Question

When adding or subtracting two fractions with denominators that are not equal, what is the first step you take?

What would you do if you didn’t know what the values of the denominators were, such as when there are variables in the denominators? For example, what denominator would you use if you were adding 1/a and 1/b ? How would your new denominator affect the numerators?

Can you come up with denominators that contain variables and aren’t equal that would require you to change only one denominator? Explain.

Answer 1

For the first question, the first step to take when adding or subtracting two fractions with denominators that are not equal is to determine their least common denominator (LCD). This is the lowest number that is a multiple of both denominators.

For the second question, if only variables are given, you can simply multiply the two variables to obtain the LCD. However, take note that you should multiply the numerator and the denominator with the variable that would result to the same LCD for both terms. For example,

(1/a)*(b/b) + (1/b)(a/a) = (b/ab) + (a/ab) = (a + b)/ab

For the third question, yes you can come up with denominators that contain variables that aren’t equal as shown in the example above.