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Solve the following fraction addition and subtraction problems:
Mathematics
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Step-by-step solution
19 stepsHere are the solutions to the fraction problems:
- :
Combine the numerators since the denominators are the same.
$$ \frac{2+3-2}{7} $$Perform the arithmetic in the numerator.
$$ \frac{5-2}{7} = \frac{3}{7} $$ The simplified answer is $\boxed{\frac{3}{7}}$.2. :
Combine the numerators.
$$ \frac{2+4-7}{9} $$Perform the arithmetic in the numerator.
$$ \frac{6-7}{9} = \frac{-1}{9} $$ The simplified answer is $\boxed{-\frac{1}{9}}$.3. :
Combine the numerators.
$$ \frac{7-5-3+8}{12} $$Perform the arithmetic in the numerator from left to right.
$$ \frac{2-3+8}{12} = \frac{-1+8}{12} = \frac{7}{12} $$ The simplified answer is $\boxed{\frac{7}{12}}$.4. :
Combine the numerators.
$$ \frac{8+7-9}{10} $$Perform the arithmetic in the numerator.
$$ \frac{15-9}{10} = \frac{6}{10} $$Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.
$$ \frac{6 \div 2}{10 \div 2} = \frac{3}{5} $$ The simplified answer is $\boxed{\frac{3}{5}}$.5. :
Combine the numerators.
$$ \frac{12-7-5+11}{15} $$Perform the arithmetic in the numerator from left to right.
$$ \frac{5-5+11}{15} = \frac{0+11}{15} = \frac{11}{15} $$ The simplified answer is $\boxed{\frac{11}{15}}$.6. :
Combine the numerators.
$$ \frac{9-5-3+10}{8} $$Perform the arithmetic in the numerator from left to right.
$$ \frac{4-3+10}{8} = \frac{1+10}{8} = \frac{11}{8} $$ The simplified answer is $\boxed{\frac{11}{8}}$.7. :
Combine the numerators.
$$ \frac{7-1}{9} $$Perform the arithmetic in the numerator.
$$ \frac{6}{9} $$Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.
$$ \frac{6 \div 3}{9 \div 3} = \frac{2}{3} $$ The simplified answer is $\boxed{\frac{2}{3}}$.8. :
Combine the numerators.
$$ \frac{10-8+7-4}{15} $$Perform the arithmetic in the numerator from left to right.
$$ \frac{2+7-4}{15} = \frac{9-4}{15} = \frac{5}{15} $$Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.
$$ \frac{5 \div 5}{15 \div 5} = \frac{1}{3} $$ The simplified answer is $\boxed{\frac{1}{3}}$.
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