Question

Find the difference. $$\frac{5}{6}-\frac{1}{9}$$

Short answer

The difference between \(\frac{5}{6}\) and \(\frac{1}{9}\) is \(\frac{13}{18}\).

Step-by-step solution

Find a common denominator

The fractions \(\frac{5}{6}\) and \(\frac{1}{9}\) have different denominators '6' and '9'. To subtract fractions, we need a common denominator. The least common multiple (LCM) of 6 and 9 is 18. This is the smallest number that both numbers can evenly divide.

Adjust the fractions to have the common denominator

Multiply both the numerator and denominator of \(\frac{5}{6}\) by '3' to get \(\frac{15}{18}\) and \(\frac{1}{9}\) by '2' to get \(\frac{2}{18}\). Doing this adjusts the fractions such that they both have 18 as a common denominator.

Subtract the fractions

Now that both fractions have the same denominator, we can directly subtract the numerators. Subtracting \(\frac{2}{18}\) from \(\frac{15}{18}\) gives us \(\frac{13}{18}\).

Simplify Figure

Since \(\frac{13}{18}\) cannot be simplified further, this is our final answer.