2.5 Adding and Subtracting Fractions with Like Denominators

Introduction

Unit 1

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Math Basics  >  Unit 2 Fractions and Decimals  >  Lesson 2.5 Adding and Subtracting Fractions with Like Denominators

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In this lesson, we're going to look at adding and subtracting fractions that have like denominators. So we'll start off with this problem, three eighths plus two eighths. Now, to see how we can solve this, we're first going to look at an image. So here we have an image representing three eighths. We have three out of eight of the boxes shaded in blue. Now we want to add two eighths to that. So since each of these small boxes represents an 8th, we really just need to add two of those boxes. So we have the three eighths that we started with, plus two more eighths added to that. Now we can see that we have a total of five out of the eight boxes shaded in which we represent as five eighths. So if you'll notice, all we really did with our fractions was add the numerators we had, the three plus two gave us a total of five, and then we kept the denominator the same. Both of our fractions had a denominator of eight. So in our answer, we still have a denominator of eight. So when the denominators are the same, just add, or if it's a subtraction problem, you would subtract the numerators and keep the denominator the same. Now, in this example, we have mixed fractions, four and two sevenths minus one and five sevenths. Now, when you're adding or subtracting mixed fractions, there's more than one way then you can approach these. But my recommendation is to convert them to improper fractions first. I find that that's the best way to avoid making mistakes. So when adding or subtracting mixed fractions, it's often simplest to convert them to improper fractions first. So let's do that with these. The four and two sevenths would become 30 over seven. And then when we convert the second fraction, one and five sevenths becomes twelve sevenths. And of course we're subtracting them so we bring down our subtraction sign. Now, since they have the same denominator of seven, all we have to do is subtract the numerators. 30 minus twelve will give us 18, and then keep the denominator of seven the same. Now, technically this is our answer, 18 sevenths. But sometimes you may be asked to change your answer back to a mixed fraction. So we're going to do that here. Now remember, when you're changing from an improper to a mixed fraction, you just do the long division. So you would do 18 divided by seven. The final answer would end up being two and four sevenths. So when adding and subtracting fractions with a like denominators, you add or if it’s a subtraction problem, subtract the numerators, keep the same denominator. And then of course, when you're adding or subtracting mixed fractions, remember it's simplest to convert them to improper fractions first, although there are other ways that you can solve it as well. And simplify the answer if it needs to be simplified.

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