1.2 Commutative and Associative Properties
1.3 Identity and Inverse Properties
2.3 Fractions Equal to Whole Numbers
2.4 Converting Mixed and Improper Fractions
2.5 Adding and Subtracting Fractions with Like Denominators
2.6 Adding and Subtracting Fractions with Unlike Denominators
2.9 Understanding Keep, Change, Flip
3.1 Converting Fractions to Decimals
3.2 Converting Decimals to Fractions
3.3 Converting Integers to Decimals and Fractions
3.7 Understanding Proportional Ratios
3.8 Identifying Proportional Ratios
3.9 Comparing Ratios with Rates and Prices
3.11 Converting Percent to Fraction and Decimal
4.1 Operations and Expressions
4.3 Expressions with Addition and Subtraction
4.4 Expressions with Multiplication and Division
4.5 Expressions with Exponents
4.6 Expressions with Decimals and Fractions
4.10 Understanding Distributive Property
4.11 Using the Distributive Property
4.12 Combining Like Terms with Distributive Property
5.2 The Goal of Solving Equations
5.3 Checking the Answer to an Equation
5.4 Solving Equations with Addition and Subtraction
5.5 Solving Equations with Multiplication
5.6 Solving Equations with Division
5.7 Starting a Two-Step Equation
5.8 Solving Two-Step Equations
5.9 Simplifying and Solving Two-Step Equations
5.11 Translating Math Expressions
5.12 Translating Math Equations
5.13 Strategies for Algebraic Word Problems
6.2 Comparing Integers and Decimals
6.4 Graphing Inequalities on Number Lines
6.5 Writing Inequalities from Number Lines
6.6 Translating Inequalities from Word Problems
6.7 Solving Inequalities with Addition and Subtraction
6.8 Solving Inequalities with Multiplication and Division
6.9 Inequalities with Negative Numbers
6.10 Solving Inequalities with Negative Numbers
6.11 One-Step Inequality Word Problems
6.12 Writing Inequalities Different Ways
6.13 Solving Two-Step Inequalities
Math Basics > Unit 2 Fractions and Decimals > Lesson 2.5 Adding and Subtracting Fractions with Like Denominators
Click play to watch the video and answer the questions for points!
Fill in the answers by dragging the numbers to the correct spots.
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.
Hi, I'm Mia!
With over 12 years of experience as a classroom teacher, tutor, and homeschool parent, my specialty is easing math anxiety for students of all ages. I'm committed to empowering parents to confidently support their children in math!