Final answer:
The equivalent ratio of cups of banana to cups of apple juice for the ratio 1/4:1/3 is 3:4, after finding the least common multiple of the denominators and scaling both fractions accordingly.
Step-by-step explanation:
To find a ratio equivalent to 1/4:1/3, we can either simplify or scale both parts of the ratio by the same factor. In this case, we want to scale up since we can't simplify these fractions any further. What we're looking for is the least common multiple (LCM) of the denominators 4 and 3, which is 12. This way, we can express both fractions with the same denominator to easily compare them.
To scale the fraction 1/4 up to have a denominator of 12, we need to multiply both the numerator and the denominator by 3: 1/4 * 3/3 = 3/12.
Similarly, we multiply the fraction 1/3 by 4 to get an equivalent fraction with a denominator of 12: 1/3 * 4/4 = 4/12.
Therefore, the ratio of cups of banana to cups of apple juice that is equivalent to 1/4:1/3 will be 3/12:4/12, which simplifies to 3:4.