Converting a Mixed Number to an Improper Fraction: Fraction Conversion
December 10, 2023 by JoyAnswer.org, Category : Mathematics
How do you convert a mixed number into an improper? Discover how to convert a mixed number into an improper fraction. This article explains the steps for this conversion in mathematics.
How do you convert a mixed number into an improper?
To convert a mixed number to an improper fraction, follow these steps:
Example:
Let's use the mixed number 3 1/4 as an example.
Steps:
Multiply the whole number by the denominator of the fractional part:
Add the result to the numerator of the fractional part:
Place the sum obtained in step 2 as the new numerator, and retain the denominator:
- The result is .
Conclusion:
So, the improper fraction equivalent of the mixed number 3 1/4 is .
General Formula:
If you have a mixed number , the corresponding improper fraction is given by:
In this formula:
- is the whole number,
- is the numerator of the fractional part, and
- is the denominator of the fractional part.
Simply follow these steps, and you can easily convert any mixed number into an improper fraction.
How can you transform a mixed number into an improper fraction?
There are two main ways to transform a mixed number into an improper fraction:
Method 1: Multiply and Add
- Multiply the whole number part of the mixed number by the denominator of the fractional part.
- Add the result from step 1 to the numerator of the fractional part.
- Write the sum as the numerator of the improper fraction, and keep the denominator the same.
Example:
Convert the mixed number 3 1/4 into an improper fraction.
Solution:
- 3 x 4 = 12
- 12 + 1 = 13
- The improper fraction is 13/4.
Method 2: Least Common Multiple (LCM)
- Find the least common multiple (LCM) of the denominators of the whole and fractional parts of the mixed number.
- Multiply the whole number by the LCM divided by the denominator of the whole number.
- Multiply the numerator and denominator of the fractional part by the LCM divided by the denominator of the fractional part.
- Add the results from step 2 and 3.
- Write the sum as the numerator of the improper fraction, and the LCM as the denominator.
Example:
Convert the mixed number 3 1/3 into an improper fraction.
Solution:
- LCM of 3 and 3 is 3.
- 3 x (3/3) = 3
- 1 x (3/3) = 3
- 3 + 3 = 6
- The improper fraction is 6/3.
Both methods are valid for transforming mixed numbers into improper fractions. Choose whichever method you find easier and more convenient.
