Question

find the difference. write your answer as a mixed number.
$2\frac{3}{6} - \frac{5}{6} = \boxed{?} \frac{\boxed{?}}{\boxed{?}}$

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \( 2\frac{3}{6} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 2\frac{3}{6} \), we have \( a = 2 \), \( b = 3 \), \( c = 6 \). Then \( 2\times6 + 3 = 12 + 3 = 15 \), so \( 2\frac{3}{6}=\frac{15}{6} \).

Step2: Subtract the fractions

Now subtract \( \frac{5}{6} \) from \( \frac{15}{6} \). When subtracting fractions with the same denominator, we subtract the numerators: \( \frac{15 - 5}{6}=\frac{10}{6} \).

Step3: Simplify the fraction and convert to mixed number

Simplify \( \frac{10}{6} \) by dividing numerator and denominator by their greatest common divisor, which is 2. So \( \frac{10\div2}{6\div2}=\frac{5}{3} \). Now convert \( \frac{5}{3} \) to a mixed number. Divide 5 by 3: 3 goes into 5 once with a remainder of 2. So \( \frac{5}{3}=1\frac{2}{3} \).

Answer:

\( 1\frac{2}{3} \) (or in the boxed form as per the problem's layout: the whole number is 1, the numerator is 2, the denominator is 3)