Question

A strip of wood `78` inches long is to be cut into pieces `3` `3/4` inches long. How many pieces can be cut?

Answer 1

`20` pieces can be cut and a piece of `3` inches will be left out,

Explanation:

When an object of size `x` (whether length-wise, weight-wise or size-wise) into equal pieces of `y` size, the outcome in number of pieces is given by `x-:y=x/y`.

Here 1 strip of wood `78` inches long is to be cut into pieces `3 3/4=(3xx4+3)/4=15/4` inches long, the number of pieces that can be cut is

`78/(15/4)=(26cancel(78)xx4)/(5cancel(15))=(26xx4)/5=104/5`

(note that dividing by a fraction means multiplying by its multiplicative inverse)

As `104` when divided by `5` gives `20` as quotient and `4` as remainder,

we will have `20` pieces of length `3 3/4` (note that they are together `20xx15/4=75` inches long) and a piece of `78-75` i.e. `3` inches long will be left out.