Borrowing Techniques for Adding and Subtracting Fractions

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<h3>Borrowing Techniques for Adding and Subtracting Fractions</h3>

A mixed number has a whole number and a fraction. A fraction is a number that is less than whole and that has a denominator underneath a numerator. To add or subtract mixed numbers, add or subtract the fractions, then add or subtract the whole numbers. If the fraction portion of a mixed number, such as 2 5/6, is more than the fraction portion of the mixed number you’re trying to subtract from, such as 3 1/6, you must “borrow” from the whole number of the mixed number you’re trying to subtract from to make its fraction bigger.

Step 1

“Borrow” 1 from the whole number 4 in the first mixed number in the equation 4 1/4 – 2 3/4 by subtracting 1 from 4. This leaves 3 as the whole number in the first mixed number in the equation.



Step 2

Convert the 1 you subtracted from 4 into a fraction with a denominator of 4. This equals 4/4.

Step 3

Add 4/4 to the fraction of the first mixed number: 4/4 plus 1/4 equals 5/4. The equation now equals 3 5/4 – 2 3/4.

Step 4

Subtract the fraction portions of the mixed numbers: 5/4 minus 3/4 equals 2/4.

Step 5

Subtract the whole numbers: 3 minus 2 equals 1. This leaves 1 2/4.



Step 6

Find the largest number that divides evenly into the numerator 2 and denominator 4 to reduce the fraction 2/4 to its lowest terms. The largest divisible number is 2.

Step 7

Divide both the numerator and denominator by 2: 2 divided by 2 equals 1, and 4 divided by 2 equals 2. This leaves 1 1/2 reduced to its lowest terms.

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.