Question

What is `8/11+6/7xx21/36`?

Answer 1

`27/22 = 1 5/22`

Explanation:

Remember to always count how many terms there are in an expression. That tells you where to start. There are 2 terms in this example.

`8/11 + 6/7xx21/36`

`8/11 + cancel6/cancel7xxcancel21^3/(cancel36^6)" "larr` only cancel across multiplication

`8/11 +cancel3^1/cancel6^2`

`8/11+1/2" "larr` find common denominator

`(16+11)/22`

`27/22 = 1 5/22`

Answer 2

`27/22 -> 1 5/22`

Explanation:

Given:`" "8/11+6/7xx21/36`

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Multiply has a higher importance than add when the question is written this way. So it is done first.

`color(blue)("Consider the expression part "6/7xx21/36`

Look at this example: `2xx4` gives the same answer as `4xx2`

So for multiply you can swap thing round. This property is called Commutative.

so: `color(blue)(6/7)xxcolor(red)(21/36)" is the same as " color(blue)(6/(color(red)(36))xx(color(red)(21))/7)`

`(cancel(6)^1)/(cancel(36)^6) xx(cancel(21)^3)/(cancel(7)^1)`

`=1/6xx3/1=3/6 -> (3-:3)/(6-:3) =1/2`

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`color(blue)("Putting it all together")`

`8/11+6/7xx21/36" "=" " 8/11+1/2`

Multiply by 1 and you do not change the value

`(8/11color(red)(xx1))+(1/2color(magenta)(xx1))`

But there are many ways to write 1

`(8/11color(red)(xx2/2))+(1/2color(magenta)(xx11/11))`

`16/22+11/22 = 27/22 -> 1 5/22`