How do you subtract mixed numbers?

To subtract mixed numbers, convert them to improper fractions, find a common denominator, subtract, and simplify.

When subtracting mixed numbers, the first step is to convert each mixed number into an improper fraction. A mixed number consists of a whole number and a fraction. To convert it, multiply the whole number by the denominator of the fraction and add the numerator. This sum becomes the new numerator, while the denominator remains the same. For example, to convert \(2 \frac{3}{4}\), you calculate \(2 \times 4 + 3 = 11\), so it becomes \(\frac{11}{4}\).

Next, ensure both fractions have a common denominator. If they don't, find the least common multiple (LCM) of the denominators and convert each fraction accordingly. For instance, if you have \(\frac{11}{4}\) and \(\frac{5}{6}\), the LCM of 4 and 6 is 12. Convert \(\frac{11}{4}\) to \(\frac{33}{12}\) and \(\frac{5}{6}\) to \(\frac{10}{12}\).

Now, subtract the numerators while keeping the common denominator. Using our example, \(\frac{33}{12} - \frac{10}{12} = \frac{23}{12}\).

Finally, simplify the resulting fraction if possible. If the result is an improper fraction, you may convert it back to a mixed number. For \(\frac{23}{12}\), divide 23 by 12 to get 1 with a remainder of 11, so it becomes \(1 \frac{11}{12}\).

By following these steps, you can accurately subtract mixed numbers and express the result in its simplest form.