Visualizing the Magic: How to Multiply Fractions Using Models

Multiplying fractions is a fundamental skill in mathematics, and while the process is straightforward, visualizing it can provide a deeper understanding.

By using models, we can see how fractions multiply to create a new value. In this blog post, we’ll walk through a step-by-step guide on multiplying fractions using visual aids.

Step-by-step Guide:

1. Basics of Multiplying Fractions:

When multiplying fractions, we multiply the numerators together for the new numerator and the denominators together for the new denominator.

2. Setting Up Models:

Draw models (like rectangles) for each fraction. Shade the portion represented by the fraction. For instance, for \(\frac{1}{3}\), shade one-third of the rectangle.

3. Visualizing the Multiplication:

Overlay the models to see the shared shaded area. This area represents the product of the two fractions.

4. Calculating the Product:

Multiply the numerators together for the new numerator and the denominators together for the new denominator. Simplify the fraction if possible.

Example 1:

Multiply \(\frac{2}{3}\) by \(\frac{3}{4}\) using models.

Solution:

The product’s numerator is \(2 \times 3 = 6\) and the denominator is \(3 \times 4 = 12\). So, \(\frac{2}{3} \times \frac{3}{4} = \frac{6}{12}\), which simplifies to \(\frac{1}{2}\).

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Example 2:

Multiply \(\frac{1}{5}\) by \(\frac{2}{7}\) using models.

Solution:

The product’s numerator is \(1 \times 2 = 2\) and the denominator is \(5 \times 7 = 35\). So, \(\frac{1}{5} \times \frac{2}{7} = \frac{2}{35}\).

Practice Questions:

1. Multiply \(\frac{3}{4}\) by \(\frac{2}{5}\) using models.

2. Multiply \(\frac{1}{6}\) by \(\frac{4}{9}\) using models.

3. Multiply \(\frac{5}{8}\) by \(\frac{3}{7}\) using models.

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Answers:

1. \(\frac{3}{10}\)

2. \(\frac{2}{9}\)

3. \(\frac{15}{56}\)

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Visualizing the Magic: How to Multiply Fractions Using Models