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How to add fractions with unlike denominators

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How to add fractions with unlike denominatorsHow to add fractions with unlike denominators

Online Math Game: Adding Fractions with Unlike Denominators

Add fractions with unlike denominators in this interactive math game for kids. Students will have the opportunity to practice addition with fractions that do not have the same denominator. Students will be required to find common denominators in order to add the fractions. They will be asked to simplify the fractions if possible. Here are the types of questions students can expect to encounter in this online math lesson:

* Solve a word problem containing fractions with unlike denominators.

* Solve addition problems with fractions in a vertical format.

* Solve fractional addition problems in a horizontal format. Use fraction strips to visualize the math problem.

How to add fractions with unlike denominatorsHow to add fractions with unlike denominators

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How to add fractions with unlike denominatorsHow to add fractions with unlike denominators

Level

This lesson is labeled as Level D and is targeted toward fourth graders.

Common Core Standard Alignment

5.NF.2
Number and Operations – Fractions
Use Equivalent Fractions As a Strategy to Subtract and Add Fractions: Students should be able to solve word problems requiring the addition or subtraction of fractions referring to the same whole, including adding and subtracting fractions with unlike denominators. Students will use visual aids, such as fraction strips, to help them solve the math problems.

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We know that when adding fractions with the same denominator, you can add the numerators together and put them over the denominator. If needed, you can simplify the fraction.

But what happens when you have denominators that are different?

There is one extra step that needs to be done and we are going to go over that here.

How To Add Fractions With Different Denominators

When adding fractions with different denominators, you must first find the lowest common multiple of the fractions and convert them to equivalents.

Let’s look at an example:

The first step is to find the lowest or least common multiple of our denominators, which in this example are 6 and 9.

Multiples of 6 are: 6, 12, 18

Multiples of 9 are: 9, 18, 27

We can see from the multiples above, that 18 is our lowest common multiple between the 2 denominators.

We can create an equivalent fraction for 3/9 to have a denominator of 18 by multiplying the numerator and denominator by 2. The result is 6/18.

We can create an equivalent fraction for 1/6 by multiplying both the numerator and denominator by 3. The result is 3/18.

Since we now have both fractions into equivalents with the same denominator, we can add the numerators together and get 9/18.

We can look at that result and see that 9 is a factor of 18 so it can be simplified further. The simplified form of 9/18 is equal to 1/2.

If you need a refresher on simplifying fractions, check out my post here.

You can also check out my post on finding the least common or lowest common multiple here.

Be sure to check out my YouTube video above for more examples on adding fractions with different denomintors.

You can also download a free printable worksheet and answer sheet for more practice below.

Following on from our last blog on adding fractions with like denominators, adding fractions with unlike denominators is a little more complicated.

Improper fractions, or fractions with unlike denominators, may look a bit difficult. However, once you make the denominators the same, the addition is easy.

Let’s use an example:

Find the least common multiple

First, we need to find the Least Common Multiple (LCM) for the denominators. Basically, we need to find a common multiple that they share.

The common multiples of 4 are 4, 8, 12, etc.

The common multiples of 12 are 12, 24, 36, etc.

How to add fractions with unlike denominators

Now we need to find the first common value. For most students new to this, it’s easiest to sketch it out on a number line:

The least common multiple is (1, 3) = 12.

Multiply the numerator and denominator to get like denominators

Now, you’ll need to multiply the entire fraction to make the denominator become the least common multiple. In our example, this is what that looks like:

Important: you multiply both the top and the bottom by the same amount to keep the value of the fraction the same.

Add the numerators

Now the denominators (the bottom numbers) are the same. This means we can add the numerators (the top numbers):

Simplifying fractions

Finally, let’s simplify the fraction.

Think about the Greatest Common Factor: the highest number that divides evenly into both the numerator and the denominator.

8 divides into 1, 2, 4, 8

12 divides into 1, 2, 4, 6, 12

The Greatest Common Factor is 4. 8/4 = 2, and 12/4 = 3:

So the answer is:

If you are looking for worksheets to practice adding fractions with unlike denominators, why not try out our grade 5 fractions worksheets.

