 ### Introduction to Fractions

These are your very basic sheets to help explain what a fraction is and how it can be modeled.

• Fraction Matching Game Models Cards Game - This is a fun game where students match models on cards to fractions on cards. It's a lot of fun to make this like a game of concentration.
• Fractions as Models - Match the correct fraction to the models that are found in the diagram. We use rectangles and squares here for this one.
• Reducing Fractions within Models - This is a two part skill. Step one is to determine the fraction represented by the model. Step two is to reduce the fraction and find the matching fraction.
• Models to Fractions with Squares - Determine the fraction that is being modelled by the shaded shapes. The directions do not indicate that you are required to reduce the fraction.
• Models to Fractions with Unique Shapes - Write a fraction that is equivalent to the shaded area of the shapes. We use a wide variety of shape displays.
• Shade Half - This will give both you and your students a solid understanding of where they reside in their knowledge of fractions.
• Shade a Quarter- The asymmetrical shapes will cause some confusing for your non-visual learners.
• Numerator or Denominator - We are constantly using the two terms in class, but are we 100% sure kids know what we are talking about? This worksheet will help them gain mastery of that concept.
• Fraction Word Problems - These are challenging word problems that involve multiple steps.

### Basic Operations With Fractions

This set of sheets help students understand how to add, subtract, divide, and multiply fractions. We have recently sorted all worksheets by operations. You will now find basic fraction sheets and mixed number sheets together.

We work solely on sums in this section. We use visuals in the forms of models.

• Adding Mixed Fractions Worksheet 1 - Ten quick problems that have you adding two fractions or a fraction and a mixed number. These are great practice.
• Version 2 - This is another version of the original. New problems with fractions and mixed numbers.
• Version 3 - This is another version of the original. New problems with fractions and mixed numbers. We bring you froggie!
• Version 4
• Version 5

### Rewriting Fractions Worksheets

This is an advanced skill. Students have to take operations into account with exponents. Remember the "E" in PEMDAS stands for exponents.

1. Missing Numerator or Denominator Worksheet 1 - Determine the missing part (denominator or numerator) of an equal fraction.
2. Worksheet 2 - This is an extra practice version.
3. Worksheet 3
4. Worksheet 4
5. Worksheet 5

### Common Multiple and Factors Worksheets

1. Greatest Common Factors Worksheet 1 - We work on factors here. Students find the common factor between the two numbers.
2. Worksheet 2 - Another version of this worksheets for even more practice on this skill.
3. Worksheet 3
4. Greatest Common Factors Answer Key
5. Least Common Multiples Worksheet 1 - We find the smallest multiple that evenly goes into both numbers. A quick, but important skill to master.
6. Worksheet 2 - Another practice sheet for you. We would suggest doing this skill at least twice.
7. Worksheet 3
8. Least Common Multiples Answer Key

### Comparing and Converting Decimals and Fractions

Decimals and fractions are often used at all levels. These sheets will really help students gauge where they fall when presented with both forms of a number.

1. Comparing Decimals & Fractions Worksheet 1 - The fractions are all set to one hundred as a denominator to make for a nice transition into comparisons.
2. Version 2 - This is another practice sheet form you. In this section we work on fraction versus decimal and fraction versus fraction.
3. Version 3
4. Version 4
5. Version 5
6. Converting Fractions To Decimals Worksheet 1 - Switch between fractional value and decimal value. We start out easy and get progressively harder.
7. Version 2 - This is a different version for you to work with. It will help students master this skill.
8. Version 3
9. Converting Decimals To Fractions Version 1 - The difficulty of this worksheet is based on your perference. You can just have students place the number over 100 or have them formulate the reduced fraction. We'll leave that up to you.
10. Version 2 - A different version and arrangement for you. Use this to help master this skill. On later versions we recommend having students further reduceing what is available.
11. Version 3

### Writing Mixed Numbers From Fractions

You are provide with a random denominator and numerator and then you are asked to convert the fraction to a mixed number.

1. Mixed Numbers Worksheet 1 - Practice writing each fraction as a mixed number. You can decide how far you want the students to reduce the fraction.
2. Version 2 - Another version of this worksheet for you. We mix up the denominators a little better in this version.
3. Version 3
4. Version 4
5. Version 5

What Are Fractions?

