The Correct Answer and Explanation is:
The correct answer to the mathematical problem shown in the image is 5.
The image displays a division problem written as 1825 : 365. In this mathematical context, the colon symbol (:) is used to represent the division operator. Therefore, the task is to calculate the value of 1825 divided by 365.
To solve this, we need to determine how many times 365 can fit into 1825. We can approach this through estimation and multiplication. First, let’s estimate the result. The number 365 is close to 400, and 1825 is close to 1800. Dividing 1800 by 400 (or 18 by 4) gives us 4.5. This suggests the answer is likely to be a whole number near 4 or 5.
Let’s test the integer 5 by multiplying it by the divisor, 365. The calculation is as follows:
365 * 5
We can break this multiplication down:
- First, multiply 5 by the ones digit: 5 * 5 = 25. We write down the 5 and carry over the 2.
- Next, multiply 5 by the tens digit: 5 * 6 = 30. Add the carried over 2, which gives 32. We write down the 2 and carry over the 3.
- Finally, multiply 5 by the hundreds digit: 5 * 3 = 15. Add the carried over 3, which results in 18.
Combining these results, we get the number 1825. Since 365 multiplied by 5 equals exactly 1825, it means that 1825 divided by 365 is 5, with no remainder.
An alternative method is to simplify the fraction 1825/365. Both numbers end in a 5, so they are both divisible by 5. Dividing the numerator and the denominator by 5 gives:
- 1825 / 5 = 365
- 365 / 5 = 73
The simplified problem becomes 365 divided by 73. By testing multiples of 73, we find that 73 * 5 equals 365. Both methods confirm that the final answer is 5.
