Final answer:
The question is about a student dividing the fraction 7/3 by 2/9 and checking their result through multiplication. The correct check involves multiplying the result by the divisor. Fractions are divided by multiplying the dividend by the reciprocal of the divisor, and multiplication and division should consider significant figures when dealing with measured numbers.
Step-by-step explanation:
The student is performing the operation of dividing fractions and checking their work using multiplication. Specifically, they completed the division of 7/3 ÷ 2/9 and are now using multiplication to check the result. To check the result of a fraction division, you multiply the answer with the divisor. If the product is the dividend, then the initial division was correct.
To divide fractions, such as 7/3 ÷ 2/9, we multiply by the reciprocal of the divisor. Here, the reciprocal of 2/9 is 9/2. Therefore, the division turns into multiplication: 7/3 × 9/2. When we multiply these fractions, we multipliy the numerators together and the denominators together, getting 63/6, which simplifies to 10½ or 10.5. To check this, we can multiply 10.5 by 2/9. If we get 7/3 as the result, our division was correct. In multiplication and division problems, it's also important to consider significant figures. The final answer should be rounded to have the same number of significant digits as the value with the least certainty. However, since we're dealing with exact numbers (fractions) here, we don't round the result for significant figures.