How to Use Area Models to Add Fractions with Like Denominators
Area models provide a visual way to represent and add fractions with like denominators.
A step-by-step guide to Using Area Models to Add Fractions with Like Denominators
Here’s a step-by-step guide to help you with this:
Step 1: Understand the concept of an area model
An area model is a visual representation of a mathematical concept using a grid, rectangle, or square. Each section of the model represents a part of the whole, and the entire model represents the total value.
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Step 2: Create a combined area model for both fractions
Since the fractions have like denominators, you can create a single area model to represent both fractions. Draw a rectangle and divide it into equal parts based on the denominator of the fractions.
Example: To add \(\frac{2}{5}\) and \(\frac{3}{5}\):
- Draw a rectangle and divide it into 5 equal parts for the denominator 5.
Step 3: Shade the parts representing each fraction
Shade the number of parts indicated by the numerator of each fraction.
- In the example, shade 2 parts to represent \(\frac{2}{5}\) and 3 more parts to represent \(\frac{3}{5}\).
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Step 4: Add the fractions using the area model
Combine the shaded parts of the area model to represent the sum of the fractions.
- For the example above, the shaded parts from the two fractions (\(\frac{2}{5}\) and \(\frac{3}{5}\)) represent the sum of the fractions.
Step 5: Write the sum as a fraction
Count the total number of shaded parts and write the sum as a fraction with the same denominator as the original fractions.
- In the example above, there are a total of 5 shaded parts, so the sum is \(\frac{5}{5}\).
Step 6: Simplify the fraction, if necessary
If the fraction can be simplified, do so to express the sum in its simplest form.
- In this example, \(\frac{5}{5}\) can be simplified to 1.
So, using an area model, we find that \(\frac{2}{5} + \frac{3}{5} = 1\). This method helps to visually demonstrate the addition of fractions with like denominators, making it more accessible and easier to comprehend.
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