Video: Applying the Order of Operations in Mathematical Problems

Calculate [−49 ÷ (−7)] × [−33 ÷ (−11)].

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Video Transcript

Calculate negative 49 divided by negative seven times negative 33 divided by negative 11.

To answer this question, we can’t simply start at the left-hand side and work our way through the operations. Instead, we need to use the order of operations, which tells us that the first operation we will evaluate will be those given in parentheses or brackets. Next, exponents or indices will be evaluated, then, multiplication and division calculations, and, finally, addition and subtraction calculations. The acronym PEMDAS is often used to refer to the order of operations.

So taking a look at our calculation, we can see that the parentheses around negative seven and negative 11 are merely helping to separate the negative from the rest of the calculation. And indeed, the calculation could be written without these parentheses. So looking at the order of operations, the first thing we do is check if there are any calculations in parentheses. Here, we have two calculations. So we will evaluate these at the same time.

Negative 49 divided by negative seven will give us an answer of seven since two negatives divided will always give a positive value. In the same way, negative 33 divided by negative 11 will give us a positive value of three. And our calculation is now seven times three. Since there are no other calculations to worry about, then we can just simply evaluate this as 21. And this is our final answer for the calculation.

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