Plus minus mixed numbers

If possible, perform the indicated operation/s and reduce your answer to the lowest term.
1. 3 1/8 + 3/5=
2. 6 3/7 + 4/9=
3. 9 6/13 + 1 3/7=
4. 10 4/5 - 2/3=
5. 13 6/7 - 3/11=

Correct answer:

a =  3 ²⁹⁄₄₀ = 149/40
b =  6 ⁵⁵⁄₆₃ = 433/63
c =  10 ⁸¹⁄₉₁ = 991/91
d =  10 ²⁄₁₅ = 152/15
e =  13 ⁴⁵⁄₇₇ = 1046/77

Step-by-step explanation:

$$\begin{gathered} a_1=3\frac{1}{8}=3+\frac{1}{8}=\frac{3\cdot 8+1}{8}=\frac{24+1}{8}=\frac{25}{8}=3\frac{1}{8}=3.125 \\ a=a_1+\frac{3}{5}=\frac{25}{8}+\frac{3}{5}=\frac{125}{40}+\frac{24}{40}=\frac{125+24}{40}=\frac{149}{40}=3\frac{29}{40}=3.725 \end{gathered}$$

$$\begin{gathered} b_1=6\frac{3}{7}=6+\frac{3}{7}=\frac{6\cdot 7+3}{7}=\frac{42+3}{7}=\frac{45}{7}=6\frac{3}{7}\doteq 6.4286 \\ b=b_1+\frac{4}{9}=\frac{45}{7}+\frac{4}{9}=\frac{405}{63}+\frac{28}{63}=\frac{405+28}{63}=\frac{433}{63}=6\frac{55}{63}=6.873 \end{gathered}$$

$$\begin{gathered} c_1=9\frac{6}{13}=9+\frac{6}{13}=\frac{9\cdot 13+6}{13}=\frac{117+6}{13}=\frac{123}{13}=9\frac{6}{13}\doteq 9.4615 \\ {c}_2=1\frac{3}{7}=1+\frac{3}{7}=\frac{1\cdot 7+3}{7}=\frac{7+3}{7}=\frac{10}{7}=1\frac{3}{7}\doteq 1.4286 \\ c=c_1+c_2=\frac{123}{13}+\frac{10}{7}=\frac{861}{91}+\frac{130}{91}=\frac{861+130}{91}=\frac{991}{91}=10\frac{81}{91}=10.8901 \end{gathered}$$

$$\begin{gathered} d_1=10\frac{4}{5}=10+\frac{4}{5}=\frac{10\cdot 5+4}{5}=\frac{50+4}{5}=\frac{54}{5}=10\frac{4}{5}=10.8 \\ d=d_1-\frac{2}{3}=\frac{54}{5}-\frac{2}{3}=\frac{162}{15}-\frac{10}{15}=\frac{162-10}{15}=\frac{152}{15}=10\frac{2}{15}=10.1333 \end{gathered}$$

$$\begin{gathered} e_1=13\frac{6}{7}=13+\frac{6}{7}=\frac{13\cdot 7+6}{7}=\frac{91+6}{7}=\frac{97}{7}=13\frac{6}{7}\doteq 13.8571 \\ e=e_1-\frac{3}{11}=\frac{97}{7}-\frac{3}{11}=\frac{1067}{77}-\frac{21}{77}=\frac{1067-21}{77}=\frac{1046}{77}=13\frac{45}{77}=13.5844 \end{gathered}$$

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