Multiplying numbers with different signs
About this video
Sal finds 4 × (−5) × (−7.5) by working left to right. He reminds us that different signs give a negative product and the same signs give a positive one, so 4 × (−5) = −20, and then −20 × −7.5 = 150 because two negatives make a positive.
You'll be able to
- use sign rules to decide if a product is positive or negative.
- multiply three numbers, step by step, including a decimal.
- multiply a decimal like 7.5 by 20.
Key words
- product
- The answer when you multiply numbers.
- sign
- Whether a number is positive (+) or negative (−).
- decimal point
- The dot that separates whole numbers from parts of a number, like in 7.5.
Transcript
Find the product 4 times negative 5 times negative 7.5. So we're just multiplying three numbers right here, some are positive, some are negative. We could actually do this in any order, but let's just go left to right. So let's start with the 4 times the negative 5.
And then we'll multiply whatever we get there times negative 7.5. So let's just rewrite the problems. We have 4 times negative 5, times negative 7.5. I really don't have to write that dot there. If you just have 4 and then in parentheses a negative 5, that means 4 times negative 5.
Now, the first thing you need to realize is that a positive times a positive is obviously a positive. A positive times a negative, or a negative times a positive, when you have different signs, you're going to end up with a negative. If you have same signs, even if you have a negative times a negative, you're going to have a positive as well.
So let's just work that out in this problem. So you have 4 times negative 5. 4 times 5 would be 20. Let me do this in a different color. So 4 times 5 would be 20. But we have a positive times a negative, so it's going to be a negative. Different signs mean we're going to have a negative.
So it becomes negative 20 times negative 7.5. So let's figure out what that is. We have to multiply 20 times 7.5. We could do that out here. So 7.5 times 20. 0 times 5 is 0. 0 times 7 is 0. Put a 0 here, because we're obviously not going to multiply by 2. We're actually multiplying by 20.
So 2 times 5 is 10. 2 times 7 is 14, plus 1 is 15. And we get a 0, we get a 0, we get a 5. I'm just adding here. You get a 1. And then you count the numbers you have behind the decimal point. We only have one digit behind the decimal point in both numbers. So you only go one digit behind the decimal point in our product.
So the answer here is 150. So this is equal to 150. And now we just have to think about is it going to be positive or negative. We have a negative times a negative. They are the same sign. So it's going to result in a positive number. So our final answer is 150.
And if we actually wanted to keep the precision here, we could write 150.0.
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