Final answer:
To determine how many groups of two-thirds are in three-fifths, you divide three-fifths by two-thirds, or multiply by the reciprocal, resulting in 0.9 groups of two-thirds in three-fifths.
Step-by-step explanation:
To find how many groups of ⅔ (two-thirds) are in ⅗ (three-fifths), you need to divide ⅗ by ⅔. In mathematical terms, you are performing the operation ⅗ ÷ ⅔.
Here is the step-by-step explanation:
- Convert the division of fractions to multiplication by the reciprocal. To divide by ⅔, you multiply by ⅔'s reciprocal, which is ⅖ (three-halves).
- Multiply ⅗ (three-fifths) by ⅖ (three-halves). When multiplying fractions, you multiply the numerators together and the denominators together.
- The multiplication is then 3/5 × 3/2 = 9/10, which simplifies to 0.9. This means there are 0.9 groups of ⅔ in ⅗.
The final answer is that there are 0.9 groups of two-thirds in three-fifths. This can be understood as slightly less than one full group of ⅔ within ⅗.