Question

How do you solve `6.1p = 4.5`?

Answer 1

`p =0.7377` to 4 decimal places.

Explanation:

`6.1p = 4.5`

divide both sides by `6.1` to make only `p` alone on left side.

`(cancel6.1p)/cancel6.1 = 4.5/6.1`

`p = 0.7377`

Answer 2

`p=45/61`

Calculation method given in a lot of detail.

Explanation:

`color(blue)("Method")`

Think of the given equation as:`" "6.1xxp=4.5`

If you can change the 6.1 into 1 then the left hand side would become:`" "1xxp` and 1 times any number does not change its value.

In equations, what you do to one side of the = you do to the other side to maintain correct proportions (ratio)

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

Divide each side by 6.1`color(white)(.)` (`color(white)(.)` this is the same as multiply by `color(blue)(1/6.1 )color(white)(.)`)

`color(brown)(" "6.1p" "=" "4.5)`

`color(brown)(color(blue)(1/6.1xx)6.1xxp" "=" "color(blue)(1/6.1xx)4.5)`

`color(brown)(" "6.1/(color(blue)(6.1))xxp" "=" "4.5/(color(blue)(6.1)))`

But `6.1/6.1=1` giving:

`color(brown)(" "1xxp" "=" "4.5/(color(blue)(6.1)))`

`color(brown)(" "p" "=" "4.5/(color(blue)(6.1)))`

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If you divide 4.5 by 6.1 you get a very 'long' decimal value and if you round this down or up you will not be as precise as `4.5/6.1`. So lets keep this as a fraction. However decimal values in fractions is not good practice so lets change this to whole numbers.
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`color(white)(.)`

`color(green)(4.5/6.1" " =" "[4.5/6.1color(red)(xx1)]" "=" "[4.5/6.1color(red)(xx10/10)]" "=" "45/61 )`

So write the solution as:

`" "color(blue)(p=45/61)`