Difference and sum

If the difference of 19/13 and his answer is 6/7, Bruno's answer is:

If the sum of his answer and 6/7 is 1/2, Bruno's answer is:

If his answer is the sum of 19/13 and 6/7, Bruno's answer is :

Correct answer:

a =  55/91
b =  -5/14
c =  211/91 = 2 ²⁹⁄₉₁

Step-by-step explanation:

$$\begin{gathered} \frac{19}{13}-a=\frac{6}{7} \\ a=\frac{19}{13}-\frac{6}{7}=\frac{133}{91}-\frac{78}{91}=\frac{133-78}{91}=\frac{55}{91}=0.6044 \end{gathered}$$

$$\begin{gathered} b+\frac{6}{7}=\frac{1}{2} \\ b=\frac{1}{2}-\frac{6}{7}=\frac{7}{14}-\frac{12}{14}=\frac{7-12}{14}=\frac{-5}{14}=-\frac{5}{14}=-0.3571 \end{gathered}$$

$c=\frac{19}{13}+\frac{6}{7}=\frac{133}{91}+\frac{78}{91}=\frac{133+78}{91}=\frac{211}{91}=2\frac{29}{91}=2.3187$

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