Question

Find the sum. $$-4+\frac{1}{2}$$

Short answer

-3.5

Step-by-step solution

Identify the numbers

We have two numbers here, -4 and \(\frac{1}{2}\). -4 is a negative integer while \(\frac{1}{2}\) is a positive fraction.

Convert the numbers to the same form

To make the addition easier, it's often helpful to convert both numbers into the same form. In this case, since we're dealing with a fraction, we could convert -4 into a fraction. -4 is equivalent to \(-4 / 1\). So the equation now reads: \(-4/1 + 1/2\).

Find a common denominator

To add fractions, we need to have a common denominator. In this case, the denominators are 1 and 2. The least common multiple of these two numbers is 2. So, we will multiply both the numerator and denominator of \(-4/1\) by 2 to get \(-8/2 + 1/2\).

Add the fractions

Now that the fractions have the same denominator, they can be added. This is done by adding the numerators and keeping the denominator the same, resulting in \(-8+1 / 2 = -7/2\). This fraction is negative because the numerator is negative.

Simplify and convert to decimal

-7/2 is already simplified, but we can convert it to a decimal for easier understanding. Dividing -7 by 2 results in a decimal of -3.5. Therefore, \(-4 + \frac{1}{2} = -3.5\).