How to covert 3 4/10 (mixed fraction) into a improper fraction ?​
The correct Answer and Explanation is:
To convert the mixed fraction (3 \frac{4}{10}) into an improper fraction, follow these steps:
Step 1: Understand the Components
A mixed fraction consists of two parts: a whole number and a proper fraction. In this case:
- Whole number: (3)
- Proper fraction: (\frac{4}{10})
Step 2: Convert the Whole Number
To convert the whole number into a fraction, express it with the same denominator as the proper fraction. Since the denominator of (\frac{4}{10}) is (10), we can write (3) as:
[
3 = \frac{3 \times 10}{10} = \frac{30}{10}
]
Step 3: Add the Fractions
Now, combine the improper fraction from the whole number and the proper fraction:
[
\frac{30}{10} + \frac{4}{10} = \frac{30 + 4}{10} = \frac{34}{10}
]
Step 4: Simplify the Improper Fraction (if necessary)
The improper fraction (\frac{34}{10}) can be simplified further. Both (34) and (10) can be divided by their greatest common divisor (GCD), which is (2):
[
\frac{34 \div 2}{10 \div 2} = \frac{17}{5}
]
Final Result
Thus, the mixed fraction (3 \frac{4}{10}) is converted into the improper fraction (\frac{34}{10}), and it can also be simplified to (\frac{17}{5}).
Explanation
Converting a mixed fraction into an improper fraction is a straightforward process that helps in mathematical calculations where uniformity in fractions is necessary. By separating the whole number from the proper fraction, you can effectively express the entire value in a single fraction form. This method is useful in various applications, such as addition or subtraction of fractions, where having a single improper fraction can simplify the calculations. Remember to check if the final result can be simplified for a clearer representation, making the fraction easier to work with in further calculations.