Question

How do you solve `a/15=4/5`?

Answer 1

`color(teal)(a=12`

Explanation:

Simply use cross multiplication `...`
`color(teal)(a/15=4/5`

`or,` `color(teal)(5a=4*15`

`or,` `color(teal)(a=(4*15)/5=4*3=12`

hope that helped.

Answer 2

a = 12

Explanation:

Here, `a/15 = 4/5`
Or,`5*a` = `15*4`
Or,5a = 60
Or,a = `60/5`
Or,a = 12

Answer 3

`a=12`

Explanation:

`"Alternatively multiply both sides of the equation by"`
`"the "color(blue)"lowest common multiple of 15 and 5"`

`"the lowest common multiple of 15 and 5 is 15"`

`cancel(15)^1xxa/cancel(15)^1=cancel(15)^3xx4/cancel(5)^1`

`rArra=3xx4=12`

Answer 4

`a=12`

Explanation:

`color(blue)("Important fact")`

A fraction's structure is such that we have:

`("numerators")/("denominators") color(white)("d")->color(white)("dd") ("count")/("size indicator of what is being counted")`

You can not `color(purple)(ul("DIRECTLY"))` add, subtract or compare the 'counts' unless the 'size indicators' are the same.

Multiply by 1 and you do not change the value of something. However, 1 comes in many forms so you change the way something looks without changing its value.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

`color(green)(a/15=[4/5color(red)(xx1)] color(white)("dddd")->color(white)("dddd")a/15=[4/5color(red)(xx3/3) ])`

`color(green)(color(white)("dddddddddddddddd")->color(white)("dddd")a/15=12/15)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now that the bottom numbers or size indicators (denominators) are the same we can just compare the top numbers or counts (numerators).

Mathematically you say: multiply both sides by 15#

So we now have: `a=12`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Check")`

If we divide the left hand side by the right hand side we will get 1 if they are the same.

`12/15-:4/5`

`12/15xx5/4`

`5/15xx12/4`

`1/3xx3/1=1`