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Math for Kids23 chapters | 325 lessons

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Instructor:
*Bethany Calderwood*

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

In this lesson you will learn how to simplify improper and proper fractions. You will find the greatest common factor of the numerator and denominator and use it to reduce the fraction to its lowest terms.

Ang has a long name - Angela Marianna Cartelloni. She usually only uses her whole name when she wants to sound official. Most people at school call her 'Angela.' Her principal calls her 'Miss Cartelloni' and her music teacher calls her 'Angela Marianna.' All of these names refer to the same person. But her favorite name is her nickname 'Ang.' 'Ang' is the simplest form her name can take while still having the same value or meaning. In the same way that Ang simplifies her name, a mathematician wants to simplify fractions - taking larger numbers and making them smaller numbers with equivalent value.

A fraction represents a part of a whole number. It has a denominator on the bottom that tells how many parts are in the whole, and it has a numerator on top that tells how many parts the fraction represents. So the fraction 2/4 represents 2 parts out of a possible 4. When you are working with fractions, it is often necessary to simplify them. When you **simplify** a fraction, you write it using the smallest numerator and denominator that have the same value as the original fraction.

One type of fraction that needs to be simplified is called an improper fraction. An **improper fraction** has a larger number in the numerator than it has in the denominator. That means that the value of the fraction is greater than one, and it should be turned into a mixed number - a whole number and a fraction.

How do you simplify an improper fraction? Let's find out using the improper fraction 10/3.

Remember, the fraction line means ''divided by.'' So 10/3 is 10 divided by 3.

The answer is 3, with a remainder of one. The 3 is the whole number. The remainder becomes the fraction's new numerator, and the fraction's denominator is still 3. The simplified fraction is 3 1/3.

Many fractions that are proper fractions (with smaller numerators and larger denominators) are still not in their simplest form. They can be reduced to an equivalent fraction that refers to the same value, just like both the name 'Angela Marianna Cartelloni' and the name 'Ang' refer to the same person.

Let's simplify the fraction 3/12.

The first step is to find the factors of the numerator and of the denominator. The **factors** of a number are numbers by which it can be divided evenly.

Factors of 3: 1, 3

Factors of 12: 1, 2, 3, 4, 6, 12

Once you have found the factors of both the numerator and denominator, see which factors are in both lists--which factors they have in common.

The common factors of 3 and 12 are: 1, 3

The greatest common factor is 3.

Now that you know the greatest common factor, divide both the numerator and the denominator by the greatest common factor.

3 divided by 3 is 1. The new numerator is 1.

12 divided by 3 is 4. The new denominator is 4.

The new fraction is ¼.

If you follow these steps, you will be able to simplify fractions.

To **simplify** a fraction means writing it with the lowest possible numerator and denominator that maintain the value of the original fraction. **Improper fractions** should be turned into mixed numbers. For proper fractions, find the **factors** of the numerator and denominator, the numbers that divide evenly into them. Divide the numerator and denominator by the greatest common factor.

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Math for Kids23 chapters | 325 lessons

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- Comparing Fractions: Lesson for Kids
- Equivalent Fractions: Lesson for Kids
- How to Add Fractions: Lesson for Kids
- Fractions Games for Kids
- Fractions to Decimals: Lesson for Kids
- Fractions: Lesson for Kids
- Numerator & Denominator Lesson for Kids
- Decimals: Lesson for Kids
- Multiplying Fractions by Whole Numbers: Lesson for Kids 3:04
- How to Simplify Fractions: Lesson for Kids
- What is a Benchmark Fraction on a Number Line? 3:48
- How to Add Mixed Fractions with Different Denominators
- Multiplying Compound Fractions
- Simplifying Compound Fractions
- Dividing Compound Fractions
- Adding Compound Fractions
- Subtracting Compound Fractions
- How to Subtract Fractions with Variables
- Multiplying Fractions with Like Denominators
- Subtracting Fractions with Like Denominators
- Reducing Fractions: Rules & Practice
- Definition of Simplest Form: Lesson for Kids
- How to Add Fractions with Unlike Denominators
- How to Subtract Fractions with Unlike Denominators
- Rules for Subtracting Fractions
- Rules for Multiplying Fractions
- Rules for Dividing Fractions
- Ordering Fractions on a Number Line
- Locating Fractions on a Number Line
- How to Add & Subtract Two Fractions with Like Denominators
- How to Find Equivalent Fractions on a Number Line
- How to Subtract Mixed Fractions with Unlike Denominators
- Go to Fractions for Elementary School

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