How to Use Models to Multiply Two Fractions?

A step-by-step guide to using models to multiply two fractions

Here’s a step-by-step guide to using models to multiply two fractions:

Step 1: Identify the two fractions to be multiplied

Identify the two fractions that need to be multiplied. For example, if you need to multiply \(\frac{2}{3}\) and \(\frac{3}{4}\), these are the two fractions you will be using.

Step 2: Choose a model

Choose a model to represent the fractions. Some common models include number lines, area models, and rectangular grids. For example, you might choose an area model to represent the fractions.

To find the product of the multiplications, you can use the area model:

– The denominator in the first factor signifies the number of columns that you must draw.
– The numerator signifies the number of columns that you must shade.
– The denominator in the second factor signifies the number of rows that you must draw.
– The numerator signifies the number of rows that you must shade.

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Step 3: Draw the model

Draw the model to represent the two fractions. For example, if you are using an area model, draw two rectangles, one to represent each fraction. The size of each rectangle should be proportional to the value of the fraction.

Step 4: Divide the rectangles

Divide each rectangle into the appropriate number of parts to represent the denominator of each fraction. For example, if the first rectangle represents \(\frac{2}{3}\), divide it into three equal parts. If the second rectangle represents \(\frac{3}{4}\), divide it into four equal parts.

Step 5: Shade the appropriate parts

Shade the appropriate parts of each rectangle to represent the numerator of each fraction. For example, if the first fraction is \(\frac{2}{3}\), shade two out of the three parts of the first rectangle. If the second fraction is \(\frac{3}{4}\), shade three out of the four parts of the second rectangle.

Step 6: Count the shaded parts

Count the total number of shaded parts in the model. For example, in the area model, you would count the total number of shaded squares.

Step 7: Simplify the result

Simplify the result to its lowest terms, if necessary. For example, if the total number of shaded parts is \(6\) out of \(12\), you would simplify this to \(\frac{1}{2}\).

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Using Models to Multiply Two Fractions – Example 1

Find the product by model.
\(\frac{4}{5}×\frac{1}{3}=\)_?
The model has \(5\) columns and has \(3\) rows.
\(4\) out of \(5\) columns are shaded, which shows a factor \(\frac{4}{5}\).
\(1\) out of \(3\) rows is shaded, which shows the factor \(\frac{1}{3}\).
The part where the shaded columns and rows overlap signifies the product. There are \(4\) overlapped sections.
So, \(\frac{4}{5}×\frac{1}{3}=\frac{4}{15}\)