Questions: Change the following mixed number to an improper fraction. Reduce if possible. 6 1/49

$Change the following mixed number to an improper fraction. Reduce if possible. 6 1/49$

Transcript text: Change the following mixed number to an improper fraction. Reduce if possible. \[ 6 \frac{1}{49} \] Answer How to enter your answer (opens in new window)

Solution

Solution Steps

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part, add the numerator of the fractional part to this product, and place the result over the original denominator. Then, simplify the fraction if possible.

Step 1: Convert Mixed Number to Improper Fraction

To convert the mixed number $ 6 \frac{1}{49} $ to an improper fraction, we use the formula:

\[ \text{Improper Numerator} = \text{Whole Number} \times \text{Denominator} + \text{Numerator} \]

Substituting the values:

\[ \text{Improper Numerator} = 6 \times 49 + 1 = 294 + 1 = 295 \]

Thus, the improper fraction is:

\[ \frac{295}{49} \]

Step 2: Simplify the Fraction

Next, we check if the fraction $ \frac{295}{49} $ can be simplified. The greatest common divisor (GCD) of 295 and 49 is 1, indicating that the fraction is already in its simplest form.