Equivalent fractions represent the same portion of a whole, even though they have different numerators and denominators. According to a video titled ["Equivalent fractions | MightyOwl Math | 4th Grade - YouTube"](), you find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. This keeps the ratio the same.
Understanding Equivalent Fractions
To understand equivalent fractions, consider a visual example. Imagine a rectangle divided into ten equal parts. If six of those parts are shaded, you have the fraction 6/10. This can be visualized and understood as a fraction.
Methods to Find Equivalent Fractions
There are two primary ways to find equivalent fractions:
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Multiplication: Multiply both the numerator and denominator by the same non-zero number.
- Example: To find an equivalent fraction of 1/2, multiply both the numerator and denominator by 3: (1 3) / (2 3) = 3/6. So, 1/2 and 3/6 are equivalent fractions.
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Division: Divide both the numerator and denominator by the same non-zero number (which must be a common factor).
- Example: To find an equivalent fraction of 4/8, divide both the numerator and denominator by 4: (4 / 4) / (8 / 4) = 1/2. So, 4/8 and 1/2 are equivalent fractions.
Key Insights
- Equivalent fractions visually represent the same shaded portion of a whole, even with different numerators and denominators.
- The fundamental principle is to maintain the ratio between the numerator and the denominator. This means multiplying or dividing them by the same number.
- This concept of maintaining the same ratio and having equivalent fractions helps in mathematical comparisons and problem-solving.
- As explained in the reference, the fractions, despite having different numbers, represent the same portion, making them equivalent.
Practical Examples
| Original Fraction | Operation | Equivalent Fraction |
|---|---|---|
| 1/4 | Multiply by 2 | 2/8 |
| 2/3 | Multiply by 3 | 6/9 |
| 10/15 | Divide by 5 | 2/3 |
| 6/12 | Divide by 6 | 1/2 |
