Use the models below to write an equivalent fraction. You will need to divide the parts of the second model to make an equivalent fraction. 1. 24 = 3. 25 = 5. 56 = 2. 38 = 4. 46 = 6. 34
Correct Answers:
- 2/4 = 4/8
- 3/8 = 6/16
- 2/5 = 4/10
- 4/6 = 8/12
- 5/6 = 10/12
- 3/4 = 6/8
Understanding and Creating Equivalent Fractions
Equivalent fractions are fractions that may look different but represent the exact same value or portion of a whole. For instance, if you eat 1/2 of a cake, you’ve eaten the same amount as someone who eats 2/4 of the same cake. Mastering equivalent fractions is essential for working with fractions in addition, subtraction, and comparison.
How to Find Equivalent Fractions Using Models
This exercise provides a visual method for creating equivalent fractions. The key principle is that to create an equivalent fraction, you must multiply (or divide) both the numerator and the denominator by the same non-zero number. The models help us see why this works.
The instructions ask us to “divide the parts of the second model.” The simplest way to do this is to divide every existing part into two smaller, equal pieces. When we do this, we are doubling the total number of parts in the whole, which means we are multiplying the denominator by 2. To ensure the new fraction is equivalent, the shaded area must represent the same proportion of the whole. This means we must also double the number of shaded parts, multiplying the numerator by 2.
Example Walkthrough (Problem 5)
- Original Fraction: The first model is a rectangle divided into 6 equal squares, with 5 of them shaded. This represents the fraction 5/6.
- Dividing the Model: The task is to create an equivalent fraction using the second model. Following the instruction, we can divide each of the 6 squares in the second model into 2 smaller, equal parts (for example, by drawing a horizontal line through the middle of each square).
- New Denominator: After dividing each of the 6 original parts into 2, the total number of parts in the rectangle becomes 6 × 2 = 12. This is our new denominator.
- New Numerator: Since we multiplied the total number of parts by 2, we must also multiply the number of shaded parts by 2 to maintain an equivalent value. The new number of shaded parts is 5 × 2 = 10. This is our new numerator.
- The Equivalent Fraction: Therefore, 5/6 is equivalent to 10/12. If you shade 10 of the 12 smaller rectangles in the new model, you will see that it covers the exact same area as the 5 shaded squares in the original model.
