High School

Sinchana has 16 4/5 m of ribbon. If she divides the ribbon into 8 equal parts, then the length of each piece is ____ m.

Answer :

To find out the length of each piece when Sinchana divides her ribbon into 8 equal parts, follow these steps:

  1. Convert the Mixed Number to an Improper Fraction:

    Sinchana has [tex]16\frac{4}{5}[/tex] meters of ribbon. First, convert this mixed number into an improper fraction.

    [tex]16\frac{4}{5} = \frac{16 \times 5 + 4}{5} = \frac{80 + 4}{5} = \frac{84}{5}[/tex]

  2. Divide the Improper Fraction by 8:

    To find the length of each piece, divide the total length by 8. Dividing a fraction by a whole number is the same as multiplying the fraction by the reciprocal of that number.

    [tex]\frac{84}{5} \div 8 = \frac{84}{5} \times \frac{1}{8} = \frac{84}{40}[/tex]

  3. Simplify the Fraction:

    Simplifying [tex]\frac{84}{40}[/tex] involves finding the greatest common divisor (GCD) of 84 and 40. The GCD is 4.

    [tex]\frac{84 \div 4}{40 \div 4} = \frac{21}{10}[/tex]

  4. Convert to a Mixed Number (if necessary):

    [tex]\frac{21}{10}[/tex] can be converted back to a mixed number:

    [tex]21 \div 10 = 2\text{ remainder }1[/tex]

    So, [tex]\frac{21}{10} = 2\frac{1}{10}[/tex].

Therefore, each piece of ribbon is [tex]2\frac{1}{10}[/tex] meters long.

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