A lot of people have trouble solving math problems. If you are one of them instead of struggling, you should simply look for online tutorials that can help you figure out problems. Fractions are one mathematical challenge that a lot of people struggle with, especially when there are different denominators. The good news is even with the bottom numbers are different, you can get an answer without breaking a sweat. The following is a quick guide to help you add fractions like a pro, with or without similar denominators so you can breeze through your work.

Write Out the Fractions

First off, find yourself a pen and some paper and write down the fractions next to each other. Trying to do math in your head can make a simple task even more difficult, especially when the fractions have different denominators. You want to write them next to each other so you can clearly see what you are comparing. The example below will be completed as we work through the steps so you can see how the final answer comes to be.

How to add fractions with unlike denominators

Find the Common Denominator

You cannot add fractions that have different denominators until you identify a common denominator that they can share. The best way to do this is to find a multiple that they both share. If the numbers are small, simply multiply them against each other to find out what the common denominator is going to be.

Example: 3 x 4 = 12. This means that we will use 12 as the common denominator for our equation.

How to add fractions with unlike denominators

Multiple Each of the first numbers by the Bottom Number of the Second

This sounds confusing, but it isn’t once you get down to the equation. You want to get both fractions to have the bottom denominator of 12, so you do this by multiplying by the bottom number of the other. So, for instance, you will multiply 1/3 by 4/4, and then you will multiply 3/4 by 3/3. It seems like you are changing the numbers, but in reality, 3/3 or 4/4 is the same as multiplying by 1, and any number multiplied by one is the same. It is the same fraction, but we are just changing the way it looks to make the math easier.

Example: 1/3 x 4/4 = 4/12

How to add fractions with unlike denominators

Multiple Both Numbers of the Second Fraction by the Bottom Number of the First

This is the exact same thing we just did, only this time we are changing the fraction of the second number in the equation. Once again, we are really just multiplying by one, so the number of the fraction is not changing at all.

Example: 3/4 x 3/3 = 9/12

How to add fractions with unlike denominators

Write out the New Fractions

Now that they both have the same denominator, we want to line the fractions up next to each other to make the math easier. By placing them side by side we get a cleaner image, and now that the numbers are the same the answer will seem a lot closer.

Example: Our new equation is 4/12 + 9/12

How to add fractions with unlike denominators

Add the Numerators

Start the problem by looking at the numerators (the top numbers of the fraction). Then add the two numbers together and carry them into the solution. This will be the numerator of our answer.

Example: 4+9 = 13. That makes our new numerator 13.

How to add fractions with unlike denominators

Carry the Common Denominator

When you add fractions, you only add the top number. That means that the common denominator will not change once you add the two fractions together. Since our common denominator was 12, it will remain our denominator in the solution.

How to add fractions with unlike denominators

Put the Numbers Together

Now that we know the denominator and the numerator, we can put them together. Remember, the numerator goes on top, and the denominator goes on the bottom. Therefore, we now have the solution to our math problem.

How to add fractions with unlike denominators

Simplify and Reduce

After you find the solution, you need to simplify or reduce your fraction. Our answer is a prime number so it cannot be simplified, but if we had a result like 6/8 then we would divide by two, and the final answer would be 3/4. However, our answer can be reduced, because the numerator is higher than the denominator.

Example: 13/12 reduces to 1 1/12

How to add fractions with unlike denominators

Submit Your Answer and Try Again

Now that you know how to solve equations that ask you to add fractions with different denominators try a few examples on your own as practice. The more you complete these types of problems, the easier it will be to solve fraction problems in the future. This can help you out while measuring anything in the future from foods to medicines to chemicals in the lab. Here are some practice equations to get you started.

Examples, solutions, videos, and lessons to help students learn how to add fractions with like or unlike denominators.

How to add fractions with unlike denominators

The following examples shows how to add fractions with like denominators and unlike denominators. Scroll down the page for more examples and solutions.

Adding Fractions with Common or Like Denominators

When we add fractions that have the same, or common denominators, we add only the numerators. The denominators stay the same.

