How do you simplify #(2n)/5 + (-n/6)#?

Question

Eli Assouline · Accepted Answer

#(7n)/30#

Consider #+(-n/6)#

This is like #(+1)xx(-1)xxn/6#

Multiply plus and minus and the answer is minus

So #(+1)xx(-1)xxn/6 = -n/6#

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Giving:#" "(2n)/5-n/6#

To be able to directly add or subtract the top numbers of fraction (count) the bottom numbers (size indicators) must be the same.

#("top number")/("bottom number")->("count")/("size indicator")->("numerator")/("denominator")#

So we need to make the bottom numbers the same. I chose 30

#color(brown)("Write as: ")((2n)/5xx1)-(n/6xx1)#

#color(brown)("But 1 comes in many forms")#

#((2n)/5xx6/6)-(n/6xx5/5)#

#(2nxx6)/(5xx6) -(nxx5)/(6xx5)#

#(12n)/30-(5n)/30 color(brown)(larr" Now we can directly subtract the counts")#

#color(brown)("but ")12n-5n= 7n#

#=>(12n)/30-(5n)/30 = (7n)/30#

Eva Abramson · Answer

undefined To simplify (2n)/5 + (-n/6), you can find a common denominator and combine the fractions. The common denominator is 30. Multiply the numerator and denominator of (2n)/5 by 6, and multiply the numerator and denominator of (-n/6) by 5. This gives you (12n)/30 + (-5n)/30. Combine the numerators to get (12n - 5n)/30. Simplify the numerator to get 7n/30. Therefore, (2n)/5 + (-n/6) simplifies to 7n/30.