Questions: Change the following mixed number to an improper fraction. Reduce if possible. 5 1/27

$Change the following mixed number to an improper fraction. Reduce if possible. 5 1/27$

Transcript text: Change the following mixed number to an improper fraction. Reduce if possible. \[ 5 \frac{1}{27} \]

Solution

Solution Steps

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part, then add the numerator of the fractional part. This sum becomes the numerator of the improper fraction, while the denominator remains the same. Finally, simplify the fraction if possible.

Step 1: Convert the Mixed Number to an Improper Fraction

To convert the mixed number $5 \frac{1}{27}$ to an improper fraction, we use the formula:

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

Substituting the given values:

\[ \text{Improper Numerator} = (5 \times 27) + 1 = 135 + 1 = 136 \]

Thus, the improper fraction is:

\[ \frac{136}{27} \]

Step 2: Simplify the Improper Fraction

The fraction $\frac{136}{27}$ is already in its simplest form because the greatest common divisor of 136 and 27 is 1.