Ways to Simplify Fractions with Decimals

Published
<h3>Ways to Simplify Fractions with Decimals</h3>

Fractions and decimals are parts of whole numbers written in two different forms. A fraction has a numerator over a denominator, which represents the number of parts you have of a whole number over the number of parts by which the whole number is divided. A decimal contains part of a whole number to the right of a decimal point. If a fraction contains a decimal in either its numerator or denominator, you can convert the decimal into a fraction so that you have two similar number formats to simplify the fraction. A fraction is simplified when the only common factor of the numerator and denominator is 1.

Step 1

Determine a fraction with a decimal that you want to simplify. For the following example, use the fraction 0.2/2.



Step 2

Convert the decimal to a fraction by placing the number to the right of the decimal point as a numerator over a denominator that corresponds to the place value of the decimal number. In the example, the decimal 0.2 extends to the tenths place, so place 2 as a numerator over 10 as a denominator, which equals 2/10. This leaves (2/10)/2, which consists of a fraction within a fraction.

Step 3

Divide the numerator by the denominator, which is equivalent to multiplying the numerator by the reciprocal of the denominator, to convert the fraction within a fraction to a single fraction. A reciprocal is a fraction flipped upside down. In the example, divide 2/10 by 2, which is equivalent to multiplying 2/10 by 1/2. This equals 2/20.

Step 4

Find the largest number that divides evenly into the numerator and denominator of the fraction. In the example, 2 is the largest number that divides evenly into 2 and 20.

Step 5

Divide both the numerator and denominator by the largest number that divides evenly into both to simplify the fraction. In the example, divide 2 by 2, which equals 1, and divide 20 by 2, which equals 10. This leaves 1/10, which is the simplified form of the fraction with a decimal.



Dave Pennells

By Dave Pennells

Dave Pennells, MS, has contributed his expertise as a career consultant and training specialist across various fields for over 15 years. At City University of Seattle, he offers personal career counseling and conducts workshops focused on practical job search techniques, resume creation, and interview skills. With a Master of Science in Counseling, Pennells specializes in career consulting, conducting career assessments, guiding career transitions, and providing outplacement services. Her professional experience spans multiple sectors, including banking, retail, airlines, non-profit organizations, and the aerospace industry. Additionally, since 2001, he has been actively involved with the Career Development Association of Australia.