Evaluate 4 1/2 − 2 −5 2/3
Responses
A
–3 1
6
–3 1 6
B
12 1
6
12 1 6
C
2 1
6
2 1 6
D
–4 1
6
–4 1 6
To evaluate 4 1/2 - 2 - 5 2/3, we first need to convert all the numbers to a common fraction or mixed number.
4 1/2 can be written as 9/2.
5 2/3 can be written as 17/3.
So, the expression becomes:
9/2 - 2 - 17/3.
Next, we need to find a common denominator to subtract the fractions. The common denominator of 2 and 3 is 6.
9/2 can be converted to an improper fraction with a denominator of 6:
9/2 = 27/6.
Now, the expression becomes:
27/6 - 2 - 17/3.
To subtract 27/6 and 17/3, we need to find the common denominator of 6 and 3, which is 6.
27/6 can be divided by 6 to become 4/1.
Now, the expression becomes:
4/1 - 2 - 17/3.
To subtract the fractions, we need to have a common denominator of 3.
4/1 can be written as 12/3.
Now, the expression becomes:
12/3 - 2 - 17/3.
Subtracting the fractions, we have:
(12 - 17)/3 = -5/3.
So, the final expression is:
-5/3 - 2.
To subtract -5/3 and 2, we need to have a common denominator of 3.
-5/3 can be converted to -15/3.
Now, the expression becomes:
-15/3 - 2.
Subtracting the fractions, we have:
-17/3.
Therefore, the answer is D) -17/3.
To evaluate the expression 4 1/2 - 2 - 5 2/3, we follow the order of operations (PEMDAS) and convert the mixed numbers to improper fractions:
4 1/2 = (4 * 2 + 1) / 2 = 9/2
5 2/3 = (5 * 3 + 2) / 3 = 17/3
Now we can rewrite the expression: 9/2 - 2 - 17/3
Next, we need to find a common denominator for the fractions. The smallest number that both 2 and 3 divide into evenly is 6. So our expression becomes: (9/2 * 3/3) - (2 * 3/3) - 17/3
This simplifies to: 27/6 - 6/6 - 17/3
Now, we can combine the fractions: (27 - 6 - 34)/6
Calculating this, we get: -13/6
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 (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction.
First, we simplify any operations inside parentheses or brackets. However, there are none in this expression.
Next, we simplify any exponents or orders. Again, there are none in this expression.
Moving on, we perform any multiplication or division from left to right. In this case, we have no multiplication, but we have division involving fractions.
4 1/2 is the same as 9/2 (this is an improper fraction).
Similarly, 5 2/3 is the same as 17/3 (another improper fraction).
So now we have the expression 9/2 - 2 - 17/3.
To subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 2 and 3 is 6.
Converting 9/2 to have a denominator of 6:
9/2 = (9/2) * (3/3) = 27/6
Now we have the expression 27/6 - 2 - 17/3.
Subtracting the fractions:
27/6 - 17/3 = (27 - (2 * 17))/(6) = (27 - 34)/6 = -7/6
Finally, we subtract 2 from -7/6:
-7/6 - 2 = (-7/6) - (12/6) = (-7 - 12)/6 = -19/6
So the answer is -19/6.
Therefore, the correct option is D: –4 1/6.