Video: Estimating and Calculating the Answer to Two-Step Word Problems

Ethan has to deliver mail to 415 houses. He delivered it to 82 houses on one street and 107 houses on another. Pick the best estimate for the number of houses he still has to deliver mail to. [A] 100 [B] 400 [C] 200 [D] 300 [E] 600. Find the exact number of houses left. [A] 522 [B] 163 [C] 333 [D] 226 [E] 604.

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Video Transcript

Ethan has to deliver mail to 415 houses. He delivered it to 82 houses on one street and 107 houses on another. Pick the best estimate for the number of houses he still has to deliver mail to: 100, 400, 200, 300, 600. After that find the exact number of houses left: 522, 163, 333, 226, or 604.

Let’s start with the estimate. Ethan has to deliver mail to 415 houses. Let’s round this to the nearest 100. If we sketch a number line of 400 to 500, where would 415 fall on this number line. 415 would fall closer to 400 than 500. To round 415 to its nearest 100, we would round it to 400.

We also know that he’s already delivered 82 houses on one street. Let’s round 82 to the nearest 100. Where does 82 fall between zero and 100? 82 is closest to 100. We would round 82 to 100. And on another street, Ethan has already delivered 107 houses their mail. On a number line, where does 107 fall between 100 and 200? 107 falls much closer to 100 than 200. So we would round 107 to 100.

Now that we’ve done all this rounding, it’s time to put the information together. Here, we could say that Ethan has to deliver mail to about 400 houses and he’s already delivered mail to how many houses. These two numbers — both of our 100s — represent the number of completed houses. He’s already completed about 200 houses from his wrap.

To find out how many he has remaining, we would subtract the completed from how many he had to start with: 200 from 400. 400 minus 200 equals 200. The best estimate for the number of houses he still has to deliver mail to is 200.

For the second half of this question, we need to find the exact number of houses remaining. We take the 415 and subtract 82. Five minus two equals three. One minus eight is not possible. So we borrow from our hundreds place turning that four into a three. And then, we would say 11 minus eight which equals three. And finally, in our hundreds place, three minus zero equals three.

All of a sudden, you notice that 333 is one of our answer choices. But it’s not the answer because we’re not finished. We’ve only subtracted the first street that Ethan delivered mail to. We need to take this 333 and substract the 107 houses he delivered mail to from the other street.

Starting in the ones place, three minus seven is not possible. We’ll borrow from our tens place. Instead of three tens, we will have two tens and 13 ones. 13 minus seven equals six. In the tens place, we now have two minus zero, which equals two. And in our hundreds place, three minus one equals two.

The exact number of houses Ethan has remaining is 226.

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