How is adding and subtracting mixed numbers different than adding and subtracting fractions?
not different at all
mixed numbers are just improper fractions
Adding and subtracting mixed numbers involves working with both whole numbers and fractions, while adding and subtracting fractions only involves working with fractions.
When adding and subtracting mixed numbers, the first step is to convert the mixed numbers into improper fractions. To do this, you multiply the whole number by the denominator of the fraction, and then add the numerator. The resulting sum becomes the new numerator, while the denominator remains the same.
After converting the mixed numbers to improper fractions, you can perform addition or subtraction. To add or subtract fractions, you need a common denominator. If the fractions have different denominators, you will need to find the least common multiple (LCM) of the denominators and then convert the fractions so they have the same denominator.
Once the fractions have a common denominator, you can perform the addition or subtraction by adding or subtracting the numerators while keeping the denominator the same. Simplify the resulting fraction if necessary.
In summary, the main difference between adding and subtracting mixed numbers and adding and subtracting fractions is that mixed numbers require converting to improper fractions and working with whole numbers, while fractions only involve finding a common denominator and performing the operation.
Adding and subtracting mixed numbers is slightly different from adding and subtracting fractions because mixed numbers contain both a whole number and a fraction. However, the underlying principles and steps for finding the sum or difference are the same.
To add or subtract mixed numbers, you follow these steps:
1. Convert the mixed numbers into improper fractions. To do this, multiply the denominator by the whole number and add the numerator. Then, place the sum over the original denominator.
2. If the denominators of the mixed numbers are different, find a common denominator by finding the least common multiple (LCM) of the denominators.
3. Once you have the improper fractions or fractions with common denominators, you can proceed with either addition or subtraction as you would with regular fractions.
For addition:
- Add the numerators together and keep the denominators the same. Simplify the resulting fraction if necessary.
- If the sum of the numerators is greater than or equal to the denominator, convert the improper fraction back into a mixed number by dividing the numerator by the denominator and the remainder becomes the new numerator.
For subtraction:
- Subtract the second numerator from the first numerator and keep the denominators the same. Simplify the resulting fraction if necessary.
- If the first numerator is smaller than the second numerator, you may need to borrow from the whole number portion of the mixed number, turning it into a fraction before subtracting.
By following these steps, you can effectively add or subtract mixed numbers and fractions.