3.65 as a Fraction

Step-by-step solution

The problem

1. Write the digits over 100. 3.65 has 2 decimal places, so put the digits (without the point) over 1 followed by 2 zeros.

   = \textcolor{#0b5c56}{\frac{365}{100}}

2. Simplify. Write both as prime factors:\begin{aligned} 365 &= 5 \times 73 \\[6pt] 100 &= 2^{2} \times 5^{2} \end{aligned}The only factor they share is 5, so the greatest common factor (GCF) is 5. Divide the top and bottom by 5.

   = \frac{365 \div 5}{100 \div 5} = \textcolor{#0b5c56}{\frac{73}{20}}

3. Write it as a mixed number. 73 ÷ 20 = 3 remainder 13: the whole number is 3 and 13 is the new numerator.

   73 \div 20 = 3\ \text{R}\ 13
   = \textcolor{#0b5c56}{3\frac{13}{20}}

All the working together