Question

How do you solve `3.25 = a/2.5`?

Answer 1

A slightly different way of thinking about the multiplication

Explanation:

`color(red)("Step 1")`

Write as `" "3.25=1/2.5xxa`

Multiply both sides by `2.5`

`3.25xx2.5=2.5/2.5xxa`

But `2.5/25=1` so the right hand side ends up as just `a`

`3.25xx2.5=a`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(red)("Step 2")`

Write `2.5` as `" "color(green)(2)color(blue)( + 1/2)`

`3.25xx2.5" "->" "color(brown)(3.25)(color(green)(2)" "+" "color(blue)(1/2))" "=a`

`" "6.5" "+" "1.5+0.125=a`

Note that:
`" "color(brown)(3.25)color(green)(xx2) =color(magenta)(6.5)`

`" "color(brown)(3.25color(blue)(xx1/2)->(3+0.25)color(blue)(1/2))->color(magenta)(1.5+0.125)`

`a=color(magenta)(6.5+1.5+0.125)=8.125`