Video: Applying the Order of Operations in a Mathematical Problem Including Decimal Numbers

Calculate (75 − 12.66) × 5.

04:22

Video Transcript

Calculate 75 minus 12.66 all in parentheses times five.

So notice in our question, we have subtraction, we have multiplication, and we have parentheses. So where do we begin? We need to follow the order of operations, sometimes called PEMDAS because we begin with P, the parentheses, sometimes called brackets. Then, we have exponents also known as powers. Then after we take care of the parentheses and the exponents, we move to multiplication and division. And this is whichever comes first, left to right. And lastly, we have addition and subtraction, following the same pattern: whichever comes first, left to right.

So we go through this list. We begin with parentheses. Do we have any parentheses? Yes, we do. So this means we must work inside of the parentheses first. And we have subtraction inside of here. So we need to take 75 and subtract 12.66. And to do so, we need to line up our decimal points and add two zeros at the end where it’s needed of this 75. So we begin on the right with zero minus six which we can’t do. So we need to borrow, which we can’t take anything from zero. So we have to move to the left. We can borrow from the five. So if we borrow from the five, it becomes a four. Now if we borrowed one from five, we can bring the one over here to making the zero a 10. So now that this number is a 10 and not a zero, we can borrow one from 10 making it nine and making our original zero a 10. So 10 minus six is four.

Now, in the next column, we have nine minus six which is three. Bring down our decimal point. And then four minus two is two. And then lastly, seven minus one is six. So, so far, we’ve worked inside the parentheses and we took 75 minus 12.66. So now, we have 62.34 times five after we’ve subtracted. So that means we only have multiplication left. There aren’t exponents we need to work with. But there is multiplication.

So we need to take 62.34 times five. So we take five times four which is 20. So we carry the two and then we take five times three which is 15 but then add two. And we get 17. Then, we take five times two which is 10. But then, we add one, so 11. We carry the one. And then five times six which is 30 plus one, so 31. Now notice that 62.34 is a decimal. So we have a decimal point. And since we have 62.34, there are two places after the decimal point. So we need that here in our answer, so 311.70, which we could write as 311.7. We don’t need the zero at the end. But either way would be correct.

Now, let’s show one more way that we could have multiplied 62.34 and five together. For 62.34 times five, we could have taken 62 times five and our decimal portion times five 0.34 times five and then added those together. And that would have given us 311.70. So looking at that, 62 times five: five times two is 10. So we carry the one. Five times six is 30. And 30 plus one is 31. So 62 times five gives us 310. And now, 0.34 times five. We take five times four which is 20. So we carry the two. And then, five times three is 15 plus two is 17. So we carry the one. And five times zero is zero. But zero plus one is one. And then, we have our decimal point with two spaces. So we do the same for our answer, 1.70. So 310 plus 1.70 would give us an answer of 311.70 or 311.7.

So once again, our final answer will be 311.70 or 311.7.

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