To add or subtract mixed numbers, follow these steps:
1. Convert the mixed numbers into improper fractions (if they aren't already).
2. If you are adding the mixed numbers, find a common denominator for the fractions. If you are subtracting, also find a common denominator.
3. Once you have a common denominator, add or subtract the numerators of the fractions, keeping the denominator the same.
4. Simplify the resulting fraction, if applicable.
5. If the numerator of the resulting fraction is greater than or equal to the denominator, convert the improper fraction back into a mixed number.
Let's look at an example:
Example 1:
Add 2 3/4 and 1 1/2.
Step 1: Convert the mixed numbers into improper fractions:
2 3/4 = (2 * 4 + 3) / 4 = 11/4
1 1/2 = (1 * 2 + 1) / 2 = 3/2
Step 2: Find a common denominator: In this case, the least common multiple of 4 and 2 is 4.
Step 3: Add the fractions: 11/4 + 3/2 = (11 * 1 + 3 * 2) / 4 = 17/4
Step 4: Simplify the resulting fraction: 17/4 cannot be simplified further.
Step 5: Since the numerator (17) is greater than the denominator (4), we convert the improper fraction into a mixed number:
17/4 = 4 1/4
Therefore, 2 3/4 + 1 1/2 = 4 1/4.
Example 2:
Subtract 3 2/3 from 5 1/6
Step 1: Convert the mixed numbers into improper fractions:
5 1/6 = (5 * 6 + 1) / 6 = 31/6
3 2/3 = (3 * 3 + 2) / 3 = 11/3
Step 2: Find a common denominator: In this case, the least common multiple of 6 and 3 is 6.
Step 3: Subtract the fractions: 31/6 - 11/3 = (31 * 1 - 11 * 2) / 6 = 9/6
Step 4: Simplify the resulting fraction: 9/6 can be simplified to 3/2.
Step 5: Since the numerator (3) is not greater than the denominator (2), we don't need to convert the improper fraction into a mixed number.
Therefore, 5 1/6 - 3 2/3 = 3/2.
adding and subtracting mixed numbers
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