An example of a math problem that involves subtracting mixed numbers and regrouping is 4 1/4 - 2 1/3. To solve this type of problem, a student must arrive at a common denominator, regroup, subtract, and simplify the answer, if necessary.
The first step in solving the example problem is to obtain a common denominator. The two denominators in the example are 4 and 3, and the common denominator should be the lowest common multiple, or the lowest number that is divisible by both numbers. The lowest common multiple of 4 and 3 is 12. Thus, the denominator of the first fraction is multiplied by 3, and the numerator must also be multiplied by 3. The resulting mixed number is 4 3/12. Multiplying the numerator and denominator of the second fraction by 4 results in 2 4/12.
Since 4/12 is greater than 3/12, the student must regroup. This is done by subtracting 1 from the whole number in the first mixed number. The 1 is then converted into a fraction with the same denominator as the other fractions, namely 12, and it is added to the fractional part of the first mixed number. Since 12/12 + 3/12 = 15/12, the first mixed number becomes 3 15/12.
Finally, solve 3 15/12 - 2 4/12. This gives the answer 1 11/12. In this example, the fractional part of the mixed number is already in its simplest form, so there is no need to simplify.