Chapter 11.3, Problem 69MR

To determine

To simplify the expression $\frac{1}{4}-\frac{1}{3}$ .

Answer to Problem 69MR

  $-\frac{1}{12}$

Explanation of Solution

Given:

The expression, $\frac{1}{4}-\frac{1}{3}$

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Solving an equation containing rational expressions
• Multiply both sides of equations by LCD(least common denominator) of all denominators.
• Remove any grouping symbols and solve the resulting equation for the variable asked in equation

Calculation:

In order to simplify the given expression, observe that the LCD of 3 and 4 is 12. So, multiply the first fraction by 3 up and down and multiply the second fraction by 4 up and down to make both the denominators equal to the LCD and then simplify the numerators over the common denominator as shown below,

  $\begin{array}{c}\frac{1}{4}-\frac{1}{3}=\frac{1}{4}\cdot \frac{3}{3}-\frac{1}{3}\cdot \frac{4}{4}\\ =\frac{3}{12}-\frac{4}{12}\\ =\frac{3-4}{12}\\ =\frac{-1}{12}\end{array}$

Thus, the given expression simplifies to $-\frac{1}{12}$ .