Evaluate 4 1/2−2−5 2/3
A
–3 1
6 –3 1 6
B
12 1
6 12 1 6
C
2 1
62 1 6
D
–4 1/6
To evaluate 4 1/2 − 2 − 5 2/3, we need to simplify each fraction and then perform the subtraction operation.
First, we simplify 4 1/2 to an improper fraction:
4 1/2 = (4 * 2 + 1)/2 = 9/2
Next, we convert 5 2/3 into an improper fraction:
5 2/3 = (5 * 3 + 2)/3 = 17/3
Now, we can rewrite the expression as:
9/2 - 2 - 17/3
To simplify this expression further, we need to find a common denominator for 2 and 3, which is 6. We can rewrite 2 as 12/6 and 17/3 as 34/6.
Now, the expression becomes:
9/2 - 12/6 - 34/6
To subtract fractions, we keep the denominators the same and subtract the numerators:
(9 - 12 - 34)/6 = -37/6
So, the simplified expression is -37/6.
Therefore, the answer is D. –4 1/6.
To evaluate 4 1/2 - 2 - 5 2/3, we need to follow the order of operations (PEMDAS) and simplify the expression step-by-step.
Step 1: Simplify the mixed numbers
4 1/2 can be written as an improper fraction: 4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2
5 2/3 can be written as an improper fraction: 5 2/3 = 5 + 2/3 = 15/3 + 2/3 = 17/3
Step 2: Perform subtraction
Now we can substitute the values into the expression: 9/2 - 2 - 17/3
Step 3: Convert all the fractions to have a common denominator
The common denominator for 2 and 3 is 6.
9/2 = (9/2) * (3/3) = 27/6
17/3 = (17/3) * (2/2) = 34/6
Step 4: Perform the subtraction
27/6 - 2 - 34/6 = 27/6 - 12/6 - 34/6 = -19/6
So, the simplified value of 4 1/2 - 2 - 5 2/3 is -19/6.
The correct option is D) –4 1/6.
To evaluate the expression 4 1/2 - 2 - 5 2/3, we need to follow the proper order of operations (PEMDAS/BODMAS).
Step 1: Evaluate any fractions or mixed numbers involved.
4 1/2 is a mixed number. To convert it to an improper fraction, we multiply the whole number (4) by the denominator (2), which gives us 8. Then, we add the numerator (1), resulting in 9. So, 4 1/2 is equal to 9/2.
Similarly, 5 2/3 can be converted to an improper fraction. Multiply the whole number (5) by the denominator (3), which gives us 15. Then, add the numerator (2), resulting in 17. So, 5 2/3 is equal to 17/3.
Now, the expression becomes: 9/2 - 2 - 17/3.
Step 2: Perform any subtraction or addition from left to right.
9/2 - 2 means subtracting 2 from 9/2. To do this, both numbers need to have the same denominator. Multiply the 2 (in the numerator and denominator) by 2, giving us 4. The expression becomes: 9/2 - 4/2.
Finally, subtract the numerators and keep the common denominator: 9/2 - 4/2 = (9 - 4)/2 = 5/2.
The expression now becomes: 5/2 - 17/3.
Step 3: Subtract again.
To subtract fractions, you need to have a common denominator. The least common multiple (LCM) of 2 and 3 is 6.
Convert both fractions to have a denominator of 6:
- Multiply the numerator and denominator of 5/2 by 3: (5 * 3)/(2 * 3) = 15/6.
- Multiply the numerator and denominator of 17/3 by 2: (17 * 2)/(3 * 2) = 34/6.
Now, the expression is: 15/6 - 34/6.
Subtract the numerators while keeping the common denominator: (15 - 34)/6 = -19/6.
Therefore, the answer is D) –4 1/6.