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Video: Using the Order of Operations to Evaluate Numerical Expressions Involving Decimals

Tim Burnham

Calculate 6 ⨯ 8 − (3 − 2.6) + 3.4.

02:59

Video Transcript

Calculate six times eight minus three minus two point six plus three point four.

Now to evaluate this expression, we’ve got to think very carefully about the order of operations. And to help us to remember those, we’ve got the acronym “PEMDAS”. P stands for parentheses. E stands for exponents. M and D stand for multiplication and division and they both got equal precedence. And A and S stand for addition and subtraction and they’ve also got equal precedence So the idea is we work our way down that list, picking out whether we’ve got parentheses, exponents, multiplication and division, or addition and subtraction and do things in that order. So first of all, let’s look for parentheses. And we do have some parentheses; so we’re going to have to evaluate the contents of those parentheses first.

So first of all, let’s calculate three take away two point six. Well the difference between three and two point six is nought point four. We can see that on a number line the jump from two point six up to three is nought point four. So we can replace three minus two point six in parentheses with just a number nought point four. So now we’re left with the expression six times eight minus nought point four plus three point four. So we’ve dealt with parentheses. Are there any exponents or powers or indices? No. So we’re looking for multiplication and division. And we do have some multiplication, six times eight. Now six times eight is forty-eight; so we can replace that.

And there is no more multiplication or division; so we’re just left with addition and subtraction. Now they’ve both got equal precedence and we’d just work from left to right as we do them. So we’re gonna do forty-eight take away nought point four first of all. So if we start off at forty-eight and take away nought point four, we’re between forty-seven and forty-eight. And in fact we’re at forty-seven point six, so we can replace these two terms here with forty-seven point six. And that leaves us with forty-seven point six plus three point four.

Now that’s forty-seven point six plus nought point four plus three or plus three plus nought point four; it doesn’t matter which way around we do it. Well it just so happens if you look at this forty-seven point six and nought point four, the nought point six and the nought point four are gonna make a whole one. So I’m gonna go from forty-seven point six plus nought point four will take me up to forty-eight. Now I need to add the three on as well. So adding three on is gonna take me up to fifty-one. So our answer is fifty-one.