Questions: Which expression uses a common denominator to rewrite 1/3 - 1/9 ? 9/9 - 1/9 9/1 - 3/1 3/3 - 1/3 3/9 - 1/9

Transcript text: Which expression uses a common denominator to rewrite $\frac{1}{3}-\frac{1}{9}$ ? \[ \frac{9}{9}-\frac{1}{9} \frac{9}{1}-\frac{3}{1} \frac{3}{3}-\frac{1}{3} \frac{3}{9}-\frac{1}{9} \]

Solution

Solution Steps

Step 1: Identify the Common Denominator

To rewrite the expression $\frac{1}{3} - \frac{1}{9}$ with a common denominator, we need to find the least common multiple (LCM) of the denominators 3 and 9. The LCM of 3 and 9 is 9.

Step 2: Rewrite Each Fraction with the Common Denominator

Convert $\frac{1}{3}$ to a fraction with a denominator of 9. To do this, multiply both the numerator and the denominator by 3:

\[ \frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9} \]

The fraction $\frac{1}{9}$ already has the denominator 9, so it remains unchanged.

Step 3: Write the Expression with the Common Denominator

Now that both fractions have the same denominator, the expression can be rewritten as:

\[ \frac{3}{9} - \frac{1}{9} \]