Solve 94÷(2×(70÷(5×8))): Complete Order of Operations Challenge

Question

Solve the following problem:

94:(2×(70:(5×8)))= 94:(2\times(70:(5\times8)))=

Video Solution

Solution Steps

00:00 Solve
00:03 We always solve inner parentheses first, even within parentheses this rule applies
00:07 Therefore, let's solve the 'innermost' parentheses first
00:11 Let's write the division when
00:29 Let's break down 70 into factors 7 and 10
00:36 Let's break down 40 into factors 4 and 10
00:43 Let's simplify what we can
00:50 Let's break down 4 into factors 2 and 2
00:55 Let's simplify what we can
01:12 Multiply by 1 (doesn't change the exercise) simply a fraction of 2
01:22 Let's divide 188 into 182 plus 6
01:27 Let's divide the fraction into two fractions and solve
01:36 And this is the solution to the question

Step-by-Step Solution

Adhering to the order of operations: Begin with the operations inside of the parentheses proceed to the multiplication and division (from left to right) and finally address the addition and subtraction (from left to right)

When there are parentheses within parentheses, we start with the innermost ones first.

94:(2×(70:(5×8)))= 94:(2\times(70:(5\operatorname{\times}8)))=

In this exercise, there are only multiplication and division operations and parentheses within parentheses.

Therefore, we will begin by addressing the operation in the inner parentheses first. After calculating this we can proceed to remove the inner parentheses. Continue doing this until no more parentheses remain.

94:(2×(70:(5×8)))=94:(2×(70:(40)))= 94:(2\times(70:(5\operatorname{\times}8)))=94:(2\times(70:(40)))=

94:(2×(70:(40)))=94:(2×(70:40))= 94:(2\times(70:(40)))=94:(2\times(70:40))=

Express the obtained value from the inner parentheses as a fraction and proceed to reduce it.

Reminder - How do we approach reducing a fraction? Divide both the numerator and denominator by the same number

94:(2×(70:40))=94:(2×(7040))= 94:(2\times(70:40))=94:(2\times(\frac{70}{40}))=
The largest number by which we can reduce the fraction is 10

94:(2×(7040))=94:(2×(70:1040:10))= 94:(2\times(\frac{70}{40}))= 94:(2\times(\frac{70:10}{40:10}))=

94:(2×(70:1040:10))=94:(2×(74))= 94:(2\times(\frac{70:10}{40:10}))= 94:(2\times(\frac{7}{4}))=

94:(2×(74))=94:(2×74)= 94:(2\times(\frac{7}{4}))= 94:(\frac{2\times7}{4})=

94:(2×74)=94:(144)= 94:(\frac{2\times7}{4})= 94:(\frac{14}{4})=

Remember that division by definition is in fact equivalent to multiplication by the reciprocal:

a1b=a×b \frac{a}{\frac{1}{b}}=a\times b

94:(144)=94×(414)= 94:(\frac{14}{4})=94\times(\frac{4}{14})=

94×(414)=(94×414)= 94\times(\frac{4}{14})=(\frac{94\times4}{14})=

(94×414)=(94×414)=(37614)= (\frac{94\times4}{14})=(\frac{94\times4}{14})=(\frac{376}{14})=

(37614)=37614= (\frac{376}{14})=\frac{376}{14}=

Reminder - How do we convert an improper fraction to a mixed number?

In order to find the numerator - check how many times the denominator goes into the numerator and add the remainder to the numerator.

For the denominator – don't change anything.

In this exercise, the numerator is 376 and the denominator is 14

14 goes into 376 26 times with a remainder of 12

37614=26 1214= \frac{376}{14}=26\text{ }\frac{12}{14}=

Let's reduce the fraction and divide by 2

26 1214=26 12:214:2= 26\text{ }\frac{12}{14}=26\text{ }\frac{12:2}{14:2}=

26 12:214:2=26 67 26\text{ }\frac{12:2}{14:2}=26\text{ }\frac{6}{7}

Therefore the answer is option b -

26 67 26\text{ }\frac{6}{7}

Answer

2667 26\frac{6}{7}