讲解这道题目---**Question 22** **Question Stem:** What is the value of the expression shown below? **Mathematical Expression:** 4 1/4 - 2 2/4 **Options:** A: 1 1/4 B: 1 3/4 C: 2 1/4 D: 2 3/4

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Let's solve this mixed number subtraction problem. We have 4 and 1/4 minus 2 and 2/4. Mixed numbers contain both whole number parts and fractional parts. The first mixed number 4 and 1/4 means 4 plus 1/4, and the second mixed number 2 and 2/4 means 2 plus 2/4. Before subtracting, let's simplify the fractions. Notice that 2/4 can be simplified. Both 2 and 4 are divisible by 2. When we divide both the numerator and denominator by 2, we get 1/2. So our expression becomes 4 and 1/4 minus 2 and 1/2. The visual strips show that 2/4 and 1/2 represent the same amount. Let's solve this mixed number subtraction problem. We need to find the value of 4 and 1/4 minus 2 and 2/4. We have four answer choices to consider. Let's understand what mixed numbers represent. The number 4 and 1/4 means 4 whole units plus 1/4 of another unit. Similarly, 2 and 2/4 means 2 whole units plus 2/4 of another unit. We can work with the whole parts and fractional parts separately. Let's solve this step by step. First, we subtract the whole number parts: 4 minus 2 equals 2. This gives us 2 whole units. Next, we need to handle the fractional parts: 1/4 minus 2/4. Now we have a problem. We need to subtract 2/4 from 1/4, but we can't do that because 1 is less than 2. We need to borrow from the whole number part. We take 1 from the 2 whole units, converting it to 4/4, and add it to the existing 1/4 to get 5/4. So 2 and 1/4 becomes 1 and 5/4. Now let's complete the subtraction. After borrowing, we have 3 and 5/4 minus 2 and 2/4. We subtract the whole numbers: 3 minus 2 equals 1. Then we subtract the fractions: 5/4 minus 2/4 equals 3/4. So our final answer is 1 and 3/4, which corresponds to option B. Now let's perform the subtraction using two methods. Method 1: We borrow 1 from the whole number 4, converting it to 4/4 and adding it to 1/4 to get 5/4. So we have 3 and 5/4 minus 2 and 2/4. Subtracting gives us 1 and 3/4. Method 2: Convert to improper fractions: 4 and 1/4 equals 17/4, and 2 and 2/4 equals 10/4. Subtracting gives 7/4, which equals 1 and 3/4. Let's convert our result and verify the answer. We found that 7/4 equals 1 and 3/4. When we divide 7 by 4, we get 1 with a remainder of 3, so 7/4 equals 1 and 3/4. Looking at our answer choices, this matches option B. We can verify this on a number line: starting at 4 and 1/4, subtracting 2 and 2/4 brings us to 1 and 3/4. Therefore, the correct answer is B: 1 and 3/4.