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Reduce to simplest form.

(8)/(6)+(-(9)/(5))=

Reduce to simplest form.\newline86+(95)= \frac{8}{6}+\left(-\frac{9}{5}\right)=

Full solution

Q. Reduce to simplest form.\newline86+(95)= \frac{8}{6}+\left(-\frac{9}{5}\right)=
  1. Simplify Fraction: Simplify each fraction to its simplest form if possible.\newlineThe fraction 86\frac{8}{6} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22. So, 8÷2=48 \div 2 = 4 and 6÷2=36 \div 2 = 3. Therefore, 86\frac{8}{6} simplifies to 43\frac{4}{3}. The fraction 95\frac{9}{5} cannot be simplified further as 99 and 55 have no common divisors other than 11.
  2. Common Denominator: Convert the fractions to have a common denominator.\newlineTo add or subtract fractions, they must have the same denominator. The denominators of the two fractions are 33 and 55. The least common multiple (LCM) of 33 and 55 is 1515. Convert each fraction to an equivalent fraction with a denominator of 1515.\newlineFor 43\frac{4}{3}, multiply both the numerator and the denominator by 55 to get (4×5)/(3×5)=2015(4 \times 5)/(3 \times 5) = \frac{20}{15}.\newlineFor 95\frac{-9}{5}, multiply both the numerator and the denominator by 33 to get 5511.
  3. Add Fractions: Add the fractions with the common denominator.\newlineNow that both fractions have the same denominator, you can add them together.\newline(2015)+(2715)=202715=715(\frac{20}{15}) + (\frac{-27}{15}) = \frac{20 - 27}{15} = \frac{-7}{15}.
  4. Check Simplification: Check if the final fraction can be simplified.\newlineThe fraction 715-\frac{7}{15} cannot be simplified further because 77 and 1515 have no common divisors other than 11.

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