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A rope is 11 m long. Two pieces are cut off. The first piece is 3 2/3 m long and the second piece is 3 1/10 m long. How much rope is left?

Mathematics

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Answer

4730 m4 \frac{7}{30} \text{ m}

Step-by-step solution

5 steps

  1. Identify the total length of the rope and the lengths of the pieces cut off.

    Total length of the rope =11= 11 m.
    Length of the first piece cut off =323= 3 \frac{2}{3} m.
    Length of the second piece cut off =3110= 3 \frac{1}{10} m.

  2. Convert the mixed numbers to improper fractions.

    323=(3×3)+23=9+23=113 m3 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \text{ m} 3110=(3×10)+110=30+110=3110 m3 \frac{1}{10} = \frac{(3 \times 10) + 1}{10} = \frac{30 + 1}{10} = \frac{31}{10} \text{ m}

  3. Calculate the total length of the pieces cut off.

    To add the fractions, find a common denominator, which is 3×10=303 \times 10 = 30.

    Total cut length=113+3110\text{Total cut length} = \frac{11}{3} + \frac{31}{10} Total cut length=11×103×10+31×310×3\text{Total cut length} = \frac{11 \times 10}{3 \times 10} + \frac{31 \times 3}{10 \times 3} Total cut length=11030+9330\text{Total cut length} = \frac{110}{30} + \frac{93}{30} Total cut length=110+9330=20330 m\text{Total cut length} = \frac{110 + 93}{30} = \frac{203}{30} \text{ m}

  4. Calculate the length of the remaining rope.

    Subtract the total cut length from the original total length of the rope.

    Remaining length=11−20330\text{Remaining length} = 11 - \frac{203}{30}

    Convert 11 to a fraction with a denominator of 30:

    11=11×3030=3303011 = \frac{11 \times 30}{30} = \frac{330}{30} Remaining length=33030−20330\text{Remaining length} = \frac{330}{30} - \frac{203}{30} Remaining length=330−20330=12730 m\text{Remaining length} = \frac{330 - 203}{30} = \frac{127}{30} \text{ m}

  5. Convert the improper fraction to a mixed number.

    12730=4730 m\frac{127}{30} = 4 \frac{7}{30} \text{ m}

    The length of the remaining rope is 4730 m4 \frac{7}{30} \text{ m}.

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