Question

A `1/2` cup serving of soup has a total of `70` Calories, `10` of which are from fat. What percentage of the Calories are from fat?

Answer 1

`14.3%`

Explanation:

Write the amount of calories as fat as a fraction of the total calories

`10/70` of the calories is made up of fat.

To find the percentage, `xx 100%`

`10/70 xx100%`

`=14.3%" "`to 1 dp

Answer 2

It is not clear if the 10 is a count of calories or cups.
This is focused more on teaching and explaining percentage. So it is a bit long.

Explanation:

`color(blue)("Explaining about percentage")`

Percentage is basically a fraction. However it is a special fraction as the bottom number (denominator) is always fixed at 100.

There are two ways of writing percentage and they both mean EXACTLY the same thing.

Suppose we have the unknown percentage of `x`. Then this can be written as: `x/100 or x%`

Another way of writing `x/100" is "x xx 1/100`

So we have:

`x color(white)("d") ubrace(xx 1/100)`
`x color(white)("ddd") %`

As these both mean the same thing then obviously
`%` means `xx1/100`

So when people write something like:

`a/b xx100 %` they are in fact writing `a/bxx100/100 =a/bxx1` which is totally correct. They have not changed the intrinsic value.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

`color(magenta)(ul("Option 1 - 10 calories:")" with a lot of explanation")`

As a fraction of the whole this is `10/70 =x/100`

Multiply both sides by `color(red)(100)`

`color(green)(10/70 =x/100 color(white)("ddd")->color(white)("ddd")10/70color(red)(xx100)=x/cancel(100)^1color(red)(xxcancel(100)^1) )`

`x~~14.29` to 2 decimal places `larr" Approximate answer"`
`x=14 2/7 larr" Exact answer"`

`color(indigo)("Remember that "x" is the top number of "x/100)`

So we have `("value of "x) xx1/100`
`color(brown)("If we now use the word 'percent' or the symbol % it")` `color(brown)(" replaces the "xx1/100)`

`bar(ul(| color(white)(2/2)("value of "x)" is "14 2/7" giving "14 2/7%color(white)(2/2)|))`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(magenta)(ul("Option 1 - 10 cups:")" with little explanation")`

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

`color(green)(10/12color(red)(xx1) color(white)("d")->color(white)("d") 10/12color(red)(xx100/100)color(white)("d")`

`color(white)("ddddddd")->color(white)("d")color(green)( 10/12color(red)(xx100color(purple)(xx1/100)) =83 1/3color(purple)(%) )`