Adding Mixed Numbers: 2 1/8 + 3 2/3
In this article, we will learn how to add two mixed numbers: 2 1/8 and 3 2/3. Adding mixed numbers can be a bit tricky, but don't worry, we'll break it down step by step.
Step 1: Convert Mixed Numbers to Improper Fractions
To add mixed numbers, we need to convert them to improper fractions first. To do this, we multiply the whole number part by the denominator and then add the numerator.
2 1/8
- Whole number part: 2
- Denominator: 8
- Numerator: 1
- Improper fraction: (2 x 8) + 1 = 17/8
3 2/3
- Whole number part: 3
- Denominator: 3
- Numerator: 2
- Improper fraction: (3 x 3) + 2 = 11/3
Step 2: Add the Improper Fractions
Now that we have converted the mixed numbers to improper fractions, we can add them.
- 17/8 + 11/3
To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. In this case, the LCM of 8 and 3 is 24.
- 17/8 = 51/24 (multiply numerator and denominator by 3)
- 11/3 = 88/24 (multiply numerator and denominator by 8)
Now we can add the fractions:
- 51/24 + 88/24 = 139/24
Step 3: Simplify the Result
Our result is an improper fraction, but we can simplify it by dividing the numerator by the denominator:
- 139 ÷ 24 = 5 with a remainder of 19
So, the result is:
5 19/24
And that's it! We have successfully added 2 1/8 and 3 2/3 to get 5 19/24.
