Question

What is the result of (-5 3/4) - (3 1/2)?

Answer 1

The result of (-5 3/4) - (3 1/2) is
`-2^{} (1)/(4)`

Step-by-step explanation:

Let's perform the calculation:

`\[ (-5 (3)/(4)) - (3 (1)/(2)) \]`

First, convert the mixed numbers to improper fractions:

`\[ = \left(-(5 * 4 + 3)/(4)\right) - \left((3 * 2 + 1)/(2)\right) \]`

`\[ = \left(-(20 + 3)/(4)\right) - \left((6 + 1)/(2)\right) \]`

`\[ = \left(-(23)/(4)\right) - \left((7)/(2)\right) \]`

Next, find a common denominator, which is 4 in this case:

`\[ = -(23)/(4) - (14)/(4) \]`

Now, subtract the numerators:

`\[ = -(23 - 14)/(4) \]`

`\[ = -(9)/(4) \]`

Finally, convert the result back to a mixed number:

`\[ = -2 (1)/(4) \]`

So,
`\((-5 (3)/(4)) - (3 (1)/(2))\) equals \(-2 (1)/(4)\).`