This math lesson is designed for 6 to 12-year-old children. It guides the child to convert improper fractions into mixed numbers using Montessori fraction insets.
What are improper fractions?
When the numerator of a fraction is greater than or equal to the numerator, it is known as an improper fraction. Numerically, they are always equal to or greater than 1(one). Examples of improper fractions are 9/2, 6/5, 8/3, etc.
What are mixed fractions?
When a fraction is represented with the quotient and remainder, it is known as a mixed fraction. It is written as a combination of a natural number and a proper fraction. It is a simplified form of an improper fraction. Examples of mixed fractions are:
Numerically, a mixed fraction is always greater than 1.
Please note: Any mixed fraction can be written as an improper fraction and any improper fraction is written as a mixed fraction.
Converting Improper Fractions to Mixed Numbers
The denominator of the mixed fraction is always the same as the improper fraction. For converting an improper fraction to mixed numbers, we have to follow the below-listed steps:
- Step 1- Divide the numerator by the denominator.
- Step 2- Get values of quotient and remainder.
- Step 3- write the quotient number, the remainder as the numerator of the fraction, and the divisor as the denominator.
Let’s look at a quick and easy example of how we can convert improper fractions to mixed numbers. Let’s say you have an improper fraction, 4/3 The first step is to divide 4 by 3. We get 1 as the quotient with a remainder of 1. Next, we will place 1 as the numerator, 3 as the denominator, and 1 as the whole number. Thus, we get the mixed fraction:
Prerequisites of learning how to convert improper fractions into mixed numbers
A child must be aware of fraction insets, what are fractions, and equivalent fractions.
Converting Improper Fractions to mixed numbers using Montessori fraction insets
- Invite the child to bring the fraction insets and the fraction problems to the table.
- Introduce the child to the fraction insets.
- Also, introduce what are improper fractions and mixed fractions and help them understand the concept of fractions as shown in the video.
- Tell them today we will add similar fractions (whose denominators are the same) and convert the result into mixed fractions.
- Now, bring the problem card on the mat showing
- Ask the child to represent ⅔ using two ⅓ fraction insets.
- Repeat step 6 for the second ⅔ fraction.
- Now combine all the fraction insets to make a complete circle. If any inset is left, keep it aside.
- Now, tell the child that a complete circle represents the whole number of the mixed fraction, the left-out fraction inset represents the numerator of the fraction, and the denominator remains the same, i.e. 3.
- The mixed fraction is written as
- Ask the child to note the answer.
Watch the video to learn how to use Montessori fraction insets to represent fractions and Invite the child to convert another improper fraction into mixed numbers.
This practical method of converting improper fractions into mixed numbers is a fun and concrete way to help them get a better understanding of math fractions concepts.
Related fraction video resources:
- Multiply and divide fractions by whole numbers
- Equivalent fractions
- Addition and subtraction of fractions
- Learn arithmetic and fractions with DIY Montessori materials
- Decimal fraction cards
For more math video resources, click here.
Video Created by: Sharmeen Niazi (Archgate Montessori Academy, Plano, TX)
This video has been added and used with the author’s permission. It is also available on the author’s YouTube, here.