Final answer:
The number that, when multiplied by 3 1/3, gives 10 is 3. This is found by dividing 10 by 3 1/3 or equivalently, multiplying 10 by 3/10.
Step-by-step explanation:
The student is asking us to find a number, which when multiplied by 3 1/3, gives the result 10. While we can employ the method of powers and roots to solve this, in this case, there is a simpler approach. By understanding fraction and whole number multiplication and division, we can find the answer to this problem.
To solve this, we need to divide 10 by 3 1/3. 3 1/3 is also known as 10/3 when converted to an improper fraction. Thus, what we are looking for is the number x such that x times 10/3 equals 10. This can be represented algebraically as x * (10/3) = 10. To isolate x, we divide both sides of the equation by (10/3), finding that x = 10 /(10/3).
Performing the division, we get x = 10 * (3/10), after inverting the divisor. Simplifying further, we multiply 10 by 3 which is 30 and then divide by 10, resulting in x = 3. Therefore, the number we are looking for is 3.