Problem 9 - Introductory Algebra for College Students

Question

Convert each improper fraction to a mixed number. $$\frac{76}{9}$$

Step-by-Step Solution

Answer

The mixed number equivalent of the improper fraction \( \frac{76}{9} \) is \(8 \frac{4}{9}\).

Step 1: Divide Numerator by Denominator

Start by dividing the numerator, \(76\), by the denominator, \(9\). The primary intention is to identify how many times the denominator can be subtract into the numerator. The division result is \(8.4444...\).

Step 2: Determine the whole number and the remainder

The quotient from the above division tells us that \(9\) goes into \(76\) eight times completely. Therefore, the whole number for our mixed number is \(8\). The balance reminders will be used to create the fractional part. So, \(9\) times \(8\) is \(72\), and when \(72\) is subtracted from \(76\), you get a remainder of \(4\).

Step 3: Write the mixed number

The mixed number will have the whole number part as \(8\), that we obtained from the above step, and the fractional part as \(4\over9\). The reminder becomes the numerator of the fraction in our mixed number, and the original denominator \(9\) remains the same for our fraction. The final mixed number is \(8 \frac{4}{9}\).