Questions: Subtract. 3/4 - 2/9 Write your answer as a fraction in simplest form.

$Subtract. 3/4 - 2/9 Write your answer as a fraction in simplest form.$

Transcript text: Subtract. \[ \frac{3}{4}-\frac{2}{9} \] Write your answer as a fraction in simplest form.

Solution

Solution Steps

To subtract fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of the denominators will serve as the common denominator. Once we have the common denominator, we convert each fraction to an equivalent fraction with this common denominator, perform the subtraction, and simplify the result if possible.

Step 1: Find the Least Common Denominator

To subtract the fractions $ \frac{3}{4} $ and $ \frac{2}{9} $, we first find the least common multiple (LCM) of the denominators $ 4 $ and $ 9 $. The LCM is $ 36 $.

Step 2: Convert to Equivalent Fractions

Next, we convert each fraction to have the common denominator of $ 36 $: \[ \frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36} \] \[ \frac{2}{9} = \frac{2 \times 4}{9 \times 4} = \frac{8}{36} \]

Step 3: Perform the Subtraction

Now, we subtract the two fractions: \[ \frac{27}{36} - \frac{8}{36} = \frac{27 - 8}{36} = \frac{19}{36} \]

Step 4: Simplify the Result

The fraction $ \frac{19}{36} $ is already in its simplest form since the greatest common divisor (GCD) of $ 19 $ and $ 36 $ is $ 1 $.