How to Calculate 1 2/1 ÷ 1 6 as a Fraction
This article will guide you through the process of dividing mixed numbers, using the example of 1 2/1 ÷ 1 6.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. In our example, 1 2/1 represents one whole and two parts of another whole. Similarly, 1 6 represents one whole and six parts of another whole.
Converting Mixed Numbers to Improper Fractions
To perform division with mixed numbers, we must first convert them to improper fractions.
Here's how to convert 1 2/1:
- Multiply the whole number (1) by the denominator of the fraction (1): 1 * 1 = 1.
- Add the numerator of the fraction (2) to the result: 1 + 2 = 3.
- Keep the original denominator (1): 3/1.
Similarly, to convert 1 6:
- Multiply the whole number (1) by the denominator of the fraction (6): 1 * 6 = 6.
- Add the numerator of the fraction (6) to the result: 6 + 6 = 12.
- Keep the original denominator (6): 12/6.
Dividing Fractions
Now we have: 3/1 ÷ 12/6.
Remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 12/6 is 6/12.
Therefore, we have: 3/1 * 6/12.
Multiplying Fractions
To multiply fractions, we multiply the numerators and the denominators:
- Numerator: 3 * 6 = 18
- Denominator: 1 * 12 = 12
This gives us 18/12.
Simplifying the Fraction
The fraction 18/12 can be simplified by finding the greatest common factor (GCF), which is 6. Dividing both numerator and denominator by 6:
- 18 ÷ 6 = 3
- 12 ÷ 6 = 2
Therefore, the final simplified answer is 3/2.
Conclusion
By converting mixed numbers to improper fractions, finding the reciprocal, multiplying the fractions, and simplifying the result, we find that 1 2/1 ÷ 1 6 equals 3/2.