Find the sum:
`3(27)/(30)+2(7)/(12)`

Answer

To find the sum of the mixed fractions \(3 \frac{27}{30} + 2 \frac{7}{12}\), we will follow these steps:

### Step 1: Convert Mixed Fractions to Improper Fractions
First, we need to convert the mixed fractions into improper fractions.

For \(3 \frac{27}{30}\):
\[ 3 \frac{27}{30} = \frac{3 \times 30 + 27}{30} = \frac{90 + 27}{30} = \frac{117}{30} \]

For \(2 \frac{7}{12}\):
\[ 2 \frac{7}{12} = \frac{2 \times 12 + 7}{12} = \frac{24 + 7}{12} = \frac{31}{12} \]

### Step 2: Add the Improper Fractions
Now we need to add the two improper fractions \(\frac{117}{30}\) and \(\frac{31}{12}\).

To add these fractions, we need a common denominator. The least common multiple (LCM) of 30 and 12 is 60.

Convert each fraction:
\[ \frac{117}{30} = \frac{117 \times 2}{30 \times 2} = \frac{234}{60} \]
\[ \frac{31}{12} = \frac{31 \times 5}{12 \times 5} = \frac{155}{60} \]

Now we can add them:
\[ \frac{234}{60} + \frac{155}{60} = \frac{234 + 155}{60} = \frac{389}{60} \]

### Step 3: Convert the Improper Fraction to a Mixed Number
To convert \(\frac{389}{60}\) into a mixed number, we divide 389 by 60.

\[ 389 \div 60 = 6 \quad \text{(whole number part)} \]
\[ 389 - (60 \times 6) = 389 - 360 = 29 \quad \text{(remainder)} \]

Thus, we have:
\[ \frac{389}{60} = 6 \frac{29}{60} \]

### Final Answer
The sum \(3 \frac{27}{30} + 2 \frac{7}{12} = 6 \frac{29}{60}\).

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