About this video
Sal rewrites 5 x (9 - 4) using the distributive law over subtraction as 5 x 9 - 5 x 4 = 45 - 20 = 25. He checks it by working out the parentheses first, 5 x 5 = 25, showing both ways give the same answer.
You'll be able to
- use the distributive law over subtraction to rewrite an expression like 5 x (9 - 4).
- evaluate the expression both ways and show the answers match.
- avoid the mistake of multiplying only the first number in the parentheses.
Key words
- distributive law over subtraction
- a x (b - c) = a x b - a x c; the outside number multiplies each part inside.
- simplify
- To work an expression out to a single value or simpler form.
- parentheses
- Brackets ( ) that group numbers together in an expression.
Transcript
Rewrite the expression five times 9 minus 4-- that's in parentheses-- using the distributive law of multiplication over subtraction. Then simplify. So let me just rewrite it. This is going to be 5 times 9 minus 4, just like that. Now, if we want to use the distributive property, well, you don't have to.
You could just evaluate 9 minus 4 and then multiply that times 5. But if you want to use the distributive property, you distribute the 5. You multiply the 5 times the 9 and the 4, so you end up with 5 times 9 minus 5 times 4. Notice, we distributed the 5. We multiplied it times both the 9 and the 4.
In the first distributive property video, we gave you an idea of why you have to distribute the 5, why it makes sense, why you don't just multiply it by the 9. And we're going to verify that it gives us the same answer as if we just evaluated the 9 minus 4 first. But anyway, what are these things?
So 5 times 9, that is 45. So we have 45 minus-- what's 5 times 4? Well, that's 20. 45 minus 20, and that is equal to 25, so this is using the distributive property right here. If we didn't want to use the distributive property, if we just wanted to evaluate what's in the parentheses first, we would have gotten-- let's go in this direction-- 5 times-- what's 9 minus 4?
9 minus 4 is 5. Let me do that in a different color. 5 times 9 minus 4. So it's 5 times 5. 5 times 5 is just 25, so we get the same answer either way. This is using the distributive law of multiplication over subtraction, usually just referred to as the distributive property.
This is evaluating the inside of the parentheses first and then multiplying by 5.
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