# How to add fractions with like denominators

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Each piece is of the hexagon. Right?

And is of the hexagon.

So, what if we wanted to add

Hmm. that would be

Count them up

So

Head on over to the next page to continue.

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Each piece is of the hexagon. Right?

And is of the hexagon.

So, what if we wanted to add

Hmm. that would be

Count them up

So

Head on over to the next page to continue.

Welcome to The Adding Fractions with Like Denominators (Simple Fraction Sums) (A) Math Worksheet from the Fractions Worksheets Page at Math-Drills.com. This math worksheet was created on 2018-08-22 and has been viewed 106 times this week and 392 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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How many times have you asked the question, “How do you add fractions?”

I’ve found that this question is asked a lot! Fractions is one of the hardest concepts in math for students to fully understand.

This lesson will lead you through adding fractions with common denominators. Once this concept is mastered, then you will be able to move onto adding fractions with unlike denominators.

Let’s get started.

## How Do You Add Fractions with Common Denominators?

These are the easiest type of fractions to add. Why? In order to add fractions, the denominators must be the same.

The term “common denominators” means that the denominators are the same.

Let’s take a look at Example 1.

## Example 1 – Horizontal Method of Adding Fractions

So, what did we do in Example 1 to add fractions? Yes, since the denominators were the same, all we needed to do was add the numerators.

Our answer to this problem (5/6) was in simplest form; however, do not forget to simplify your answer if possible.

There are two methods that are widely used when adding and subtracting fractions. The horizontal method was used in Example 1 and I will use the vertical method for Example 2.

## Example 2 – Vertical Method of Adding Fractions

Now you’ve seen the horizontal and vertical methods for adding fractions.

Yes, adding fractions with common denominators is pretty easy. Just add the numerators and keep the denominator the same!

## Adding Fractions with Common Denominators

To add fractions with a common denominator, write the sum of the numerators over the denominator.

## Can You End Up With an Improper Fraction?

YES! You may in fact add two proper fractions and end up with an improper fraction as your answer.

In this case, you may leave your answer as an improper fraction or you may rewrite it as a mixed number. Take a look!

## Can You Add Improper Fractions the Same Way?

An improper fraction is a fraction where the numerator is larger than the denominator. This indicates that the fraction represents a number larger than 1.

To answer the question, YES, we add improper fractions exactly the same way.

Let’s take a look!

Not too hard, right? Adding fractions with the same denominator is pretty easy.

Just remember, that as long as the denominators are the same, you can add the numerators. If the denominators aren’t the same, then you will need to do a little work before adding the numerators.

The best thing is that you’ll also find that subtracting fractions works exactly the same way!

I hope that you no longer need to ask, “How do you add fractions?” You are ready to rock on with the other fraction lessons. Check them out below!

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To add or subtract items, the units must be the same. For example, look at the items being added below.

2 apples + 3 apples = 5 apples

6 oranges + 3 oranges = 9 oranges

2 quarters + 5 quarters = 7 quarters

2 nickels + 3 nickels = 5 nickels

We cannot add apples and oranges unless we call them “fruits”. Similarly, we cannot add quarters and nickels unless we call them “cents”. In the name of a fraction, the unit is the denominator. For example, in the fraction “4 tenths”, the unit is the denominator, tenths. Therefore, 4 tenths + 5 tenths = 9 tenths. Look at example 1 below.

Example 1: A pizza was divided into eight equal parts (slices). If Jenny ate five slices and Eric ate two slices, then what part of the pizza did they eat altogether?

Analysis: Jenny ate “5 eighths” of the pizza and Eric ate “2 eighths”. In each of these fractions, the unit is the denominator, eighths. Since both fractions have the same units, we can add them together.

Solution: “5 eighths + 2 eighths = 7 eighths.”

The denominator of a fraction names what we are counting. In example 1, we are counting eighths. This is illustrated on the number line below.

It is not always practical to draw a number line. So we need an arithmetic procedure for adding fractions. The problem from example 1 is written using mathematical notation below:

The denominator of a fraction names the unit. The numerator indicates how many there are. For example, in the fraction five-eighths, the unit is eighths and there are 5 of them. In order to add fractions, the denominators must be the same. That is, they must have a common denominator .

These fractions have a common denominator (the denominators are the same). If the denominators were not common, you could not add these fractions.

