Question

A snail crawls 5/8 inch in 3/4 minute. What is the snails speed in inches per minute?

Answer 1

`5/6` inch/minute

Explanation:

Whenever you are working with a question of rate where two different quantities are being compared, the required units will indicate which quantity is to be divided by which.

In this case you want to know inches per minute.

Therefore: `5/8 "inches" div 3/4 "minute"`

`5/8 div 3/4`

=`5/8 xx 4/3 " "larr` multiply by the reciprocal

=`5/cancel8^2 xx cancel4/3`

=`5/6`

Answer 2

This is where the shortcut for dealing with 'divide by `3/4`' comes from.

Explanation:

Using ratio but in the fractional format giving:

`5/8" inches : "3/4" minutes "-> ("inches")/("minutes") = (" "5/8" ")/(3/4)`

`color(brown)("But we need to change "3/4" minutes into 1 minute.")` `color(brown)("We can do this by multiplying it by "4/3)`

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

Multiply by 1 but with `1=(" "4/3" ")/(4/3)`

`color(red)([(" "5/8" ")/(3/4)color(blue)(xx" "1)] " "->" "[(" "5/8" ")/(3/4)color(blue)(xx" "(" "4/3" ")/(4/3))]`

`(5/8xx4/3)/(3/4xx4/3)" " =" " (color(white)(.)5/6color(white)(.))/1 =("inches")/("minutes")`
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`color(blue)("Foot note")`

If you look at the 9th line down in the explanation you will spot that it has:

`5/8xx4/3` This is the shortcut part where

`5/8-:3/4 -> 5/8xx4/3`