Add -12/7+(3/14) write your answer as a reduced improper fraction

Answer 1

To add the fractions \(-\frac{12}{7}\) and \(\frac{3}{14}\), we need a common denominator.

The least common denominator (LCD) for \(7\) and \(14\) is \(14\).

Now, we convert \(-\frac{12}{7}\) to have the denominator \(14\): \[ -\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14} \]

Now we can add the two fractions: \[ -\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14} \]

Next, we will simplify \(\frac{-21}{14}\). The greatest common divisor (GCD) of \(21\) and \(14\) is \(7\): \[ \frac{-21 \div 7}{14 \div 7} = \frac{-3}{2} \]

Thus, the answer is: \[ \boxed{-\frac{3}{2}} \]

Answer 2

whats -4 2/3+ -1 1/3

Answer 3

To add the mixed numbers \(-4 \frac{2}{3}\) and \(-1 \frac{1}{3}\), we first convert them to improper fractions.

1. Convert \(-4 \frac{2}{3}\) to an improper fraction: \[ -4 \frac{2}{3} = -\left(4 \times 3 + 2\right) / 3 = -\frac{12 + 2}{3} = -\frac{14}{3} \]

2. Convert \(-1 \frac{1}{3}\) to an improper fraction: \[ -1 \frac{1}{3} = -\left(1 \times 3 + 1\right) / 3 = -\frac{3 + 1}{3} = -\frac{4}{3} \]

Now we can add the two improper fractions: \[ -\frac{14}{3} + -\frac{4}{3} = -\frac{14 + 4}{3} = -\frac{18}{3} \]

Next, simplify \(-\frac{18}{3}\): \[ -\frac{18 \div 3}{3 \div 3} = -6 \]

Thus, the result of \(-4 \frac{2}{3} + -1 \frac{1}{3}\) is: \[ \boxed{-6} \]

Answer 4

whats 5 3/4+ -3 1/6 as an reduced mixed number

Answer 5

To add the mixed numbers \(5 \frac{3}{4}\) and \(-3 \frac{1}{6}\), we'll first convert both mixed numbers to improper fractions and then perform the addition.

1. Convert \(5 \frac{3}{4}\) to an improper fraction: \[ 5 \frac{3}{4} = \left(5 \times 4 + 3\right) / 4 = \frac{20 + 3}{4} = \frac{23}{4} \]

2. Convert \(-3 \frac{1}{6}\) to an improper fraction: \[ -3 \frac{1}{6} = -\left(3 \times 6 + 1\right) / 6 = -\frac{18 + 1}{6} = -\frac{19}{6} \]

Now we have: \[ \frac{23}{4} + -\frac{19}{6} \]

To add these fractions, we need a common denominator. The least common denominator (LCD) for \(4\) and \(6\) is \(12\).

3. Convert both fractions to have the common denominator of \(12\):

   • For \(\frac{23}{4}\): \[ \frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12} \]

   • For \(-\frac{19}{6}\): \[ -\frac{19}{6} = -\frac{19 \times 2}{6 \times 2} = -\frac{38}{12} \]

Now we can add: \[ \frac{69}{12} - \frac{38}{12} = \frac{69 - 38}{12} = \frac{31}{12} \]

4. Convert \(\frac{31}{12}\) back to a mixed number:
   • Divide \(31\) by \(12\):
     • \(31 \div 12 = 2\) remainder \(7\).
   • Thus, we have: \[ \frac{31}{12} = 2 \frac{7}{12} \]

Therefore, the final answer, in reduced mixed number form, is: \[ \boxed{2 \frac{7}{12}} \]