Example

Adding Fractions With Uncommon or Unlike Denominators

To add fractions with uncommon denominators, we need to change the fractions to equivalent fractions with common denominators before we find the sum.

First, we would need to find the least common denominator (LCD), which is the LCM of the denominators.

Next, we write equivalent fractions using the least common denominator. Then, we proceed to add as before.

Example:

Solution:

Step 1: Find the LCD or LCM of 2 and 5

Multiples of 2: 2, 4, 6, 8, 10, 12

Multiples of 5: 5, 10, 15

The LCD or the Least Common Multiple of 2 and 5 is 10

Step 2: Write both fractions and as equivalent fractions with a common denominator of 10.

Step 3: Add the 2 equivalent fractions.

The following video shows more examples of adding fractions with uncommon or unlike denominators.

How to add fractions with unlike denominators

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In today’s lesson, the students learn to add fractions with unlike denominators. They use a multiplication chart to help them find the least common denominator. Also, they use fraction strips to give them a visual understanding of adding fractions with unlike denominators. This relates to 4.NF.B3a because the students understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

I begin by letting the students know that our lesson for today is adding fractions with unlike denominators. We review the skills from the previous day before getting started on the new skill. I begin by asking a question, “What are like denominators?” I give the students a few minutes to think about the question before answering. Student response: The denominators are the same. One student gives an example. “If you have fractions like 1/5 and 2/5, both of the denominators are the same.” I remind the students that we learned yesterday that if you have like denominators, you can go ahead and add or subtract, depending on your problem because the pieces are already the same size. We also learned yesterday, that once you add or subtract, you must write your answer in simplest form. “What is simplest form?” Continually questioning the students assures that the students are listening and paying attention because they do not know who I will call on to answer the question. Also, it allows me to ascertain how much of the information was retained by the students. Student response: by writing the factors out and whatever factor is the same in both fractions, you have to divide by it. There was one thing that the student left out that was very important in simplifying fractions. I call on another student to give me the information. Student response: Do not use the number one. I let the student know that this is correct. I share with the students that even though we are not dividing by the number 1, we are dividing by a fraction that equals 1. I remind the students that in a fraction, when the numerator and the denominator are the same, then that fraction is equivalent to 1. I go on to share with the class that we learned that any number divided by 1 will give you the same number (equivalent).

I share with the students that today, we will add fractions with unlike denominators, this means that the two denominators will be different numbers. When you have to add or subtract fractions with different denominators, you cannot just look at the numerator. You are going to have to find an equivalent fraction. We need to find an equivalent fraction because to add fractions, the denominators must be the same. Because I feel that this lesson is quite comprehensive, I have the students work along with me during whole class discussion time. The powerpoint is on the Smart board. I ask the students to take out a sheet of paper and pencil. I pass out a multiplication chart, along with the fraction strips to each student. As I work on the Smart board, the students work at their desks.

I write the problem 1/4 + 1/3 on the Smart board. I instruct the students to take out the fraction strips for 1/4 and 1/3 and lay them next to each other, as in combining the two (addition). As the students work to solve the problem with paper and pencil, they will use the multiplication chart and fraction strips to get a visual. This will give the students a conceptual understanding of adding fractions with unlike denominators.

I remind students again that we cannot add fractions with different denominators. We need to find a common denominator. On their multiplication sheet, the students look at the multiples of 3 and 4. When you find a common denominator, you have to find a number that is the same in both of your denominators. “What is the first number that you get to that is the same in your 3’s and 4’s?” Student response: 12. This is called finding the least common denominator. This means that I am trying to find the smallest number that is a multiple for both denominators. There may be other numbers that are the same, but we want to find the smallest number. If you use a larger number, we can still get to the right answer. However, let us try our best to find the smallest number.

