Change the fraction to a mixed number in simplest form. 4(14)/(12)
The Correct Answer and Explanation is:
To convert the improper fraction 4 14/12 to a mixed number in its simplest form, let’s break it down into steps:
Step 1: Simplify the Fraction Part
You are given the fraction 14/12 as part of the mixed number.
First, simplify 14/12:
- The greatest common divisor (GCD) of 14 and 12 is 2.
- Divide both the numerator (14) and the denominator (12) by 2: 1412=14÷212÷2=76\frac{14}{12} = \frac{14 \div 2}{12 \div 2} = \frac{7}{6}1214=12÷214÷2=67
Now, the mixed number becomes 4 7/6.
Step 2: Convert the Improper Fraction into a Mixed Number
Now, focus on the 7/6 part:
- 7/6 is an improper fraction, meaning the numerator is greater than the denominator.
- Divide 7 by 6: 7÷6=1 remainder 17 \div 6 = 1 \text{ remainder } 17÷6=1 remainder 1 This means 7/6 is the same as 1 1/6.
Step 3: Add the Whole Number Part
Now, add the whole number 4 from the original mixed number to the whole number 1 from 1 1/6:
- 4+1=54 + 1 = 54+1=5
Thus, the mixed number is 5 1/6.
Final Answer:
So, 4 14/12 as a mixed number in simplest form is 5 1/6.
Explanation Recap:
- First, simplified 14/12 to 7/6.
- Converted 7/6 into a mixed number, which became 1 1/6.
- Added the whole number 4 to 1, resulting in 5 1/6.
