Flipping and Multiplying Fractions


Division and multiplication are two different and closely-related operations in mathematics. In this post, we'll explain the need to flip and multiply when we divide a whole number by a fraction. Other than adding the fractions, this is another essential operation that might seem complicated for some students. This entire concept can be explained in several ways, but the approach used in this video is quite simple to understand this concept.

We'll understand this with the simple example of 6 2 = 3

The simplest one is to make two groups and divide six into the two groups. But the video will use the size model to explain best how this works. It's like having six things which are divided into groups of size two.

Let s best explain the division of fractions with the help of some examples:

If you have six sticks that need to be divided by two, the two sticks will fall into each group making three the total number for each group.

Imagine having a chocolate bar with six blocks, which will be divided by two. This means three blocks are placed into each group, i.e. three groups of chocolate.

Below is another example of dividing the fractions:

We imagine six blocks of chocolate on the number line from 0 to 6 and divide it by . Don’t be confused because this does not mean to divide six pieces into two halves. It indicates the division of six blocks into half sizes. You can ask your students this question if they have six pieces of chocolate, how many halves would fit in there The answer is two halves would fit into each piece and total halves equal to 12.

This is how the division takes place here:

6 => 6 x 2 = 12

At this point, you might have identified that the denominator in the fraction represents the number of halves that would fit into each piece. Multiply it with the whole number 6 to get the total number of halves.

Now, let's take an example of multiplying the fractions that don t have one on the numerator, such as 6 2/3.

Even if the numerator is not 1, ignore it and cut the chocolate bar into three halves (denominator) for each block, which equals 18. Now, we can achieve the fraction 2/3 by gluing any of the two 1/3, and in this way, we get 2/3 size piece. If we do this for the whole chocolate bar, it equals to 9.

That can also be seen by the following calculation:

6 2/3 => (6 x 3)/2= 18/2= 9

If you practice this with different types of fractions, you'll understand the pattern more concretely. Once the student has a common understanding of the inversion and multiplication of fractions and learns the trick along with practicing different fractions, the student will have a better understanding of multiplying fractions. Hopefully, this video will help a student better grasp this concept.

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Craig Selinger, CEO of Themba Tutors (serving Manhattan, Brooklyn, Queens, Staten Island, Bronx, Westchester, Long Island, New Jersey, and Connecticut), is a NY State licensed speech-language pathologist, executive functioning coach, and learning specialist with over 18 years of experience working professionally with over a thousand families. His expertise includes language-based learning issues, e.g. reading, writing, speaking, and listening, executive functioning, ADHD/ADD, and learning disabilities. Check out his interviews with top-notch professionals in the field on Spotify.
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