uses the properties and mental math to solve. Write your answer in simplest form. 2 1/10 + (1 2/7 + 4 9/10)

Hello!The answer is: [tex]\frac{58}{7}[/tex]Why?Since we have mixed numbers, first we need to make it fractions, then we can add/subtract the resultant fractions.Sum of fractions is not linear, to add/subtract actions we must follow the next steps: Multiply each fraction denominator by each other, it will be the new fraction denominator.Multiply first fraction numerator by the second fraction denominator.Multiply first fraction denominator by the second fraction numerator.Add/subtract each result from step 2 and 3 to get the new fraction numerator.Simplify the results.Therefore,[tex]2\frac{1}{10}=2+\frac{1}{10}=\frac{20+1}{10}=\frac{21}{10}[/tex][tex]1\frac{2}{7}=1+\frac{2}{7}=\frac{7+2}{7}=\frac{9}{7}[/tex][tex]4\frac{9}{10}=4+\frac{9}{10}=\frac{40+9}{10}=\frac{49}{10}[/tex]Now, we have all mixed numbers changed to fractions. Then, we need to add the fractions:[tex]\frac{21}{10} + \frac{9}{7} + \frac{49}{10}=\frac{147+90}{70} +\frac{49}{10}\\\\\frac{237}{70}+\frac{49}{10}=\frac{2370+3430}{700}=\frac{5800}{700}=\frac{58}{7}[/tex]Have a nice day!