Please solve this 3 3/4 +2 3/16(solve it step by step

Mathematics

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Answer

515165 \frac{15}{16}

Step-by-step solution

4 steps
  1. Convert the mixed numbers to improper fractions.

    To convert a mixed number abca \frac{b}{c} to an improper fraction, use the formula (a×c)+bc\frac{(a \times c) + b}{c}.

    334=(3×4)+34=12+34=1543 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} 2316=(2×16)+316=32+316=35162 \frac{3}{16} = \frac{(2 \times 16) + 3}{16} = \frac{32 + 3}{16} = \frac{35}{16}
  2. Find a common denominator for the fractions.

    The denominators are 4 and 16. The least common multiple (LCM) of 4 and 16 is 16.
    Convert 154\frac{15}{4} to an equivalent fraction with a denominator of 16:

    154=15×44×4=6016\frac{15}{4} = \frac{15 \times 4}{4 \times 4} = \frac{60}{16}

    Now the expression is 6016+3516\frac{60}{16} + \frac{35}{16}.

  3. Add the fractions.

    Add the numerators while keeping the common denominator:

    6016+3516=60+3516=9516\frac{60}{16} + \frac{35}{16} = \frac{60 + 35}{16} = \frac{95}{16}
  4. Convert the improper fraction back to a mixed number.

    Divide the numerator (95) by the denominator (16).
    95÷16=595 \div 16 = 5 with a remainder of 95−(16×5)=95−80=1595 - (16 \times 5) = 95 - 80 = 15.
    So, the mixed number is 515165 \frac{15}{16}.

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