Video: Adding Mixed Numbers

James has two posters. One is 5 3/8 feet wide and the other 2 7/8 feet wide. Will the two posters fit beside each other on a wall 7 feet wide?

03:24

Video Transcript

James has two posters. One is five and three-eighths feet wide and the other two and seven-eighths feet wide. Will the two posters fit beside each other on a wall seven feet wide?

This question is what we call a closed question. It can either be answered with yes or no. Either James’s two posters will fit beside each other, or they won’t. Let’s go through the problem to understand what it’s asking us. We’re told that James has two posters. We’re not given the height of these posters, but we are given the width. One of James’s posters has a width of five and three-eighths feet. And we’re told that James’s second poster has a width of two and seven-eighths feet. So the width of both posters are given to us in feet. And we’re asked whether both posters will fit next to each other on a wall seven feet wide.

To find the answer, we need to add the two widths of the posters together. If the answer is less than seven, we know they’ll fit. If the answer is greater than seven, we know that they’ll be too wide for the wall. So it might look like the question is asking us to add two mixed numbers together. We know these are mixed numbers because both measurements contain a whole number of feet and also a fraction which shows part of a foot. It’s useful that both fractions are in eighths. So it makes them easier to add together. But if we spend a moment looking at these two numbers, do we actually have to calculate the answer?

If we look at the whole number part of our mixed numbers, we can see that five plus two equals seven. There’s our seven feet. But we still need to also add the fraction part of our mixed numbers. The distance is going to be longer than seven feet then, isn’t it? So, without actually calculating the answer, we can say that the two posters will not fit beside each other on a wall seven feet wide. They’ll be too long. Well, then, we can definitely say that the answer is going to be no. Let’s just calculate the answer to check.

First, we can add the whole number of feet. As we’ve said already, five feet plus two feet equals seven feet. Now, we can add the fraction part, three-eighths plus seven-eighths. We’re adding two lots of eighths. So the answer is gonna be a number of eighths. We have three-eighths plus seven-eighths. That gives us a total of ten-eighths. Ten-eighths is an improper fraction. It’s greater than one. We know that eight-eighths is the same as one. So ten-eighths is the same as one whole and two extra eighths.

And what do we get if we add seven feet and one and two-eighths feet? We get a distance of eight and two-eighths feet. Another way of writing this would be eight and a quarter. But we don’t need to know this. We’d already worked out, without doing any calculation, that the two posters are not going to fit next to each other.

When we added the whole number parts of our mixed number together, we got the answer seven. This was before we added any fractions whatsoever. So we could tell straightaway that the total distance was going to be more than seven feet. Will the two posters fit beside each other on a seven foot wall? No, they won’t.

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