4 1/2 − 2 −5 2/3
To calculate the expression 4 1/2 - 2 - 5 2/3, let's simplify it step by step:
First, convert 4 1/2 into an improper fraction:
4 1/2 = (4 * 2 + 1)/2 = 9/2
So the expression becomes 9/2 - 2 - 5 2/3
Next, convert 5 2/3 into an improper fraction:
5 2/3 = (5 * 3 + 2)/3 = 17/3
Now the expression becomes 9/2 - 2 - 17/3
To combine fractions with different denominators, we need a common denominator. The least common multiple of 2 and 3 is 6.
Multiplying the first fraction by 3/3:
(9/2) * (3/3) = 27/6
Now the expression becomes 27/6 - 2 - 17/3
To subtract, we need a common denominator for 6 and 3, which is 6.
Multiplying 2 by 6/6 and 17/3 by 2/2:
27/6 - (2 * 6/6) - (17 * 2/3 * 2/2)
= 27/6 - 12/6 - 34/6
Now the expression becomes (27 - 12 - 34) / 6
Subtracting the numerators:
= (-19) / 6
Therefore, the simplified expression is -19/6.
To simplify the expression 4 1/2 − 2 − 5 2/3, we can follow these steps:
Step 1: Convert mixed numbers to improper fractions.
4 1/2 can be written as 9/2, and 5 2/3 can be written as 17/3.
So the expression becomes:
9/2 − 2 − 17/3
Step 2: Find a common denominator.
The denominators are 2 and 3, so the common denominator is 6.
Step 3: Rewrite the fractions with the common denominator.
Multiplying the first fraction by 3/3 and the second fraction by 2/2, we get:
(27/6) − (4/6) − (34/6)
Step 4: Combine the fractions.
Now we can subtract the fractions using the common denominator:
27/6 − 4/6 − 34/6
Step 5: Perform the subtraction.
Subtracting the numerators, we get:
(27 − 4 − 34)/6
Simplifying the numerator gives:
(-11)/6
Therefore, the expression 4 1/2 − 2 − 5 2/3 simplifies to -11/6.
To subtract mixed numbers and whole numbers, we need to convert the mixed numbers to improper fractions before performing the subtraction. Here's how we can do it step by step:
Step 1: Convert the mixed numbers to improper fractions:
4 1/2 = (4 * 2 + 1) / 2 = 9/2
-5 2/3 = (-5 * 3 + 2) / 3 = -13/3
Step 2: Subtract the fractions:
9/2 - 13/3
To subtract fractions, we need to have a common denominator. The common denominator for 2 and 3 is 6. Let's convert the fractions to have a common denominator:
(9/2) * (3/3) = 27/6
(13/3) * (2/2) = 26/6
Now, we can subtract the fractions:
27/6 - 26/6 = (27 - 26) / 6 = 1/6
Step 3: Convert the result back to a mixed number (if desired):
1/6 can be written as 0 1/6
Therefore, 4 1/2 - 2 - 5 2/3 equals 0 1/6.