 6 do, but 4 and 12 do not.  Multiply 18 by 2 and get 36.  Check to see if all the numbers divide into 36.  3 and 6 still do.  4 and 12 do now. therefore. 36 is the lowest common denominator.