Add −1/27+(3/14) . Write your answer as a reduced improper fraction

Answer 1

To add the fractions \(-\frac{1}{27}\) and \(\frac{3}{14}\), we first need to find a common denominator.

The denominators are 27 and 14. The least common multiple (LCM) of 27 and 14 can be calculated as follows:

• The prime factorization of 27 is \(3^3\).
• The prime factorization of 14 is \(2 \times 7\).
• The LCM is obtained by taking the highest power of each prime:
  • From 27, we take \(3^3\).
  • From 14, we take \(2^1\) and \(7^1\).

So, the LCM is: \[ 27 \times 2 \times 7 = 378. \]

Now we convert each fraction to have the common denominator of 378:

1. For \(-\frac{1}{27}\): \[ -\frac{1}{27} = -\frac{1 \times 14}{27 \times 14} = -\frac{14}{378}. \]

2. For \(\frac{3}{14}\): \[ \frac{3}{14} = \frac{3 \times 27}{14 \times 27} = \frac{81}{378}. \]

Now we can add the two fractions: \[ -\frac{14}{378} + \frac{81}{378} = \frac{81 - 14}{378} = \frac{67}{378}. \]

Next, we check if \(\frac{67}{378}\) can be reduced. The numerator, 67, is a prime number and does not divide 378, so \(\frac{67}{378}\) is already in its simplest form.

Therefore, the answer is: \[ \frac{67}{378}. \]

Answer 2

it says its wrong

Answer 3

Let’s reevaluate the addition of the fractions \(-\frac{1}{27} + \frac{3}{14}\) step by step.

1. Identify the common denominator:

   • The denominators are \(27\) and \(14\).
   • The least common multiple (LCM) of \(27\) and \(14\) is \(378\).

2. Convert each fraction:

   • To convert \(-\frac{1}{27}\) to a denominator of \(378\): \[ -\frac{1}{27} = -\frac{1 \times 14}{27 \times 14} = -\frac{14}{378}. \]

   • To convert \(\frac{3}{14}\) to a denominator of \(378\): \[ \frac{3}{14} = \frac{3 \times 27}{14 \times 27} = \frac{81}{378}. \]

3. Add the fractions: \[ -\frac{14}{378} + \frac{81}{378} = \frac{81 - 14}{378} = \frac{67}{378}. \]

So the calculation is correct and results in \(\frac{67}{378}\).

Let's check whether this is the correct answer:

• The numerator \(67\) is prime, and it does not share any factors with \(378\).

Considering the possibility that there might be an error in interpreting the problem, let's once more simplify or double-check the addition:

Since both fractions are correctly converted and summed, if the output states otherwise, please verify whether the input of the fractions is exact. Based on the given fractions, the answer remains:

\[ \frac{67}{378} \]

If you have feedback or further details about why the answer might be considered wrong, feel free to share!