Using the distributive property, evaluate three times 43 minus three times 10.
Let’s take a look at the distributive property. Here’s an illustration of the distributive property. It shows us that if we have two groups, four times three plus four times four, they will have the same value as multiplying four times seven. The pink dot show us four times three, the yellow dots four times four. And the green dots have taken the three and the four, added together to form seven, and then multiplied four times seven.
We want to use the same idea with our subtraction problem. We’re trying to solve three times 43 minus three times 10. What we’re going to do here is take out our three, move it to the beginning of the problem. If we do that, we’re left with 43 minus 10. We’ve just rearranged our problem to say three times 43 minus 10.
And because of the distributive property, we know that we haven’t changed its value at all. These two equations are exactly the same; three times 43 minus 10 will be equal to three times 43 minus three times 10. The one on the left, however, should be easier to solve.
We’ll start here. What is 43 minus 10? 33. Bring down your three. Now, we need to multiply three times 33. Three times 33 is 99. Using the distributive property, we showed that 99 equals three times 43 minus three times 10.