Fractions represent a small portion of a whole. They are an exciting concept to explain to children as fractions and percentages are often the part of mathematics we use most often in our lives. The word "fraction" is derived from the Latin Word "fractio," which means dividing or breaking things down. Civilizations have used this form of math for a long time. They are also extremely practical as they help you break down how anything will be divided amongst members. In the olden days, people used them to break down food and supplies since no form of currency was available.

Their Role in Math

In Mathematics, you can use fractions to define a numerical value. They are generally used to express a portion of a whole so that you can quickly identify the ratio one portion serves. The simplest way to explain this is by using an example. If we take a pizza, for example, then the pizza represents the whole number 1. If the pizza is cut into 8 slices, each slice would be 1/8th of the pizza. Each pizza slice can be defined as 1 out of 8, 1 of 8, or 1/8th of the pizza. If we select 4 parts of the pizza, that is also half of the pizza.

## How Do You Define Fractions?

All fractions have two major parts that help us identify their origins. The Arabs initially brought about the line between the fractions. Before that, no one tried to distinguish between the two parts of a mathmathical fragments. Due to this aesthetic change, we also got different parts of a fraction that helped us define it. The two parts are the denominator and the numerator.

Numerators

The numerator is the part of the fraction that talks about the the number of parts that exist relative to a complete unit and how many of those sections are selected as being a part of the fraction. The numerator represents the upper area (above the line) and is placed before the fractional bar.

Denominators

The denominator represents the total number of pieces in the whole. It means the number of parts that something has been divided into so you know what the fraction is out of. The denominator is placed in the value's lower portion and below the fraction bar.

Forms of Fractions

There are many different form of fractions that you must know about. Like any other mathematical quantity, they don't always make sense.

Proper Form

A proper fraction is a value where the numerator number has a lower value than the denominator. They will make rational sense since we acknowledge that fractions are a more minor part of something whole. For example, 3/7, 8/9, and 6/11 all follow this form.

Improper Form

Improper fractions are ones where the numerator has a greater value than the denominator. It's known as an improper fraction because it doesn't make sense practically for there to be a more significant portion than 1 whole unit. If we simplify these improper values, we will generally get a number greater than 1. Improper form don't simply mean a value that is less than 1.

Mixed Form

Mixed fractions are a combination of a whole number and a proper form. The mixed form generally represents improper fractions in a more proper form. We find that you can represent almost any number in the form of a mixed fraction as long as it's greater than one. You can easily transform an improper form into a mixed form.

Unit Form

Unit Fractions are some of the easiest to decipher basic they are presented very clearly. We find that with unit fractions, that numerator is generally 1. These unit forms allow you to simplify values so that you can easily understand what a more significant number of fractions will look like.

Like

Fractions that have the same denominators will be called like form. These are simple values, and all have the same denominator, so they're easy to calculate. For example, 7/2, 5/2, and 3/2 are all like fractions.

Unlike Fractions

Converse unlike fractions, are values that do not have the same denominators. Simplifications for these kinds of fractions are different. They involve equalizing the denominator using the lowest common multiples.

Examples of unlike fractions are 2/3, 3/4, and 7/8.

Equivalent Fractions

The term "equivalent" fshould give this one away. Equivalent fractions represent the same portion of the same whole. For example, an equivalent fraction is something like 2/4 and 1/2, as both equate to each other. Just like this, 1/3 and 3/9 are the same.

Tips To Teach Children These Concepts

One of the most challenging tasks for a teacher or parent is to explain how fractions work to children who don't quite understand the concept.

Make it Fun

The way to do this is by making fractions fun. We gave you the example of a pizza. That's an incentive you can bring into your home or your classroom.

Practical Examples

Introducing real-life examples of fractions to children is a great way to cement the concept of fractions into their malleable brains. You can use chocolate bars, grapes, or chips to help identify denominators and numerators with students. Many teachers find that LEGO blocks help many children correctly identify fractions in the classroom and the real world.

Accurate Representations

In older children, who are maybe not that wowed by the food. You can use the representation of a number line to impart a more graphical and mathematically accurate understanding to students regarding fractions. Many teachers also use toy trains and their cabins to explain to their students how fractions work in real life.

The best way to teach children about fractions is by going slow and using several representations. You also want to interlink fractions with percentages as these two topics are often linked in Mathematics Textbooks.

Final Thoughts

This concept is a notable topic that is important to teach in the mathematics classroom. There are many different types of fractions and knowing about them helps you explain the concept better to children. The idea is to bring yourself down to the child's level and impart information so they will understand and remember.