Evaluating the Expression: Step-by-Step Instructions for Beginners

Let's evaluate the expression step by step. The expression is:

5 - (4 ÷ (1/4)) + (1 1/2)

1. Convert Mixed Number to Improper Fraction:

The mixed number 1 1/2 can be converted into an improper fraction. To do this:

• Multiply the whole number (1) by the denominator (2): 1 × 2 = 2.
• Add the numerator (1) to this result: 2 + 1 = 3.
• The improper fraction is then: 3/2.
2. Simplify the Division:

Next, we need to simplify 4 ÷ (1/4). Dividing by a fraction is equivalent to multiplying by its reciprocal.

• The reciprocal of (1/4) is (4/1) or just 4.
• So, 4 ÷ (1/4) = 4 × 4 = 16.
3. Substitute Back into the Expression:

Now we can rewrite the original expression:

5 - 16 + 3/2

4. Convert Whole Numbers to Common Denominator:

To combine these numbers, it helps to convert everything into fractions. The whole numbers can be expressed with a denominator of 1:

• 5 = 5/1 = 10/2 (multiply numerator and denominator by 2)
• 16 = 16/1 = 32/2 (multiply numerator and denominator by 2)

Now the entire expression looks like:

(10/2) - (32/2) + (3/2)

5. Combine the Fractions:

Since they all have a common denominator of 2, we can combine them directly:

(10 - 32 + 3) / 2 = (-22 + 3) / 2 = -19 / 2

6. Final Result in Mixed Number Form:

The answer can be expressed as a mixed number:

• -19/2 is equal to -9 1/2 (since 19 divided by 2 equals 9 with a remainder of 1).

Final Answer: The evaluated expression is -9 1/2 (or as an improper fraction -19/2).