Question

How do you evaluate `16\div ( 0.8\div 0.04)`?

Answer 1

`=0.8`

Explanation:

Although there are two divisions, they are not equally important.
One is in a bracket which means it has to be done first.

We are dividing 16 by the answer to a division.

`16 div (0.8 div 0.04)`

`= 16 div 0.8/0.04" "larr` multiply by the reciprocal

`= 16 xx0.04/0.8" "larr` dividing BY a fraction is uncomfortable

`=16 xx 0.04/0.8 xx10/10" "larr (10/10 = 1)`

`=16 xx0.4/8`

`=cancel(16)2 xx0.4/cancel8`

`=0.8`
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Note that: `color(blue)(12 div 6 div 2)` and `color(red)(12 div (6div2)`) are different!

`color(blue)(12 div 6 div 2)" "` and `color(red)(12 div (6div2)`

`=color(blue)(2 div 2)" " =color(red)(12 div 3`

`=color(blue)(1)" " =color(red)(4)`

Answer 2

`4/5 = 0.8`

Explanation:

`color(blue)("Step 1")`

Do the brackets first so we have: `0.8-:0.04`

`color(green)(0.8/0.04-= 0.8/0.04color(red)(xx1)" " =" " 0.8/0.04 color(red)(xx100/100))`

`" "=" "color(green)(80/4 = 20)`

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`color(blue)("Step 2")`

Divide the contents of the brackets into the 16 giving

`" "color(green)(16/20 -= (16color(red)(-:4))/(20color(red)(-:4)) = 4/5)`
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`color(blue)("Step 3")`

Make the answer the same format as the question which is decimal.

`color(brown)("Notice that the denominator of 20 in "16/20" is "2xx10)`

`" "color(green)(16/20-=(16color(red)(-:2))/(20color(red)(-:2)) = 8/10 = 0.8`