Converting Mixed Numbers to Improper Fractions: Step-by-Step Guide

Converting Mixed Numbers to Improper Fractions: Step-by-Step Guide

Converting a mixed number to an improper fraction involves expressing the whole number and the fraction part separately. Here's a step-by-step guide on how to do it:

Step 1: Identify the Mixed Number

A mixed number consists of a whole number part, a fraction part, and the word "and" between them. For example, in the mixed number 3 1/4, 3 is the whole number, 1 is the numerator of the fraction, and 4 is the denominator.

Step 2: Convert the Fraction Part

To convert the fraction part of the mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator of the fraction.
2. Add the numerator of the fraction to the result from step 1.
3. Place the result from step 2 over the original denominator.

Step 3: Write the Improper Fraction

The result from step 2 becomes the numerator of the improper fraction, and the denominator remains the same.

Step 4: Simplify (if Necessary)

If the improper fraction can be simplified further, divide both the numerator and the denominator by their greatest common divisor (GCD) until no common factors remain.

Example: Converting 3 1/4 to an Improper Fraction

Given the mixed number 3 1/4, let's convert it to an improper fraction:

Step 2: Convert the Fraction Part

1. Multiply the whole number (3) by the denominator (4): 3 * 4 = 12
2. Add the numerator (1) to the result from step 1: 12 + 1 = 13

Step 3: Write the Improper FractionThe improper fraction is 13/4.

Step 4: Simplify (if Necessary)In this case, the fraction 13/4 cannot be simplified further, so the final result is 13/4.

So, the mixed number 3 1/4 can be converted to the improper fraction 13/4.

Remember that converting mixed numbers to improper fractions is a straightforward process that involves multiplying, adding, and placing the result over the original denominator. This conversion can be particularly useful when performing mathematical operations involving fractions or when comparing fractions.