To evaluate the expression -3/4 + 5 - 2 ÷ 4 - 2 + 1/2, we need to follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Let's break it down step by step:
- Identify the operations in the expression: The operations present are: addition (+), subtraction (−), and division (÷).
- Perform the division first: Calculate -2 ÷ 4.
-2 ÷ 4 = -1/2. - Rewrite the expression: Substituting back gives us -3/4 + 5 - 1/2 - 2 + 1/2.
- Combine like fractions: To do the addition and subtraction more easily, we can convert all terms into a common fraction. The common denominator for these fractions (4, 2) is 4:
- -3/4 is -3/4 (no change)
- 5 can be expressed as 20/4 (since 5 = 20/4).
- -1/2 can be expressed as -2/4 (since -1/2 = -2/4).
- -2 can be expressed as -8/4 (since -2 = -8/4).
- 1/2 converts to 2/4.
- Now rewrite the expression: Now the expression is -3/4 + 20/4 - 2/4 - 8/4 + 2/4.
- Combine the fractions: Add and subtract the numerators while keeping the common denominator:
- Numerator: -3 + 20 - 2 - 8 + 2 = 9.
- The new fraction is 9/4.
- Convert to a mixed number: Since 9/4 can also be expressed as a mixed number, we divide 9 by 4:
- 9 ÷ 4 = 2 R1, which gives us 2 1/4.
Thus, the final answer to the expression is: 2 1/4 or 9/4.