Question

If 10 percent piece was cut off from a $7m$ long ribbon
(i)What fraction of ribbon was cut?
(ii)What is the length of each ribbon cut in meters?

Answer 1

Hint: A fraction represents a part of a whole. Here, in this case $7m$ is the total length of the ribbon. Therefore, $7m \Rightarrow 100\% $. And a $10\%$ Piece was cut off from the 7m long ribbon. By assuming $x$ as the length of the piece that was cut off we can calculate the length of the ribbon that was cut off.

Complete step-by-step solution:
It is given in the question that the total length of the ribbon is $7m$ and the $10\% $ piece was cut off from that total length.
Let $x$ be the length of the ribbon that was cut off from the total length of $7m$
Here $7m \Rightarrow 100\% $
$x \Rightarrow 10\% $
The value of $x$ can be calculated as follows
$x = \dfrac{{7 \times 10}}{{100}}m$
$x = 0.7m$
$ \Rightarrow $ That the ribbon can be divided into $10$ equal parts of $0.7m$ length each out of a$7m$ long ribbon.
(i)Fraction of ribbon that was cut off:
${\text{Fraction}} = \dfrac{{{\text{length of the ribbon that was cut off}}}}{{{\text{Total length of the ribbon}}}}$
$\text{Fraction} = \dfrac{{0.7m}}{{7m}}$
$\text{Fraction} = \dfrac{1}{{10}}$
Fraction of ribbon that was cut off from the $7m$ long ribbon is $\dfrac{1}{{10}}$
(ii)Length of each part of the ribbon:
Length of the ribbon that was cut off is $0.7m$ (from the above)
${\text{Length of the ribbon remaining = Total length of the ribbon - Length of ribbon that was cut off}}$
${\text{Length of the ribbon remaining = }}7m - 0.7m = 6.3m$
Therefore, the length of each part of the ribbon are $0.7m$ and $6.3m$.

Note: Length of each part of the ribbon can also be calculated in other ways. By using the formula ${\text{Length of each part = Fraction of each part }} \times {\text{ Total length }}$ we can get the length of each part. Since the fraction of ribbon that was cut off is $\dfrac{1}{{10}}$ the fraction of the remaining part will be $1 - \dfrac{1}{{10}} = \dfrac{9}{{10}}$.