Question

1. -6 2/7 + 3 1/14
2. -3.8 + 7.2
3. -18 1/2 + 27 3/5
4. -12 + 4 3/5

Explanation:

Step1: Convert mixed - numbers to improper fractions

• For \(27\frac{1}{3}\), \(27\frac{1}{3}=\frac{27\times3 + 1}{3}=\frac{81+1}{3}=\frac{82}{3}\)
• For \(18\frac{1}{2}\), \(18\frac{1}{2}=\frac{18\times2+1}{2}=\frac{36 + 1}{2}=\frac{37}{2}\)

Step2: Find a common denominator

The common denominator of 2 and 3 is 6. \(\frac{82}{3}=\frac{82\times2}{3\times2}=\frac{164}{6}\), \(\frac{37}{2}=\frac{37\times3}{2\times3}=\frac{111}{6}\)

Step3: Perform the addition and subtraction

\(-\frac{37}{2}+\frac{82}{3}=-\frac{111}{6}+\frac{164}{6}=\frac{- 111 + 164}{6}=\frac{53}{6}=8\frac{5}{6}\)

For \(-6\frac{2}{7}+3\frac{1}{14}\):

Step1: Convert mixed - numbers to improper fractions

\(-6\frac{2}{7}=-\frac{6\times7 + 2}{7}=-\frac{42+2}{7}=-\frac{44}{7}\), \(3\frac{1}{14}=\frac{3\times14+1}{14}=\frac{42 + 1}{14}=\frac{43}{14}\)

Step2: Find a common denominator

The common denominator of 7 and 14 is 14. \(-\frac{44}{7}=-\frac{44\times2}{7\times2}=-\frac{88}{14}\)

Step3: Perform the addition

\(-\frac{88}{14}+\frac{43}{14}=\frac{-88 + 43}{14}=-\frac{45}{14}=-3\frac{3}{14}\)

For \(-3.8 + 7.2\):

Step1: Perform the addition

\(-3.8+7.2=7.2-3.8 = 3.4\)

For \(-12+4\frac{3}{5}\):

Step1: Convert the mixed - number to an improper fraction

\(4\frac{3}{5}=\frac{4\times5+3}{5}=\frac{20 + 3}{5}=\frac{23}{5}\)

Step2: Rewrite - 12 with a denominator of 5

\(-12=-\frac{12\times5}{5}=-\frac{60}{5}\)

Step3: Perform the addition

\(-\frac{60}{5}+\frac{23}{5}=\frac{-60 + 23}{5}=-\frac{37}{5}=-7\frac{2}{5}\)

Answer:

1. \(8\frac{5}{6}\)
2. \(-3\frac{3}{14}\)
3. \(3.4\)
4. \(-7\frac{2}{5}\)