This leads us to the following procedure for adding fractions with a common denominator.

Procedure: To add two or more fractions that have the same denominators, add the numerators and place the resulting sum over the common denominator. Simplify your result, if necessary.

Let’s look at some examples of adding fractions using this procedure.

In example 3, we needed to simplify the result: We reduced six-ninths to lowest terms, which is two-thirds.

In example 4, we simplified the result by converting the improper fraction to a whole number.

Avoid This Common Mistake!

Some students mistakenly add the denominators as well as the numerators. This is mathematically incorrect, as shown below.

To add fractions, add only the numerators, and place the sum over the common denominator.

So far, we have added only two fractions at a time. We can add more than two fractions using the procedure above. This is shown in the examples below.

To add two or more fractions that have the same denominators, add the numerators and place the resulting sum over the common denominator. Simplify your result, if necessary.

### Exercises

Directions: Add the fractions in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

Note: To write the fraction three-fourths, enter 3/4 into the form.

You’ve reached your daily practice limit of 12 questions.

## Online Math Game: Adding and Subtracting Fractions with Like Denominators

Add and subtract fractions with like denominators in this online math lesson for kids. In this interactive math game, students will become comfortable finding the sum and the difference of math problems that contain fractions with like denominators. After completing this math lesson, students should demonstrate proficiency in the following math skills:

* Use fraction strips to solve an addition or subtraction math problem containing fractions.

* Add or subtract the numerators when the denominators are the same. Simplify fractions when possible.

* Solve word problems that contain fractions.

* Fill in the missing fraction to complete the equation.

## Guided Practice

Students enjoy using the iKnowit.com interactive math lessons because their math practice time feels like a fun game. Whenever a student answers a question correctly, an animated character on the screen will do a funny trick or dance around cheerfully. Phrases of positive reinforcement appear on the screen for a correct answer as well.

An incorrect answer will bring up a detailed explanation page with an easy-to-read graphic depicting how to obtain the correct answer to the question. This feature helps students learn from their mistakes as they progress through the lesson.

If a student becomes “stuck” and needs a little push in the right direction, he or she can click the “Hint” icon on the lower left hand corner of the screen. A box will pop up containing a clue that will help the student solve the problem correctly. The teacher or parent can turn the hint feature on or off at will.

Members who sign up for an iKnowit.com account will be able to access the helpful administrative tools we offer on the site. Teachers or parents can set up a class roster or family roster, add students, assign lessons, and track their students’ progress. grades. Teachers will assign a class code and give each student an individual username and password. When students log in, they see a kid-friendly version of the site with an “Assignments from the Teacher” tab on the top of the page, as well as recommended math topics to try out.

e encourage you to browse through the hundreds of math lessons available on our website. We’ve got topics covering a variety of concepts like basic addition, subtraction, multiplication, and division, place value, time and money, fractions, measurement, and much more. To see more fourth grade math games, please go to our Grade 4 Math Page.

## Level

This lesson is designated as Level D and is typically appropriate for fourth grade students.

## Common Core Standard Alignment

4.NF.3
Number and Operations – Fractions
Build fractions from unit fractions by applying and expanding understanding of operations on whole numbers.

## You might also be interested in.

Time to the Nearest Minute (Level D)
Tell what time it is to the nearest minute on the analog clock.

Simplifying Fractions (Level D)
Practice reducing fractions into simplest form.

Once we have converted two fractions to equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerators.

### Add or subtract fractions with different denominators

1. Find the LCD.
2. Convert each fraction to an equivalent form with the LCD as the denominator.
3. Add or subtract the fractions.
4. Write the result in simplified form.

### Example

 $\Large\frac<1><2>+\Large\frac<1><3>$ Find the LCD of $2$, $3$. Change into equivalent fractions with the LCD $6$. $\Large\frac<1\cdot\color<3>><2\cdot\color<3>> +\Large\frac<1\cdot\color<2>><3\cdot\color<2>>$ Simplify the numerators and denominators. $\Large\frac<3><6>+\Large\frac<2><6>$ Add. $\Large\frac<5><6>$

Remember, always check to see if the answer can be simplified. Since $5$ and $6$ have no common factors, the fraction $\Large\frac<5><6>$ cannot be reduced.

### Try It

Watch the following video to see more examples and explanation about how to add two fractions with unlike denominators.

