How do you simplify `4 1/4 div 2`?

While using fractions, we convert division into multiplication by taking the multiplicative inverse or reciprocal of the divisor.

As reciprocal of a fraction is nothing but numerator and denominator reversed, if we have to divide `a/b` by `c/d`, we just multiply `a/b` and `d/c`.

If one of the numbers is not a fraction, we write it as fraction. For example `p` as `p/1`.

Hence `4 1/4-:2`

= `(4xx4+1)/4-:2/`

= `17/4xx1/2=(17xx1)/(4xx2)=17/8`

= `(2xx8+1)/8=(2xx8)/8+1/8=2 1/8`

Given:`" "4 1/4 -:2`

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Consider the `4 1/4`

Write as:`" "4+1/4`

Multiply by 1 and you do not change the value, but 1 comes in many forms. So we can change the way it looks without changing the intrinsic value.

Multiply the 4 by 1 but in the form of `color(magenta)(1=4/4)`

`[4color(magenta)(xx4/4)]+1/4`

`[16/4]+1/4" "=" "(16+1)/4`

`"So "4 1/4" is the same as "17/4`
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Putting it all together: `-> 17/4-:2`

`color(magenta)("Shortcut method "->" Invert the 2 and multiply")`

`color(blue)(17/4xx1/2 = 17/8) larr" shortcuts make calculation faster"`

'.............................................................................................
`color(magenta)("First principle method "->" turn the 2 into quarters")`

Multiply the 2 by 1 but in the form of `color(green)(1=4/4)`

`17/4-:[2color(green)(xx4/4)]`

`17/4-:8/4`

Fraction structure is `("count")/("size indicator")" "->" "("numerator")/("denominator")`

`color(brown)("As both the size indicators are the same we can just divide counts")`

`=> 17/4-:8/4" "=" "17-:8" "=" "color(blue)(17/8)`