Evaluate 4 1/2 − 2 − 5 2/3
A. -3 1/6
B. 12 1/6
C. 2 1/6
D. -4 1/6
To evaluate the expression 4 1/2 − 2 − 5 2/3, we first need to convert all the mixed numbers into improper fractions.
4 1/2 = 9/2
5 2/3 = 17/3
Now we can rewrite the expression as:
9/2 - 2 - 17/3
To simplify the expression, we need a common denominator. The least common multiple of 2 and 3 is 6, so we can rewrite the expression as:
(9/2)(3/3) - (2)(3/3) - (17/3)(2/2)
= 27/6 - 6/6 - 34/6
Now we can subtract the fractions:
27/6 - 6/6 - 34/6
= (27 - 6 - 34)/6
= -13/6
So the answer is -13/6, which can also be expressed as -2 1/6. Therefore, the correct answer is:
D. -4 1/6
To evaluate the expression 4 1/2 - 2 - 5 2/3, we need to perform the operations in the correct order, which is known as the order of operations (PEMDAS).
First, simplify 4 1/2.
4 1/2 is equivalent to 4 + 1/2.
4 + 1/2 = 8/2 + 1/2 = 9/2.
So, the expression becomes 9/2 - 2 - 5 2/3.
Next, simplify 5 2/3.
5 2/3 is equivalent to 5 + 2/3.
5 + 2/3 = 15/3 + 2/3 = 17/3.
Now, the expression becomes 9/2 - 2 - 17/3.
To subtract fractions, we need a common denominator.
The least common multiple of 2 and 3 is 6.
So, converting 9/2 and 17/3 to have a common denominator of 6:
9/2 = 9/2 * 3/3 = 27/6.
17/3 = 17/3 * 2/2 = 34/6.
Now, the expression becomes 27/6 - 2 - 34/6.
Subtracting the fractions 27/6 and 34/6:
27/6 - 34/6 = (27 - 34)/6 = -7/6.
So, the final answer is -7/6.
Therefore, the correct answer option is D. -4 1/6.
To evaluate the expression 4 1/2 - 2 - 5 2/3, we need to follow the order of operations, which is often remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Let's simplify step by step:
Step 1: Simplify the mixed numbers
4 1/2 can be written as an improper fraction:
4 1/2 = (4 * 2 + 1) / 2 = 9/2
5 2/3 can also be written as an improper fraction:
5 2/3 = (5 * 3 + 2) / 3 = 17/3
Now the expression becomes: 9/2 - 2 - 17/3
Step 2: Find a common denominator
To subtract fractions, we need a common denominator. In this case, the common denominator is 2 * 3 = 6.
Step 3: Rewrite the fractions with the common denominator
9/2 = (9/2) * (3/3) = 27/6
17/3 = (17/3) * (2/2) = 34/6
The expression now becomes: 27/6 - 2 - 34/6
Step 4: Subtract the fractions and perform the remaining operations
27/6 - 2 - 34/6 = (27 - 34) / 6 = -7/6
Step 5: Simplify the answer
We can rewrite -7/6 as a mixed number:
-7/6 = -1 1/6
Therefore, the answer is option A. -3 1/6.