### Example

 $\Large\frac<7><12>+\Large\frac<5><18>$ Find the LCD of $12$ and $18$. Rewrite as equivalent fractions with the LCD. $\Large\frac<7\cdot\color<3>><12\cdot\color<3>> +\Large\frac<5\cdot\color<2>><18\cdot\color<2>>$ Simplify the numerators and denominators. $\Large\frac<21><36>+\Large\frac<10><36>$ Add. $\Large\frac<31><36>$

Because $31$ is a prime number, it has no factors in common with $36$. The answer is simplified.

### Try It

You can also add more than two fractions as long as you first find a common denominator for all of them. An example of a sum of three fractions is shown below. In this example, you will use the prime factorization method to find the LCM.

Add $\Large\frac<3><4>+\Large\frac<1><6>+\Large\frac<5><8>$. Simplify the answer and write as a mixed number.

What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would add three fractions with different denominators together.

Rewrite each fraction with a denominator of 24.

Add the fractions by adding the numerators and keeping the denominator the same.

Write the improper fraction as a mixed number and simplify the fraction.

## Subtracting Fractions

When you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions. Below are some examples of subtracting fractions whose denominators are not alike.

### Example

$15$ is ‘missing’ three factors of $2$

### Try It

The following video provides two more examples of how to subtract two fractions with unlike denominators.

### Example

 $\Large\frac<1><2>-\left(-\Large\frac<1><4>\right)$ Find the LCD of $2$ and $4$. Rewrite as equivalent fractions using the LCD $4$. $\Large\frac<1\cdot\color<2>><2\cdot\color<2>> – (-\Large\frac<1><4>)$ Simplify the first fraction. $\Large\frac<2><4>-\left(-\Large\frac<1><4>\right)$ Subtract. $\Large\frac<2-\left(-1\right)><4>$ Simplify. $\Large\frac<3><4>$

One of the fractions already had the least common denominator, so we only had to convert the other fraction.

## Adding and Subtracting Fractions that Contain Variables

In the next example, one of the fractions has a variable in its numerator. We follow the same steps as when both numerators are numbers.

### Example

Solution:
The fractions have different denominators.

 $\Large\frac<3><5>+\Large\frac<8>$ Find the LCD. Rewrite as equivalent fractions with the LCD. $\Large\frac<3\cdot\color<8>><5\cdot\color<8>> +\Large\frac<5>><8\cdot\color<5>>$ Simplify the numerators and denominators. $\Large\frac<24><40>+\Large\frac<5x><8>$ Add. $\Large\frac<24+5x><40>$

We cannot add $24$ and $5x$ since they are not like terms, so we cannot simplify the expression any further.

### Try It

Watch the following video to see more examples of how to add and subtract fractions with unlike denominators that contain variables.

Well…it’s time. It’s time for your students to learn how to add and subtract fractions. I can’t say it will be easy or that there won’t be tears. I can say that it will take you several days and you should be prepared.

You need to understand that there is adding and subtracting with like and unlike denominators.

If you need some awesome anchor charts for Adding & Subtracting Fractions check them out here! You can also check out the guided math units that I have in my TpT store.

### With like denominators

2. Keep the denominator the same.
3. Simplify/reduce
4. If there are whole numbers- add those up

### With unlike denominators

1. Find the least common denominator of the fractions (LCD)
2. Rewrite the problem with the common denominators.
3. Simplify if you can.
4. If there are any whole numbers- add those up as well.

## How to Subtract Fractions

### With like denominators

1. Subtract the numerators.
2. Keep the denominator the same.
3. Simplify/reduce
4. If there are whole numbers- subtract those.

### With unlike denominators

1. Find the least common denominator of the fractions (LCD)
2. Rewrite the problem with the common denominators.
3. Simplify if you can.
4. If there are any whole numbers- subtract those up as well.

## Trust yourself!

You may end up doubting yourself when it comes to adding and subtracting fractions. Keep that calculator handy. One of my favorite apps ever is the fraction calculator app. You mayyyyy want to download it right now!!

## Guided Math

You know it’s hard to make sure your students completely understand the math lesson. I love giving them skills to practice during the math block. Are you looking for ways to implement Guided Math into your classroom? Check out this FREE Guide to Implement Guided Math in 10 Days!