On the Smart board, I show the students how to change their fractions into equivalent fractions with 12 as a denominator. I remind them of what we learned during our equivalent fraction lesson. “Multiply the numerator and denominator by the same number.” Together, we find the equivalent fraction for 1/4 which is 3/12, and the equivalent fraction for 1/3 is 4/12. I let the students know that at this point, we are doing the exact same thing that we did on yesterday’s lesson because now we have common denominators. Together, we add the fractions to get 7/12. To give the students the visual, the students take out their fraction strips for twelfths. They take out 7 of them and line them up below the 1/4 and 1/3. From the picture of Student Work, you can see that the students learned that 1/4 = 3/12 and 1/3 = 4/12 because those amounts are lined under each of those fractions. I tell the students that they do not need fraction stirps to find the answer. This is just to give them a visual of what the math calculations actually mean.

I remind the students to write all of their answers in simplest form. We do this by listing all of the factors that are common in our numerator and denominator. In this problem, 7 and 12. The factors for 7 are 1 and 7. The factors for 12 are 1, 2, 3, 4, 5, and 12. The only number common in both numbers is 1. Therefore, the answer is already written in simplest form.

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How to add fractions with unlike denominatorsThe Adding Fractions with Unlike Denominators (A) Math Worksheet Page 1 How to add fractions with unlike denominatorsThe Adding Fractions with Unlike Denominators (A) Math Worksheet Page 2

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.

How to add fractions with unlike denominators

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.

How to add fractions with unlike denominators

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.

Do not add denominators!

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.

Here’s the traditional way to add fractions with two different denominators:

  1. Find the LCM of the two denominators. Suppose you want to add the fractions 3/4 + 7/10.
  2. Increase the terms of each fraction so that the denominator of each equals the LCM.
  3. Substitute these two new fractions for the original ones and add.

Do you need like denominators to add fractions?

In order to add fractions, the fractions must have a common denominator. We need the pieces of each fraction to be the same size to combine them together. Let’s say we need to add 2/7 and 3/7 together.

What are the steps for adding and subtracting fractions?

Step 1: Find the Lowest Common Multiple (LCM) between the denominators. Step 2: Multiply the numerator and denominator of each fraction by a number so that they have the LCM as their new denominator. Step 3: Add or subtract the numerators and keep the denominator the same.

What are the 4 steps for adding and subtracting fractions?

Adding and Subtracting Fractions Examples

  • − #1: Find a common denominator. #2: Multiply to get both numerators over the same denominator.
  • + #1: Find a common denominator. #2: Multiply to get both numerators over the same denominator.
  • − #1: Find a common denominator.
  • + #1: Find a common denominator.

How do you add with different denominators?

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.

What are the ways to add?

Use a number line if you’re just learning to add. Draw a line, then write numbers along the line from 0-15. Circle the first number you want to add. Start at that number. Then, count down your number line, moving the same number of spaces as the second number you’re adding.

What are fractions with different denominators called?

From definition (1) we can say that the fractions with different denominators are called unlike fractions.

What are the 3 types of fractions?

In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions.

Are all fractions less than 1?

Fractions that are greater than 0 but less than 1 are called proper fractions. In proper fractions, the numerator is less than the denominator. When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction. An improper fraction is always 1 or greater than 1.

What is the greatest fraction less than 1?

Also note that, for integral values of the numerator and denominator (simplified), xx+1 is the largest fraction less than 1. Thus, it is impossible to find a definite largest rational number less than 1.

What is proper fraction with example?

A proper fraction is a fraction whose numerator is smaller than its denominator. An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

What is proper fraction explain?

: a fraction in which the numerator is less or of lower degree than the denominator.

Do you know fraction give some examples?

You can recognize a fraction by the slash that is written between the two numbers. We have a top number, the numerator, and a bottom number, the denominator. For example, 1/2 is a fraction. So 1/2 of a pie is half a pie!

What are the parts of fraction?

A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator.

What fraction of a day is 8 hours?

What is a fraction math is fun?

A Fraction (such as 3/8) has two numbers: NumeratorDenominator. The top number is the Numerator, it is the number of parts you have. The bottom number is the Denominator, it is the number of parts the whole is divided into.

What fraction is the same as 1 4?

Answer: The fractions equivalent to 1/4 are 2/8, 3/12, 4/16 etc. Equivalent fractions have same value in reduced form. Explanation: Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number.