To find fractions that are equivalent to 2/3, we can multiply both the numerator (the top number) and denominator (the bottom number) by the same non-zero integer. This method works because multiplying by one (which is what multiplying both numbers by the same integer is doing) does not change the value of the fraction.
Here are a few examples:
- 4/6: 2 * 2 = 4 and 3 * 2 = 6, so 2/3 = 4/6.
- 6/9: 2 * 3 = 6 and 3 * 3 = 9, so 2/3 = 6/9.
- 8/12: 2 * 4 = 8 and 3 * 4 = 12, so 2/3 = 8/12.
- 10/15: 2 * 5 = 10 and 3 * 5 = 15, so 2/3 = 10/15.
- 0/0: Although 0/0 is an undefined fraction, it represents that 0 is also equivalent to 2/3 in the sense of ratios.
In fact, any fraction can be created that is equivalent to 2/3 by simply choosing a different integer to multiply both parts. For example, if we multiply by 10, we would get 20/30, and if we multiply by 1000, we would get 2000/3000.