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Question Video: Applying the Order of Operations in Mathematical Problems Mathematics

Calculate [21 − (−19)] ÷ 5 × 3.


Video Transcript

Calculate open brackets 21 minus negative 19 close brackets divided by five times three.

To answer a question like this, it’s important to realise that if we started at the left-hand side and worked our way through each operation in turn until the end, then we would not be obeying the order of operations. We can recall that the order of operations, which is often seen with the acronym PEMDAS, stands for parentheses, exponents, multiplication division, addition, and subtraction. To evaluate a calculation that has a number of different operations, then we must perform them in this sequence.

So taking a look at our calculation, we can see that our set of parentheses around negative 19 is helping to distinguish the negative sign. So we don’t need to do anything with that to start off with. To begin with our order of operation then, we see if there are any parentheses or brackets. We can see that the calculation 21 minus negative 19 is contained within a set of brackets. So we perform this calculation first. When we subtract a negative number, it becomes an equivalent calculation to addition. This will give us the calculation 21 plus 19 divided by five times three.

Continuing with our calculation in brackets, 21 plus 19 will give us 40 divided by five times three. The next stage in our order of operations is exponents, for example, squares or cubes. And in this case, our calculation doesn’t have any of those. So we move to the next step of multiplication and division. In this step in our order of operations, if we have more than one multiplication or division, then we perform these in order from left to right. Since our first operation here would be 40 divided by five, then we calculate this first giving us an answer of eight times three. We know I have just one calculation left to do, eight times three, which gives us a final answer of 24.

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