Final answer:
To form 8/12 from 2/3, you can multiply 2/3 by any fraction where the numerator and denominator are the same, because that's equivalent to multiplying by 1. Since 8/12 simplifies to 2/3, we find that they are equivalent fractions, and multiplying by a fraction equal to 1 does not change the value of 2/3.
Step-by-step explanation:
To find by what fraction equal to 1 the fraction 2/3 should be multiplied to form 8/12, we first simplify 8/12 to its lowest terms. Upon simplification, 8/12 becomes 2/3, which indicates that 8/12 and 2/3 are equivalent fractions.
Therefore, multiplying 2/3 by a fraction equal to 1 (which could be any fraction where the numerator is equal to the denominator) will give us 8/12 in its simplified form.
Another way to think about this is by finding a fraction that, when multiplied by 2/3, would not change its value. Any number divided by itself is 1, such as 2/2, 3/3, 4/4, etc.
So, we can multiply 2/3 by 1 in the form of any of these fractions to get an equivalent fraction. Since 2/3 is already in simplest form and is equivalent to 8/12, it can be inferred that 2/3 multiplied by 1 (or any fraction like 4/4, 5/5, etc.) would yield the same value as 2/3, which is 8/12 in unsimplified form.