# How to Model Multiplication of Fractions

Updated on August 30, 2013

## Multiplying Fractions

When multiplying fractions we multiply the parts separately to create a new fraction.

## Modeling Fraction Multiplication

We model the multiplication of fractions in order to visually understand how two fractions multiply to complete the correct product.

Using an area model we can visualize the fractions that we will be multiplying. By diving the rectangle in two different ways allows you to create the visual model of fraction multiplication.

## Model Fractions

In order to model the first fraction divide the rectangle into the number of the first denominator.

The example on the right will be 5/6 x 2/3.

I divided the rectangle into six equal pieces and shaded five of those pieces.

This model the fraction 5/6.

In this model I drew horizontal lines to divide the fraction evenly. it is important in creating a multiplication model that you divide it with horizontal or vertical lines and not dividing it into rectangular pieces. In order to model the second fraction I will use the opposite direction lines and then break it into rectangle to model the problem.

## Model Fraction Multiplication

Use rectangles to model fraction multiplication.

## Showing the Multiplication Fraction

In order to multiply the second fraction we need to divide the rectangle into thirds for this example.

Since the second fraction is 2/3.

I drew lines vertically to divide the rectangle into thirds.

I then shade 2 of the three pieces overlapping the already colored horizontal lines.

This creates a new area model with an area of 18 which will be our new denominator.

The new denominator is the number of pieces that were colored with both colors.

Ten pieces have been double shaded in this new area model.

Ten is our new numerator and 18 is the new denominator.

10/18 is the new fraction.

## Reducing the Fraction

Reducing the fraction can be done by grouping together rows and columns. The above fraction can be reduced to 9th be group together two of the rows. A total of 5 groups were shaded and there are 9 total groups.

Reducing fractions can be done in several ways. Important to note for all my teacher friends, simplifying is not part of the common core. What exactly does that mean for reducing fractions.

## Fraction Multiplication Models

The multiplication fraction model is modeled through area models as shown.

## Fraction Model Example Number 2

Example Number 2

3/10 x 2/5

This fraction model was split into 5th and 10th.

The vertical was divided into 5ths and the horizontal was divided into 10ths.

Two of the columns were shaded. Three of the rows were shaded.

5 time 10 is 50. The area model shows 50 total squares.

3 rows times 2 columns. 3 times 2 is 6.

The new fraction is 6 over 50
.

This can be reduced to 3/25.

## Draw a Rectangle

See if you can create a model of a multiplication problem. Lined paper is an easy way to create horizontal rows. Using a straight edge to create an area model for the vertical lines will help you keep a straight columns and create your model.

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