Borrowing Techniques for Adding and Subtracting Fractions

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.