(3 1/5*0,75)+(1/5:11/5)=

Mathematics

ScanSolve AI Answer

Answer

13755\frac{137}{55}

Step-by-step solution

4 steps
  1. Convert the mixed number and decimal to fractions in the first parenthesis.

    The mixed number 3153 \frac{1}{5} can be converted to an improper fraction:

    315=(3×5)+15=15+15=1653 \frac{1}{5} = \frac{(3 \times 5) + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5}

    The decimal 0.75 (from 0,75) can be converted to a fraction:

    0.75=75100=340.75 = \frac{75}{100} = \frac{3}{4}

    So the first parenthesis becomes:

    (165×34)\left(\frac{16}{5} \times \frac{3}{4}\right)
  2. Perform the multiplication in the first parenthesis.

    165×34=16×35×4=4820\frac{16}{5} \times \frac{3}{4} = \frac{16 \times 3}{5 \times 4} = \frac{48}{20}

    Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:

    4820=125\frac{48}{20} = \frac{12}{5}
  3. Perform the division in the second parenthesis.

    To divide by a fraction, multiply by its reciprocal:

    15:115=15×511\frac{1}{5} : \frac{11}{5} = \frac{1}{5} \times \frac{5}{11}

    Now, multiply the fractions:

    15×511=1×55×11=555\frac{1}{5} \times \frac{5}{11} = \frac{1 \times 5}{5 \times 11} = \frac{5}{55}

    Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5:

    555=111\frac{5}{55} = \frac{1}{11}
  4. Perform the final addition using the results from Step 2 and Step 3.

    We need to add 125\frac{12}{5} and 111\frac{1}{11}. To add fractions, find a common denominator. The least common multiple of 5 and 11 is 5×11=555 \times 11 = 55.
    Convert 125\frac{12}{5} to a fraction with denominator 55:

    125=12×115×11=13255\frac{12}{5} = \frac{12 \times 11}{5 \times 11} = \frac{132}{55}

    Convert 111\frac{1}{11} to a fraction with denominator 55:

    111=1×511×5=555\frac{1}{11} = \frac{1 \times 5}{11 \times 5} = \frac{5}{55}

    Now, add the fractions:

    13255+555=132+555=13755\frac{132}{55} + \frac{5}{55} = \frac{132 + 5}{55} = \frac{137}{55}

    The final answer is 13755\frac{137}{55}.

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