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Add the following mixed numbers: e) 3/4 + 4 1/6 f) 7 1/3 + 16 4/7 g) 5 1/4 + 10 1/3

Mathematics

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17 steps

Here are the solutions for the remaining mixed number addition problems:

Part e· 4 steps

34+416\frac{3}{4} + 4\frac{1}{6}

  1. The whole number is 4.

  2. Find a common denominator for the fractions 34\frac{3}{4} and 16\frac{1}{6}.

    The least common multiple of 4 and 6 is 12.

    34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} 16=1×26×2=212\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
  3. Add the fractions.

    912+212=9+212=1112\frac{9}{12} + \frac{2}{12} = \frac{9+2}{12} = \frac{11}{12}
  4. Combine the whole number and the fraction.

    4+1112=411124 + \frac{11}{12} = 4\frac{11}{12}

    The final answer is \boxed{\text{4\frac{11}{12}}}.

Part f· 4 steps

713+16477\frac{1}{3} + 16\frac{4}{7}

  1. Add the whole numbers.

    7+16=237 + 16 = 23
  2. Find a common denominator for the fractions 13\frac{1}{3} and 47\frac{4}{7}.

    The least common multiple of 3 and 7 is 21.

    13=1×73×7=721\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21} 47=4×37×3=1221\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}
  3. Add the fractions.

    721+1221=7+1221=1921\frac{7}{21} + \frac{12}{21} = \frac{7+12}{21} = \frac{19}{21}
  4. Combine the whole number and the fraction.

    23+1921=23192123 + \frac{19}{21} = 23\frac{19}{21}

    The final answer is \boxed{\text{23\frac{19}{21}}}.

Part g· 4 steps

514+10135\frac{1}{4} + 10\frac{1}{3}

  1. Add the whole numbers.

    5+10=155 + 10 = 15
  2. Find a common denominator for the fractions 14\frac{1}{4} and 13\frac{1}{3}.

    The least common multiple of 4 and 3 is 12.

    14=1×34×3=312\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} 13=1×43×4=412\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
  3. Add the fractions.

    312+412=3+412=712\frac{3}{12} + \frac{4}{12} = \frac{3+4}{12} = \frac{7}{12}
  4. Combine the whole number and the fraction.

    15+712=1571215 + \frac{7}{12} = 15\frac{7}{12}

    The final answer is \boxed{\text{15\frac{7}{12}}}.

Part h· 5 steps

4710+8164\frac{7}{10} + 8\frac{1}{6}

  1. Add the whole numbers.

    4+8=124 + 8 = 12
  2. Find a common denominator for the fractions 710\frac{7}{10} and 16\frac{1}{6}.

    The least common multiple of 10 and 6 is 30.

    710=7×310×3=2130\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30} 16=1×56×5=530\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
  3. Add the fractions.

    2130+530=21+530=2630\frac{21}{30} + \frac{5}{30} = \frac{21+5}{30} = \frac{26}{30}
  4. Simplify the fraction.

    2630=26÷230÷2=1315\frac{26}{30} = \frac{26 \div 2}{30 \div 2} = \frac{13}{15}
  5. Combine the whole number and the simplified fraction.

    12+1315=12131512 + \frac{13}{15} = 12\frac{13}{15}

    The final answer is \boxed{\text{12\frac{13}{15}}}.

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