Teach me this question---**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 the problem 4 and 1/4 minus 2 and 2/4. First, we need to understand what mixed numbers are. A mixed number consists of a whole number part and a fractional part. For example, 4 and 1/4 means 4 plus 1/4, which we can visualize as 4 complete circles plus one quarter of another circle. Similarly, 2 and 2/4 means 2 complete circles plus 2 quarters, or half of another circle. To subtract mixed numbers, we can convert them to improper fractions first. 4 and 1/4 equals 4 times 4 plus 1, all over 4, which gives us 17/4. Similarly, 2 and 2/4 equals 2 times 4 plus 2, all over 4, which gives us 10/4. Now we can subtract: 17/4 minus 10/4 equals 7/4. Finally, we convert 7/4 back to a mixed number: 1 and 3/4. The correct answer is B: 1 and 3/4. We can visualize this as one complete circle plus three quarters of another circle. To verify our answer, we can add 1 and 3/4 back to 2 and 2/4, which should give us 4 and 1/4, confirming our solution is correct. Now let's convert our mixed numbers to improper fractions. For 4 and 1/4, we multiply the whole number 4 by the denominator 4, then add the numerator 1. This gives us 16 plus 1, which equals 17, all over 4. So 4 and 1/4 becomes 17/4. Similarly, for 2 and 2/4, we multiply 2 by 4 and add 2, giving us 8 plus 2, which equals 10, all over 4. So 2 and 2/4 becomes 10/4. Now we have 17/4 minus 10/4, which is much easier to calculate. Now we can perform the subtraction. We have 17/4 minus 10/4. Since both fractions have the same denominator, we keep the denominator as 4 and subtract only the numerators: 17 minus 10 equals 7. So our result is 7/4. We can visualize this as having 17 quarter pieces, removing 10 quarter pieces, leaving us with 7 quarter pieces. Now we need to convert our improper fraction 7/4 back to a mixed number. We divide 7 by 4, which gives us 1 with a remainder of 3. This means we have 1 whole and 3/4 remaining, so 7/4 equals 1 and 3/4. We can visualize this as one complete circle plus three quarters of another circle. Looking at our answer choices, this matches option B: 1 and 3/4. Let me show you an alternative method for subtracting mixed numbers directly. First, we subtract the whole numbers: 4 minus 2 equals 2. Then we subtract the fractions: 1/4 minus 2/4 equals negative 1/4. Since we can't have a negative fraction, we borrow 1 from the whole number part. We rewrite 2 as 1 plus 1, then convert that 1 to 4/4. Now we have 1 plus 4/4 minus 1/4, which equals 1 and 3/4. We can verify this answer by adding: 1 and 3/4 plus 2 and 2/4 equals 4 and 1/4, which confirms our answer is correct. The answer is B.