Question

How do you multiply `4 2/3 div 1 5/8`?

Answer 1

The question is given in fractions so the answer has to be in fractions.

`2color(white)(.)34/39`

Explanation:

`color(brown)("Multiply any number by 1 and you do not change its value")`
`color(brown)("This is a 'trick' to convert a whole number into a fraction."`

We know that `4xx1 =4`

But `3/3` is another way of writing 1

So instead of writing `4xx1 =4` we could write `4xx 3/3 =4`

But `4xx3/3" is the same as "(4xx3)/3 =12/3`

So `12/3` is 4 converted into thirds!
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`color(blue)("Answering your question")`

Given:`color(green)(" "4 2/3 -: 1 5/8)`

Converting 4 into thirds and 1 into eights

`color(green)(" "(12/3 + 2/3) -: (8/8+5/8))`

`color(green)(" "14/3-:13/8)`

Using the shortcut rule of: when dividing turn the divisor (what you are dividing by) upside down and then multiply

`color(green)(" "14/3xx8/13)`

`color(green)(" "(14xx8)/(3xx13))`

`color(green)(" "112/39)`

`color(blue)(" "2 34/39)`
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`color(brown)("Another trick")`

Suppose you have the whole number of say 6. Although not normally done it is perfectly correct to write 6 as `6/1`

So if you have `3 -: 6` you are permitted to write it as

`3/1-: 6/1 = 3/1 xx1/6 = (3xx1)/(1xx6) = 3/6`