# How To Subtract Fractions With Unlike Denominators Step By Step

How To Subtract Fractions With Unlike Denominators Step By Step – To add or subtract fractions with different denominators, we must first write them as equivalent fractions with the same denominator. We use the techniques from the previous section to find the LCM of the denominator of the fraction. Remember we call this the LCD (lowest common denominator). When we find the LCD, we only use the denominators of fractions, not the numerators.

Next, we can use the Equivalent Fractions property to algebraically change the fraction to an equivalent. Remember that two fractions are equivalent if they have the same value. The steps for finding the LCD and properties of equivalent fractions are repeated below for reference.

## How To Subtract Fractions With Unlike Denominators Step By Step

After we have converted the two fractions into equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerator. Try the examples and practice questions below to brush up on these skills.

## How To Subtract Fractions With Different Denominators

Remember that you must always check if the answer can be simplified. Since [latex]5[/latex] and [latex]6[/latex] have no common factors, the fraction [latex]Largefrac[/latex] cannot be reduced.

Watch the following video to see more examples and explanations of how to add two fractions with different denominators.

One of the fractions already has a lowest common denominator, so we just had to recalculate the other fraction.

### Adding And Subtracting Fractions With Unlike Denominators — Process

Since [latex]31[/latex] is a prime number, it has no common factors with [latex]36[/latex]. The answer is simplified.

When we use the Equivalent Fractions property, it’s a quick way to find the number you need to multiply by to get the LCD. Write down the factors for the denominators and the LCD just as you did to find the LCD. The “missing” factors for each denominator are the numbers you need.

Twelve has two [latex]2[/latex] factors, but only one of [latex]3[/latex] — so it is “missing” [latex]3[/latex]. We multiplied the numerator and denominator [latex]Largefrac[/latex] by [latex]3[/latex] to obtain an equivalent fraction with the denominator [latex]36[/latex].

### Subtract Fractions With Unlike Denominators

Eighteen is one factor less than [latex]2[/latex] — so multiply the numerator and denominator [latex]Largefrac[/latex] by [latex]2[/latex] to get an equivalent fraction with the denominator [latex] 36[/latex]. We will use this method when subtracting fractions in the next example. It’s the moment you’ve been worrying about. It’s time to teach students how to add and subtract fractions with different denominators. There are SO many components and skills that are really needed to complete this task! What is the teacher doing???

Do you teach them a “trick” like the butterfly method or cross multiplication? Have you spent days teaching students how to find the least common multiple? Do children only guess the correct number? NOT!!! STOP DOING THAT NOW!

Don’t get me wrong, I used exactly those strategies. And my students who were fast math teachers got it. Even a few high school kids figured it out after a while.

But, as with so many other subjects, my struggling special education students LOST. I just described it as it should be. The reason some students are lost is that all these “tips” and “tricks” have no concrete basis. Children may learn rules to follow, but they have no idea WHY they follow those rules. In order for students to truly understand this topic, they MUST be able to see the why behind the math!

After years of experimenting, I finally found a way to teach this that ALL students found accessible and even…fun!

Looking for more ideas for combining math lessons and engaging students? Check out my FREE tutorial for an engaging math lesson! It has tons of ideas for adding variety to your math lessons while keeping students engaged and learning!

### The Best Way To Teach Adding And Subtracting Fractions

Step 2: Mark the rectangle on the left 1/2, draw a vertical line down the middle. Shade 1 of 2 parts.

Step 3: Mark the rectangle on the right 1/3, draw two lines horizontally and shade 1 of the 3 parts.

Step 4: Take a vertical line from 1/2 the rectangle and overlay it over the thirds model. Then take the horizontal lines from the 1/3 rectangle and place them over the 1/2 model. (This step may take a few tries for the kids to get used to, but they will, and it will be AMAZING!)

### How To Subtract Fractions With Different Denominators (a Step By Step Guide)

Step 6: Draw a new rectangle below the first two into which you will insert all the new pieces of the same size. Be sure to draw the same number of parts as the denominators of the above fractions.

Step 7: Shade the parts from the above fractions into a new rectangle and estimate the sum of the two fractions.

When subtracting fractions, steps 2-5 above are identical. Once you’ve created your fraction models with equivalent fractions, things are a little different. After all, you take away!

#### Subtracting Fractions Worksheets

Starting with step 6: Count how many pieces the model on the right has. Cross as many parts in the model on the left.

After about two days of using this in class, almost every student had that “ah-ha” moment. They started asking if they could try to do it without a model. I told them to continue using the models for another day to find the common denominator, but to skip modeling the answer and just skip writing the addition or subtraction statement using the new equivalent fractions. After another day and more pleading, I let the students SHOW ME how to find equivalent fractions without a model. It was amazing! Moreover, many of them began to realize that they could use different equivalent fractions because they could see that they could find a lower common denominator.

It’s pretty smooth at that point. I spend at least a week on this topic, and sometimes more. The last few days can be used to help a few students who are still struggling to get the hang of it, or understand the models but aren’t ready to move away from them and just use the algorithm. Challenge students with more difficult denominators or have them add more than 3 fractions at a time.

### Subtract Fractions Calculator

It can be difficult to come up with enough math problems to use, so this is a paid product that I like to use in class to keep students engaged. Now we will learn about subtracting fractions with different denominators, and fractions are parts of a whole, that is, they represent part of a collection. The word fraction comes from ‘fractio’, a Latin word meaning ‘to break’. Egyptians used fractions to solve mathematical problems, including dividing food and supplies.

The ancient Romans wrote fractions as words, not as numbers. Indians were the first to write fractions as numbers that appeared as one number above another. The Arabs were the first to add a line between numbers and distinguish them as numerators and denominators.

For example, when you cut a whole watermelon in two, both halves become half a whole watermelon or a piece of watermelon. One half of a watermelon is then mathematically represented as 12. When you further cut the two halves of the watermelon into two parts, the whole watermelon is divided into four parts or quarters of the whole watermelon. Then the watermelon portion will be represented as ¼. Another perfect example that can illustrate this concept is pizza. The pizzas come as rounds that can be shared or divided into 4-6 pieces or more, depending on the size. In this case, each piece of pizza represents a part of the whole, which is pizza. What are the parts of a fraction? The numerator and the denominator form two parts of the fraction. The horizontal line that separates the numerator and the denominator is called a fraction. The denominator is the number of parts into which the whole is divided, and is located below the division line. The counter shows the number of parts of the fraction presented or selected. The space is above the fraction. For example, in the fraction 1227, 12 is the numerator and 27 is the denominator. Why do we use fractions? Fractions tell us what part of the whole you have, need or want. Fractions are also easier to understand than decimals. They help to better visualize a concept or system. Types of Fractions: There are four basic types of fractions. These are: Unit fraction – a fraction with 1 as numerator. For example, 12, 14 are proper fractions – they have a numerator whose value is less than the denominator. Example: 49, 910 Improper fractions – They have a numerator whose value is greater than the denominator. Example: 37, 128 Mixed Fraction – Consists of a whole number with a special fraction. Example 5 34, 10 12 How do you simplify fractions? To simplify a fraction, you can follow one of the following steps as needed: Find the greatest common factor: To do this, write down the factors and the numerator and