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