Question

Compare simplifying before multiplying fractions with simplifying after multiplying the fractions

Answer 1

We will start using a new way to indicate simplifying fractions. When a numerator or
a denominator gets simplified, we will cross it out with a slash and write the new
numerator or denominator next to it (either above it or below it).The number you divide by (the 4) does not get indicated in any way! You only
think about it in your mind: “I divide 12 by 4, and get 3. I divide 20 by 4, and get 5.”You may not see any advantage over the “old” method yet, but this shortcut will
come in handy soon.

Answer 2

We can compare this using example:

Suppose the two fractions are
`(20)/(25)` and
`(12)/(36)`

When we simplify before multiplying:

`(20)/(25)` (dividing both numerator and denominator by 5) in simplified form becomes
`(4)/(5)`

Similarly
`(12)/(36)` becomes
`(1)/(3)`

Now multiplying:

`(4)/(5) *(1)/(3)` =
`(4)/(15)`

When we simplify after multiplying:

`(20)/(25) *(12)/(36)` =
`(240)/(900)`

Now simplifying this:

Dividing both numerator and denominator by 10; we get

`(24)/(90)`

Now dividing by 2:

`(12)/(45)`

Now dividing by 3:

`(4)/(15)`

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Now, we can see and compare that when we multiply after simplifying, the result is simplified and calculation is easier.

When we do not simplify and multiply at first, the results are bigger numbers and it is difficult to simplify bigger numbers.