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How do you simplify #10\div [ ( 1+ 5\div 6]#?

Answer 1

Nova Allen

#60/11=5 5/11#

To evaluate an expression with #color(blue)"mixed operations"# there is a particular order that must be followed.

Follow the order as set out in the acronym PEMDAS

{Parenthesis (brackets), Exponents (powers), Multiplication, Division, Addition, Subtraction ]

#rArr10-:[(1+5-:6)]#

Evaluating the #color(blue)"inner bracket first"#

#5-:6=5/6larrcolor(red)"division in exact form"#

#rArr1+5/6=1 5/6=11/6larrcolor(red)" inner bracket"#

The expression is now reduced to.

#10-:11/6#

#=10/1xx6/11#

#=(10xx6)/(1xx11)#

#=60/11larrcolor(red)" improper fraction"#

#=5 5/11larrcolor(red)" mixed number"#

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Answer 2

Riley Anderson

To simplify (10 \div [(1 + \frac{5}{6})]), you first evaluate the expression inside the parentheses, then perform the division.

(1 + \frac{5}{6} = \frac{6}{6} + \frac{5}{6} = \frac{11}{6})

So, (10 \div \frac{11}{6} = 10 \times \frac{6}{11} = \frac{60}{11})

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.