Video: Using Order of Operations to Evaluate Numerical Expressions Involving Decimal Numbers

Calculate 68.7 − 9.9 ÷ 3.3 − 2.5.


Video Transcript

Calculate 68.7 minus 9.9 divided by 3.3 minus 2.5.

When answering a question like this, it can be very tempting simply to work from left to right and calculating every operator as we get it. But this would be incorrect. We need to use a standard order of operators, which we often see written in the acronym PEMDAS. The letters of PEMDAS stand for parentheses, exponents, multiplication, division, and addition, subtraction.

We consider multiplication and division to be on the same level in the order of operations. That means if there’s a calculation that has more than one multiplication or multiplication and divisions, then we carry those out in order from left to right. And the same is true for addition and subtraction. If we have one or more addition or subtraction calculations, then we do those in order from left to right.

So, let’s move on then to check our calculation. The first thing we check is if there’s any calculation in parentheses. There’s not here, so let’s check the next thing. Is there anything written with an exponent, for instance a square or third power? Nope, so, let’s move on then. Checking multiplication, division, we can see that in the middle of our calculation there is a division calculation. So, this is the first thing we’re going to evaluate.

When it comes to a decimal division such as 9.9 divided by 3.3, we first need to make the divisor into a whole number. So, if we multiplied 3.3 by 10, that would give us 33. However, we must also multiply our dividend 9.9 by the same power of 10. This means that 9.9 divided by 3.3 is equivalent to 99 divided by 33, which is three.

So, going back to our original calculation, we now have 68.7 minus three minus 2.5. And so, now, what we’re left with is two separate subtraction calculations. So, according to our order of operations, we carry these out in order from left to right. So, to calculate 68.7 minus three, if we’re using the column method, we need to put our three in the ones column underneath the eight of 68.7, since it’s also in the ones column.

And it could be helpful to add a decimal point and a zero as a placeholder after our three. So, 68.7 take away three will give us 65.7. And putting that into our calculation will leave us 65.7 minus 2.5. And finally, since there’s one operation remaining, we can work this out, giving a final answer of 63.2.

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