Subtract Fractions and Mixed Numbers
Fractions with Common Denominators

Fractions with the same denominator are subtracted by placing the difference of the numerators over the common denominator.  After subtracting, write the fraction in simplest form (if necessary).


710-410=n



710-410=310

Fractions with Different Denominators

Find the least common denominator (LCD) of the fractions.

Example


Find310-320

The least common multiple of 10 and 20 is 20, then

310×22=620 and 320×11=320 


The lowest common denominator (LCD) of the fractions is 20, then


620-320=320

Simplify the difference (not needed in this example)


Mixed Numbers

To subtract mixed numbers without borrowing, subtract the fractional parts and then subtract the whole numbers.

Subtraction of mixed numbers may involve borrowing

Example

Find 5 − 1 2/3.

Rename 5 as 4 + 1, and then rename 1 using 3 as a denominator (Any fraction with the same numerator and denominator is equivalent to 1)


Subtract the fractions

33-23=13

Subtract the whole numbers

4 − 1 = 3

The result is

313

Example


Find613-245.

First, rename the fractions so they have common denominators:


13×55=515

45×33=1215



Since we can't take 12 from 5, we clearly need to borrow.  Rename 6 as 5 + 1, then rename 1 as 15/15.  This gives us


6515=5+1515=5+1515+515=52015

Now we're ready to subtract.


52015-21215=3815