How is adding and subtracting mixed numbers similar to adding and subtracting fractions? How is adding and subtracting mixed numbers different than adding and subtracting fractions?
Give examples to explain your answer.
Mixed numbers are, normally, changed to fractions before adding or subtracting:
10 1/2 + 6 1/4 = 21/2 + 25/4 = 42/4 + 25/4 = 67/4 = 16 3/4.
Note: The fractions were placed over a common denominator.
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Mixed numbers are, normally, changed to fractions before adding or subtracting:
10 1/2 + 6 1/4 = 21/2 + 25/4 = 42/4 + 25/4 = 67/4 = 16 3/4.
Note: This might not be right bc I am only in 5th grade
Adding and subtracting mixed numbers is similar to adding and subtracting fractions because mixed numbers are essentially a combination of whole numbers and proper fractions. In both cases, the process involves combining or separating parts of a whole.
The similarity can be understood by considering an example of adding mixed numbers. Let's say we want to add the mixed number 2 1/2 to 3 3/4.
1. Add the whole numbers: 2 + 3 = 5.
2. Add the fractions: 1/2 + 3/4.
- To find a common denominator, we can multiply 2 with 4 to get LCD (Least Common Denominator) of 8.
- Convert both fractions to have the same denominator: 1/2 can be multiplied by 4/4 to become 4/8, and 3/4 remains the same.
- Now, we can add the two fractions: 4/8 + 3/8 = 7/8.
3. Combine the whole number and fraction: 5 + 7/8.
- The fraction can be written as an improper fraction: 7/8.
- The final answer is 5 7/8.
Similarly, when subtracting mixed numbers, we follow similar steps. For example, subtracting 3 1/3 from 4 2/3:
1. Subtract the whole numbers: 4 - 3 = 1.
2. Subtract the fractions: 2/3 - 1/3 = 1/3.
3. Combine the whole number and fraction: 1 + 1/3.
- The final answer is 1 1/3.
However, adding and subtracting mixed numbers are different from adding and subtracting fractions in one significant way. When adding or subtracting mixed numbers, we need to consider the regrouping of whole numbers. In fractions, we only focus on the numerator and denominator.
For example, let's say we want to subtract 1 1/4 from 2 3/4:
1. If the fraction being subtracted (1/4) is larger than the fraction we are subtracting from (3/4), we need to borrow from the whole number.
2. We borrow 1 from the whole number, making it 1 less (2 - 1 = 1), and add it to the fraction we are subtracting from (3/4 + 1 = 7/4).
3. Subtract the fractions: 7/4 - 1/4 = 6/4.
4. Combine the whole number and fraction: 1 + 6/4.
- The fraction can be simplified: 6/4 = 1 2/4 = 1 1/2.
- The final answer is 1 1/2.
Thus, adding and subtracting mixed numbers involve additional steps of regrouping whole numbers compared to adding and subtracting fractions.