Here are more examples of equivalent fractions, illustrating that they represent the same portion of a whole, even though they look different:
- Understanding Equivalent Fractions: Equivalent fractions are fractions that have different numerators and denominators but represent the same value. You can find equivalent fractions by multiplying or dividing both the numerator and denominator of a fraction by the same non-zero number.
Examples of Equivalent Fractions:
Here are some examples to further illustrate the concept.
Example 1:
- 1/3, 2/6, 3/9, 4/12, 5/15... All these fractions are equivalent. They are derived by multiplying both the numerator and the denominator of 1/3 by 2, 3, 4, 5, and so on respectively.
Example 2:
- 2/5, 4/10, 6/15, 8/20... These are equivalent fractions obtained by multiplying the numerator and denominator of 2/5 by 2, 3, 4, and so on.
Example 3:
- 3/4, 6/8, 9/12, 12/16... These fractions are equivalent as they can all be simplified back to 3/4.
Example 4: Simplifying for Equivalence
Sometimes, it is easier to see the equivalency by simplifying fractions to their lowest terms.
- For example: 10/15 and 4/6. While they look different, both can be simplified. 10/15 simplifies to 2/3 (dividing both by 5). 4/6 also simplifies to 2/3 (dividing both by 2). Hence, they are equivalent.
Examples Summarized in a Table:
| Original Fraction | Equivalent Fractions | Method |
|---|---|---|
| 1/4 | 2/8, 3/12, 4/16, 5/20 | Multiplying numerator & denominator by 2, 3, 4, 5 |
| 2/3 | 4/6, 6/9, 8/12, 10/15 | Multiplying numerator & denominator by 2, 3, 4, 5 |
| 3/5 | 6/10, 9/15, 12/20, 15/25 | Multiplying numerator & denominator by 2, 3, 4, 5 |
| 8/12 | 2/3 (simplified), 4/6, 16/24 | Dividing numerator & denominator by 4, multiplying by 2 |
These examples highlight that equivalent fractions, despite having different appearances, represent the same proportional amount. Understanding and identifying equivalent fractions is a fundamental concept in mathematics.
