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 this expression, we need to perform the calculations in the correct order following the order of operations (PEMDAS).
First, we need to subtract 2 from 4 1/2:
4 1/2 - 2 = 3 1/2
Next, we need to subtract 5 2/3 from the result we just found:
3 1/2 - 5 2/3
To subtract these mixed numbers, we need to find a common denominator:
2/3 * 2/2 = 4/6
So, the expression becomes:
3 1/2 - 5 4/6
Now we can subtract the whole numbers and fractions separately:
3 - 5 = -2
1/2 - 4/6
To subtract fractions, we need a common denominator:
2/2 * 3/3 = 6/6
So, the expression becomes:
1/2 - 4/6 = 3/6 - 4/6 = -1/6
Putting it all together, we have:
-2 - 1/6 = -2 1/6
Therefore, the answer is:
D. -4 1/6
To evaluate the expression 4 1/2 - 2 - 5 2/3, we need to follow the order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
First, we deal with the subtraction of fractions:
4 1/2 is the same as 9/2.
Next, we perform the subtraction:
9/2 - 2 becomes (9/2) - (4/2) = 5/2.
Now, we move on to the mixed numbers:
5 2/3 is the same as 17/3.
Finally, we subtract the result from the previous step:
5/2 - 17/3.
To subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 6.
Converting 5/2 to have a denominator of 6, we get 15/6.
Converting 17/3 to have a denominator of 6, we get 34/6.
Now, we can subtract:
15/6 - 34/6 = -19/6.
The final answer is -19/6, which is equivalent to -3 1/6.
Therefore, the correct answer is A. -3 1/6.
To evaluate the expression 4 1/2 − 2 − 5 2/3, we can follow these steps:
Step 1: Convert all the mixed numbers to improper fractions.
4 1/2 becomes (4 × 2 + 1) / 2 = 9/2
5 2/3 becomes (5 × 3 + 2) / 3 = 17/3
Now the expression becomes: 9/2 - 2 - 17/3
Step 2: Find the common denominator among all the fractions.
The common denominator between 2 and 3 is 6.
Step 3: Rewrite all the fractions with the common denominator.
9/2 becomes 27/6
17/3 becomes 34/6
Now the expression becomes: 27/6 - 12/6 - 34/6
Step 4: Perform the subtraction.
27/6 - 12/6 - 34/6 = (27 - 12 - 34) / 6 = -19/6
Step 5: Simplify the resulting fraction, if possible.
In this case, -19/6 cannot be simplified further.
The final result is -19/6. To express it as a mixed number, we divide the numerator (19) by the denominator (6):
19 ÷ 6 = 3 remainder 1
Therefore, the final result is -3 1/6.
So, the correct answer is:
A. –3 1/6