How do you subtract two negative mixed numbers?

Question

Cameron Arnold · Accepted Answer

To perform such calculations I would first write both mixed numbers as improper fractions.

The easiest way to perform such calculation is (in my opinion) to write the numbers as improper fractions, then find the lowest common denominator and finally substract the numerators.

Autumn Arnold · Answer

undefined To subtract two negative mixed numbers, follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Subtract the second fraction from the first one.
3. If necessary, simplify the resulting fraction.
4. Convert the result back to a mixed number, if preferred.

Here's an example:

Subtract $ -3 \frac{1}{2} $ from $ -5 \frac{3}{4} $:

1. Convert mixed numbers to improper fractions:
   $ -5 \frac{3}{4} = -\left(5 + \frac{3}{4}\right) = -\frac{20}{4} - \frac{3}{4} = -\frac{23}{4} $
   $ -3 \frac{1}{2} = -\left(3 + \frac{1}{2}\right) = -\frac{6}{2} - \frac{1}{2} = -\frac{7}{2} $

2. Subtract the second fraction from the first one:
   $ -\frac{23}{4} - (-\frac{7}{2}) = -\frac{23}{4} + \frac{7}{2} $

3. Find a common denominator and perform the subtraction:
   $ -\frac{23}{4} + \frac{7}{2} = -\frac{23}{4} + \frac{14}{4} = -\frac{9}{4} $

4. Convert the result back to a mixed number if needed:
   $ -\frac{9}{4} = -\left(2 + \frac{1}{4}\right) = -2 \frac{1}{4} $

So, subtracting $ -3 \frac{1}{2} $ from $ -5 \frac{3}{4} $ yields $ -2 \frac{1}{4} $.