Converting a Mixed Number to an Improper Fraction: Fraction Conversion

There are two main ways to transform a mixed number into an improper fraction:

Method 1: Multiply and Add

1. Multiply the whole number part of the mixed number by the denominator of the fractional part.
2. Add the result from step 1 to the numerator of the fractional part.
3. 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:

1. 3 x 4 = 12
2. 12 + 1 = 13
3. The improper fraction is 13/4.

Method 2: Least Common Multiple (LCM)

1. Find the least common multiple (LCM) of the denominators of the whole and fractional parts of the mixed number.
2. Multiply the whole number by the LCM divided by the denominator of the whole number.
3. Multiply the numerator and denominator of the fractional part by the LCM divided by the denominator of the fractional part.
4. Add the results from step 2 and 3.
5. 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:

1. LCM of 3 and 3 is 3.
2. 3 x (3/3) = 3
3. 1 x (3/3) = 3
4. 3 + 3 = 6
5. 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.