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Simplify the following fractions: c) 2/12 + 3/4, d) 9/8 + 12/9, e) 3/4 + 5/6 + 2/4

Mathematics

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Here are the solutions to the fraction addition problems:

A)

  1. Find a common denominator for 5 and 3.

    The least common multiple is 15.

    25+43=2×35×3+4×53×5\frac{2}{5} + \frac{4}{3} = \frac{2 \times 3}{5 \times 3} + \frac{4 \times 5}{3 \times 5}
  2. Rewrite the fractions with the common denominator and add them.

    =615+2015=6+2015=2615= \frac{6}{15} + \frac{20}{15} = \frac{6 + 20}{15} = \frac{26}{15}
  3. Convert the improper fraction to a mixed number.

    =11115= 1\frac{11}{15}

    The final answer is 11115\boxed{\text{1}\frac{11}{15}}.

    B)

  4. Find a common denominator for 2 and 7.

    The least common multiple is 14.

    92+67=9×72×7+6×27×2\frac{9}{2} + \frac{6}{7} = \frac{9 \times 7}{2 \times 7} + \frac{6 \times 2}{7 \times 2}
  5. Rewrite the fractions with the common denominator and add them.

    =6314+1214=63+1214=7514= \frac{63}{14} + \frac{12}{14} = \frac{63 + 12}{14} = \frac{75}{14}
  6. Convert the improper fraction to a mixed number.

    =5514= 5\frac{5}{14}

    The final answer is 5514\boxed{\text{5}\frac{5}{14}}.

    C)

  7. Find a common denominator for 12 and 4.

    The least common multiple is 12.

    812+34=812+3×34×3\frac{8}{12} + \frac{3}{4} = \frac{8}{12} + \frac{3 \times 3}{4 \times 3}
  8. Rewrite the fractions with the common denominator and add them.

    =812+912=8+912=1712= \frac{8}{12} + \frac{9}{12} = \frac{8 + 9}{12} = \frac{17}{12}
  9. Convert the improper fraction to a mixed number.

    =1512= 1\frac{5}{12}

    The final answer is 1512\boxed{\text{1}\frac{5}{12}}.

    D)

  10. Find a common denominator for 8 and 9.

    The least common multiple is 72.

    98+129=9×98×9+12×89×8\frac{9}{8} + \frac{12}{9} = \frac{9 \times 9}{8 \times 9} + \frac{12 \times 8}{9 \times 8}
  11. Rewrite the fractions with the common denominator and add them.

    =8172+9672=81+9672=17772= \frac{81}{72} + \frac{96}{72} = \frac{81 + 96}{72} = \frac{177}{72}
  12. Convert the improper fraction to a mixed number.

    =23372= 2\frac{33}{72}
  13. Simplify the fractional part by dividing the numerator and denominator by their greatest common divisor, which is 3.

    =233÷372÷3=21124= 2\frac{33 \div 3}{72 \div 3} = 2\frac{11}{24}

    The final answer is 21124\boxed{\text{2}\frac{11}{24}}.

    E)

  14. Find a common denominator for 4, 2, and 6.

    The least common multiple is 12.

    34+52+46=3×34×3+5×62×6+4×26×2\frac{3}{4} + \frac{5}{2} + \frac{4}{6} = \frac{3 \times 3}{4 \times 3} + \frac{5 \times 6}{2 \times 6} + \frac{4 \times 2}{6 \times 2}
  15. Rewrite the fractions with the common denominator and add them.

    =912+3012+812=9+30+812=4712= \frac{9}{12} + \frac{30}{12} + \frac{8}{12} = \frac{9 + 30 + 8}{12} = \frac{47}{12}
  16. Convert the improper fraction to a mixed number.

    =31112= 3\frac{11}{12}

    The final answer is 31112\boxed{\text{3}\frac{11}{12}}.

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