The Correct Answer and Explanation is:
The correct answer is 8.5.
The mathematical problem presented in the image is a division of two decimal numbers: 22.1 divided by 2.6. To solve this, the most straightforward method is to convert the division problem into one involving whole numbers, which simplifies the calculation significantly.
The first step is to make the divisor, which is 2.6, a whole number. We can achieve this by multiplying it by 10. This process effectively moves the decimal point one place to the right, turning 2.6 into 26. However, to keep the division problem equivalent and ensure the final answer remains correct, we must also perform the same operation on the dividend, which is 22.1. Multiplying 22.1 by 10 also moves its decimal point one place to the right, resulting in 221. This fundamental rule ensures the ratio between the two numbers is preserved. Thus, the original problem of 22.1 ÷ 2.6 becomes the equivalent problem of 221 ÷ 26.
Now, we can proceed with long division using these whole numbers. We ask how many times 26 can go into 221. By estimating, we can see that 26 is close to 25, and 25 goes into 200 eight times. Let’s try multiplying 26 by 8. The calculation is 26 × 8 = 208. This number is less than 221, so 8 is the first digit of our answer. We subtract 208 from 221, which leaves a remainder of 13 (221 – 208 = 13).
Since we have a remainder, we place a decimal point in our answer after the 8. We then add a zero to our remainder of 13, making it 130. Now we must determine how many times 26 goes into 130. We can again estimate. Since 26 × 10 is 260, half of that would be 130. Therefore, 26 × 5 is exactly 130. We place 5 as the next digit in our answer. Subtracting 130 from 130 results in a remainder of 0. Since the remainder is zero, the division is complete.
The final result of the long division is 8.5. Therefore, 22.1 divided by 2.6 equals 8.5.
