Question

Question #42209

Answer 1

3

Explanation:

`color(blue)("Preamble")`

A fractions structure (using description ) is

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

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

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

Consider: `a-:b`. The dividend is `a`

I am assuming the interpretation of your question is

`1 1/2" dividend by " 1/2`

`1 1/2color(white)("dddd") -: color(white)("ddddd")1/2`

Note that `1 1/2` is the same as `3/2` so we have:

`3/2-:1/2`

There are two approaches.

`color(brown)("Approach 1:")`

As the bottom numbers (numerators) are the same we can just divide the top numbers and totally forget about the bottom ones.

`color(brown)("Approach 2: - shortcut method")`

Turn the `1/2` upside down and multiply

`3/cancel(2)^1xxcancel(2)^1/1color(white)("d")=color(white)("d")3/1=3`

Notice that the two's completely cancel out confirming Approach 1

The shortcut method works when the denominators are not the same. Explaining why is not provided as I do not wish to confuse you.