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

2 Answers
Sep 12, 2016

#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#

Sep 18, 2016

#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#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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#