True or false?

Which of the following is true?

A. Three and three ninths plus seven and six-elevenths equal ten and eighty-seven ninety ninths.
B. two and three-eighths plus six and four-fifths equals eight and twelve fortieth
C. three and three sevenths plus four and two-thirds equals seven and two twenty ones.
D. four and five-sixths plus five sevenths equal nine and ten thirteenths

Result

A=

Yes

No

B=

Yes

No

C=

Yes

No

D=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a_1=3+\frac{3}{9}+7+\frac{6}{11}=\frac{359}{33}=10\frac{29}{33}\doteq 10.8788 \\ {a}_2=10\frac{87}{99}=10+\frac{87}{99}=\frac{10\cdot 99+87}{99}=\frac{990+87}{99}=\frac{1077}{99}=\frac{359}{33}=10\frac{29}{33}\doteq 10.8788 \\ {a}_1=a_2 \\ A=1 \end{gathered}$$

$$\begin{gathered} b_1=2\frac{3}{8}+6\frac{4}{5}=\frac{19}{8}+\frac{34}{5}=\frac{95}{40}+\frac{272}{40}=\frac{95+272}{40}=\frac{367}{40}=9\frac{7}{40}=9.175 \\ {b}_2=8\frac{12}{14}=8+\frac{12}{14}=\frac{8\cdot 14+12}{14}=\frac{112+12}{14}=\frac{124}{14}=\frac{62}{7}=8\frac{6}{7}\doteq 8.8571 \\ {b}_1\ne b_2 \\ B=0 \end{gathered}$$

$$\begin{gathered} c_1=3\frac{3}{7}+4\frac{2}{3}=\frac{24}{7}+\frac{14}{3}=\frac{72}{21}+\frac{98}{21}=\frac{72+98}{21}=\frac{170}{21}=8\frac{2}{21}\doteq 8.0952 \\ {c}_2=7\frac{2}{21}=7+\frac{2}{21}=\frac{7\cdot 21+2}{21}=\frac{147+2}{21}=\frac{149}{21}=7\frac{2}{21}\doteq 7.0952 \\ {c}_1\ne c_2 \\ C=0 \end{gathered}$$

$$\begin{gathered} d_1=4\frac{5}{6}+\frac{5}{7}=\frac{29}{6}+\frac{5}{7}=\frac{203}{42}+\frac{30}{42}=\frac{203+30}{42}=\frac{233}{42}=5\frac{23}{42}\doteq 5.5476 \\ {d}_2=9\frac{10}{13}=9+\frac{10}{13}=\frac{9\cdot 13+10}{13}=\frac{117+10}{13}=\frac{127}{13}=9\frac{10}{13}\doteq 9.7692 \\ {d}_1\ne d_2 \\ D=0 \end{gathered}$$

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