Question

A strip of wood \[78\] inches long is to be cut into pieces \[3\dfrac{3}{4}\] inches long. How many pieces can be cut?

Answer 1

Hint: As we know that we have given an object (or a thing) of size \[x\] (whether length wise, weight wise, volume wise, area wise) and we want to cut it into equal parts of size \[y\] then we can find the outcome or total number of pieces of wooden logs as per given formula that is \[x-y=\dfrac{x}{y}\].

Complete step by step solution:
Firstly we will convert the given mix fraction that is \[3\dfrac{3}{4}\] inches into an improper fraction.
So, the given mix fraction \[3\dfrac{3}{4}\] inches becomes \[\dfrac{15}{4}\] inches.
Now, It is given in the question that we have one \[(1)\] strip of wooden \[\log \] of \[78\] inches long that is to be cut into \[\dfrac{15}{9}\] inches long pieces.
On further simplifying the above expression we will get, on performing the division of \[104\] by \[5\] the whole division can not take place because we know that \[104\] is not completely divisible by \[5\].
So, we can conclude that on dividing \[104\] by \[5\] we get \[20\] as quotient and \[4\] as remainder.
Which implies we will have \[20\] pieces of wooden log or (strip) each of them having length \[\dfrac{14}{4}\] inches. Which can be written as \[3\dfrac{3}{4}\] inches.
Moreover, \[20\times \dfrac{15}{4}=75\] inches long wooden strips and a piece of length \[(78\,\,\,-\,75\,=3)\] inches long will be left out.

Note: Dividing by a fraction means multiplying by its multiplicative inverse. i.e. $\dfrac{a}{\left(\dfrac{b}{c}\right)}=\dfrac{a\times c}{b} \,\,\,\,\,\,\,\,(\because $ multiplicative inverse of $\dfrac{b}{c}$ is $\dfrac{c}{a})$
Also, convert a mixed fraction to an improper fraction follow these steps:
• Multiply the whole number of parts by the fraction’s denominator and add that to the numerator.
• Then write the result on top of the denominator. i.e. $a\dfrac{b}{c}=\dfrac{a\times c+b}{c}$