Situation: Find the value of this fraction computation:

6 ( 1/2 + 2/3 + 3/4 )
show calculation with and without distribution
math portfolio
help fast

6(1/2 + 2/3 + 3/4)

1st - Distribute the six to each of the fractions. Just multiple across so 6*1 = 6 and 6/2 = 3. Do it to the other 2.
6/1 * 1/2 = 3
6/1 * 2/3 = 4
6/1 * 3/4 = 18/4
2nd - Add the whole numbers so it would be 7+18/4
3rd - Combine them. 7 can be written as 28/4 so 28/4+18/4 = 46/4
46/4 can be reduced to 23/2 or 11.5

To find the value of the fraction computation: 6 (1/2 + 2/3 + 3/4), you can solve it in two ways: with and without distributing the 6. Let's go through both methods.

Method 1: Without Distribution
When not distributing, you first need to find a common denominator for the fractions.

Step 1: Find the Common Denominator
The denominators in the given fractions are 2, 3, and 4. The smallest common multiple of these three numbers is 12. Therefore, we need to convert all the fractions to have 12 as their denominator.

Step 2: Convert Fractions
To convert the fractions, multiply both the numerator and denominator by the appropriate factors to get the common denominator of 12.

1/2 becomes (1/2) * (6/6) = 6/12
2/3 becomes (2/3) * (4/4) = 8/12
3/4 remains unchanged as it already has a denominator of 4.

Step 3: Add the Converted Fractions
Now that all the fractions have a common denominator of 12, add them together:

6/12 + 8/12 + 3/4 = (6 + 8)/12 + 3/4 = 14/12 + 3/4 = 17/12

Therefore, the value without distributing the 6 is 17/12.

Method 2: With Distribution
If you distribute the 6 to each term, the calculation becomes:

6 * 1/2 + 6 * 2/3 + 6 * 3/4

Step 1: Multiply the Numerator by 6
Perform the multiplication:

6 * 1/2 = 6/2 = 3
6 * 2/3 = 12/3 = 4
6 * 3/4 = 18/4 = 9/2

Step 2: Add the Products
Now, add these products:

3 + 4 + 9/2

Step 3: Convert Mixed Fraction to Improper Fraction
To add the mixed number (4) and the fraction (9/2), convert the mixed number to an improper fraction:

4 = 4/1

Step 4: Find the Common Denominator
The denominators are 1 and 2. The common denominator is 2.

Step 5: Convert the Mixed Fraction
Convert the mixed number to the same denominator:

4/1 = (4/1) * (2/2) = 8/2

Step 6: Add the Fractions
Now, add the fractions:

3 + 8/2 + 9/2 = 3 + (8 + 9)/2 = 3 + 17/2

Step 7: Convert to Mixed Number (Optional)
If required, convert the improper fraction to a mixed number:

(3 * 2 + 17) / 2 = 23/2

Therefore, the value with distributing the 6 is 23/2.

In summary, the value of the fraction computation 6 (1/2 + 2/3 + 3/4) is 17/12 without distributing the 6 and 23/2 with distributing the 6.