Comparing mixed numbers

Which of the following expression will give a sum of 7 and 3/10?
A. 3 and 1/5+ 4 and 2/2
B. 3 and 1/10+4 and 2/10
C. 1/10+ 7 and 2/5
D. 2 and 1/10+ 5 and 3/10

Correct answer:

x = B

Step-by-step explanation:

$$\begin{gathered} v=7\frac{3}{10}=7+\frac{3}{10}=\frac{7\cdot 10+3}{10}=\frac{70+3}{10}=\frac{73}{10}=7\frac{3}{10}=7.3 \\ A=3\frac{1}{5}+2/2=\frac{21}{5}=4\frac{1}{5}=4.2 \\ B=3\frac{1}{10}+4\frac{2}{10}=\frac{31}{10}+\frac{42}{10}=\frac{31+42}{10}=\frac{73}{10}=7\frac{3}{10}=7.3 \\ C=\frac{1}{10}+7\frac{2}{5}=\frac{1}{10}+\frac{37}{5}=\frac{1}{10}+\frac{74}{10}=\frac{1+74}{10}=\frac{75}{10}=\frac{15}{2}=7\frac{1}{2}=7.5 \\ D=2\frac{1}{10}+5\frac{3}{10}=\frac{21}{10}+\frac{53}{10}=\frac{21+53}{10}=\frac{74}{10}=\frac{37}{5}=7\frac{2}{5}=7.4 \\ B=v=7\frac{3}{10} \\ x=B \end{gathered}$$

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