Answer :

To determine how many pieces each 5 1/6 meters long can be cut from a cloth that is 77 1/2 meters long, we need to solve a division problem involving fractions.

First, let's convert these mixed numbers to improper fractions to make the calculation easier.

  1. Convert 5 1/6 to an improper fraction:

    • Multiply the whole number (5) by the denominator (6) and then add the numerator (1):
      [tex]5 \times 6 + 1 = 31[/tex]
    • So, [tex]5 \frac{1}{6} = \frac{31}{6}[/tex]

  2. Next, convert 77 1/2 to an improper fraction:

    • Multiply the whole number (77) by the denominator (2) and then add the numerator (1):
      [tex]77 \times 2 + 1 = 155[/tex]
    • So, [tex]77 \frac{1}{2} = \frac{155}{2}[/tex]

Now, divide the total cloth length by the length of each piece:

  1. Perform the division [tex]\frac{155}{2} \div \frac{31}{6}[/tex].

    • Dividing fractions is the same as multiplying by the reciprocal. So, we set up the equation:
      [tex]\frac{155}{2} \times \frac{6}{31}[/tex]
    • Multiply the numerators and the denominators:
      • Numerators: [tex]155 \times 6 = 930[/tex]
      • Denominators: [tex]2 \times 31 = 62[/tex]
    • The result is: [tex]\frac{930}{62}[/tex]

  2. Simplify the fraction:

    • Divide both the numerator and the denominator by their greatest common divisor, which is 62:
      [tex]\frac{930 \div 62}{62 \div 62} = \frac{15}{1} = 15[/tex]

So, you can cut 15 pieces of cloth, each 5 1/6 meters long, from a 77 1/2 meters piece of cloth.

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Rewritten by : Barada