Question

A recipe calls for a total of `3 2/3` cups flour and sugar. if the recipe calls for `1/4`cup of sugar, how much flour is needed?

Answer 1

This is very detailed as I wish to make some principles about fractions clear.

`3 5/12`

Explanation:

This question boils down to `3 2/3-1/4`

A fractions structure is that of:

`("count")/("size indicator of what you are counting") ->("numerator")/("denominator")`

You can not directly add or subtract the counts (numerators) unless the size indicators (denominators) are the same.

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`color(blue)("Consider "3 2/3)`

Write as `3+2/3`

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

`color(green)( [3color(red)(xx1)]+2/3`

`color(green)( [3color(red)(xx3/3)]+2/3`

`" "9/3" "+2/3" "=" "11/3`
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`color(blue)("Putting it all together")`

`3 2/3-1/4" "->" "11/3-1/4`

But the size indicators are not the same. I chose to make them become 12

`11/3-1/4" "->" "color(green)( [11/3color(red)(xx1)]-[1/4color(red)(xx1)])`

`color(green)( " "->" "[11/3color(red)(xx4/4)]-[1/4color(red)(xx3/3)])`

`color(green)(" "->" "44/12" "-" "3/12)`

Now we may subtract the counts

`" "->" "(44-3)/12" "=" "41/12`

But this is the same as `12/12+12/12+12/12+5/12`

`" "=" "1color(white)(2)+color(white)(2)1color(white)(2)+color(white)(2)1color(white)(2)+5/12" "=" "3 5/12`