Find equivalent fractions using area models: two models
Some fractions look different but are actually the same size! 🤔 These are called equivalent fractions. We can use two identical shapes to see how this works.
Do this: Read the concept below, then try the quiz or activity.
Concept
Equivalent fractions are fractions that represent the exact same amount, even though they have different numerators and denominators. Using two identical area models makes this easy to see.
Visual Comparison: Let's find a fraction that is equivalent to 1/2. 1. Model 1: Draw a rectangle. Divide it into 2 equal parts (because the denominator is 2). Shade 1 of those parts (because the numerator is 1). This is 1/2. 2. Model 2: Draw another rectangle that is the exact same size right underneath the first one. 3. Divide it differently: Let's divide this second rectangle into 4 equal parts. 4. Shade it to match: Now, shade the parts in the second rectangle until the shaded area is the exact same length as the shaded area in the first rectangle. You will see that you need to shade 2 of the parts. 5. Write the new fraction: The fraction for the second model is 2/4.
Conclusion: Since the shaded areas are exactly the same size, we have proven that 1/2 = 2/4. They are equivalent fractions! You can do this again by dividing the second rectangle into 6, 8, or 10 pieces to find more equivalent fractions.
Key Idea: If two fractions are equivalent, they take up the same amount of space in identical wholes. It's like having one big piece of cake or two smaller pieces that add up to the same amount.
Try it
Practice: Find equivalent fractions using area models: two models.