Simplifying Mixed Numbers: 1 1/6 + 3/4
This article will guide you through the process of adding the mixed number 1 1/6 and the fraction 3/4.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction, like 1 1/6. It represents a value greater than one.
Converting Mixed Numbers to Fractions
To add mixed numbers and fractions, we need to convert them all into fractions. Here's how we convert 1 1/6 into a fraction:
- Multiply the whole number by the denominator: 1 * 6 = 6
- Add the numerator: 6 + 1 = 7
- Keep the original denominator: 7/6
Therefore, 1 1/6 is equivalent to 7/6.
Finding a Common Denominator
Before adding fractions, they need to have the same denominator. The least common denominator for 6 and 4 is 12.
- 7/6: Multiply numerator and denominator by 2: (7 * 2) / (6 * 2) = 14/12
- 3/4: Multiply numerator and denominator by 3: (3 * 3) / (4 * 3) = 9/12
Adding the Fractions
Now we can add the fractions:
14/12 + 9/12 = 23/12
Simplifying the Result
The fraction 23/12 is an improper fraction (the numerator is greater than the denominator). To express it as a mixed number:
- Divide the numerator by the denominator: 23 / 12 = 1 remainder 11
- The quotient (1) becomes the whole number part: 1
- The remainder (11) becomes the numerator of the fraction: 11
- The denominator stays the same: 12
Therefore, 23/12 is equivalent to 1 11/12.
Conclusion
The sum of 1 1/6 and 3/4 is 1 11/12. By converting the mixed number to a fraction, finding a common denominator, and adding the fractions, we successfully simplified the expression.