The Correct Answer and Explanation is:
The correct answer is 56.
To solve the division problem 22,064 ÷ 394, we can use estimation to narrow down the options and then perform long division for an exact answer.
Step 1: Estimation
First, let’s estimate the answer by rounding the numbers to values that are easier to calculate. We can round the dividend, 22,064, down to 22,000. We can round the divisor, 394, up to 400.
Now, we perform the simpler division:
22,000 ÷ 400
To simplify this further, we can cancel the two zeros from both numbers, which gives us:
220 ÷ 4 = 55
This estimation tells us that the correct answer should be very close to 55. Looking at the four choices provided (560, 506, 56, and 5.6), the number 56 is the most plausible option. The other options are either too large or too small compared to our estimate.
Step 2: Long Division
To find the exact answer and confirm our estimate, we can use the method of long division.
- Set up the problem: Place 22,064 inside the division bracket and 394 outside.
- Divide the first part of the dividend: 394 cannot go into 2, 22, or 220. So, we look at how many times 394 goes into 2206. Based on our estimate, we can try 5. Let’s multiply: 394 × 5 = 1970. This fits. We place the 5 above the 6 in the dividend.
- Subtract and bring down: Subtract 1970 from 2206, which leaves 236. Then, bring down the next digit from the dividend, which is 4, to make the new number 2364.
- Divide again: Now we need to find how many times 394 goes into 2364. Let’s try multiplying 394 by 6: 394 × 6 = 2364. It fits perfectly. We place the 6 next to the 5 in our answer.
- Final subtraction: Subtract 2364 from 2364, which results in a remainder of 0.
The calculation shows that 22,064 divided by 394 is exactly 56, which confirms that our estimation was correct.
