Evaluation of the Expression with Proper Fractions and Mixed Numbers

To evaluate the expression, we need to perform the calculations step by step. The expression is given as:

5 + (5 – 4 ÷ 1/4) + 1 1/2

Let's simplify it:

1. First, we handle the division portion: -4 ÷ 1/4. Dividing by a fraction is the same as multiplying by its reciprocal, so:
2. -4 ÷ 1/4 = -4 × 4/1 = -16.

Substituting this back into the expression gives:

5 + (5 - (-16)) + 1 1/2

1. Now simplify inside the parentheses: 5 - (-16) = 5 + 16 = 21.

Now we can substitute that back:

5 + 21 + 1 1/2

Next, let's convert the mixed number 1 1/2 to an improper fraction:

1. The improper fraction for 1 1/2 is 3/2.

Now we have:

5 + 21 + 3/2

Next, convert the whole numbers to fractions with the same denominator to add them. As 5 and 21 can be converted as follows:

1. 5 = 10/2
2. 21 = 42/2

Now we can rewrite the expression as:

10/2 + 42/2 + 3/2 = (10 + 42 + 3)/2 = 55/2

The final answer as an improper fraction is:

55/2

We can convert this into a mixed number if needed:

55 ÷ 2 = 27 with a remainder of 1.

So the mixed number would be:

27 1/2

This means the evaluated expression is 27 1/2 or as an improper fraction 55/2.

Thus, the answer is:

55/2 or 27 1/2.