Video: Solving Word Problems by Adding Two Whole Numbers

2994 children visited the book fair last week, and 6846 children visited the fair this week. Find the total number of children who visited the fair.

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Video Transcript

2994 children visited the book fair last week, and 6846 children visited the fair this week. Find the total number of children who visited the fair.

We’re given two numbers in this problem, and there’re two amounts of children who visit a book fair. 2994 children visited the book fair last week. And then the second number we’re given is the number of children who visited the fair this week, 6846. Now, which word in this problem tells us what we’ve got to do with these two numbers? Well, it’s this word here. We’re asked to find the total. We need to calculate all the children who visited the fair.

So to find the total number of children who visited the fair, we need to add together 2994 and 6846. And both of these numbers are four-digit numbers. We might think to ourselves that a quick way to find the answer is to use column addition. In fact, we will use this method to check our answer. But in fact, there’s a quicker way to find the answer. We can actually work out the answer in our heads. Let’s look carefully at the two numbers that are in the bar model that we’ve drawn.

What can we say about 2994? Is there a way we could change 2994 to make it easier to add? Well, 2994 is only six away from 3000. What if we take away six from 6846 and then add it to 2994? That way, the total will stay the same. In a way, what we’ve just done is make the first bar larger and the second bar smaller. But the whole total has stayed exactly the same. By adding six to 2994, the first number that we need to add has become a lot easier to work with, 3000. And we can complete the subtraction quickly too. Because there’re already six ones in this number. 6846 take away those six ones equals 6840.

And this is a sort of calculation now that we can do in our heads. 6840 has six thousands, and 3000 has three thousands. We know that six plus three equals nine. So we can use this very simple fact to help us to find the answer. 6840 plus 3000 equals 9840. We found the answer quickly by adjusting the answers to make them easier to work with. Let’s check our answer using column addition.

Six plus four equals 10. Four plus nine equals 13 plus the one ten underneath equals 14 tens. Eight plus nine equals 17 plus the one hundred underneath equals 18 hundreds. And, finally, six plus two equals eight plus the one thousand underneath equals nine thousands. The total number of children who visited the fair was 9840 children.