Find the value of this fraction computation: 6(1/2+2/3+3/4)
I need help finding the calculation without distribution. Thank you!
For with distribution I got
6(1/2 + 2/3) + 3/4) =
3 + 4 + 9/2 =
7 9/2 or 23/2 or 11 1/2
12 is the common denominator ... 6(6/12 + 8/12 + 9/12)
6(23/12) = ?
what about w/o
It will be there be patient
To find the value of the expression 6(1/2 + 2/3 + 3/4) without using distribution, we can use the concept of a common denominator.
Step 1: Find the Least Common Denominator (LCD) for the fractions 1/2, 2/3, and 3/4.
The LCD is the smallest number that is a multiple of all the denominators.
The denominators are 2, 3, and 4. To find the LCD, we need to prime factorize each number:
2 = 2^1
3 = 3^1
4 = 2^2
Now, we take the highest power of each prime factor:
2^2 * 3^1 = 12
Therefore, the LCD is 12.
Step 2: Rewrite each fraction with the LCD as the denominator.
1/2 = 6/12
2/3 = 8/12
3/4 = 9/12
Step 3: Distribute the constant 6 to each fraction.
6(6/12 + 8/12 + 9/12) = (6 * 6/12) + (6 * 8/12) + (6 * 9/12)
Step 4: Simplify each fraction multiplication.
(36/12) + (48/12) + (54/12)
Step 5: Add the fractions.
(36 + 48 + 54)/12
Step 6: Perform the addition.
138/12 = 11.5
Therefore, the value of the expression 6(1/2 + 2/3 + 3/4) is 11.5.