Adding and Subtracting Fractions

Adding and subtracting fractions doesn't have to be hard to understand.

Here are some step-by-step mini-lessons to walk through the process.

First... adding with "like denominators," and why the denominator remains the same when adding and subtracting fractions.

Moving on to unlike or "different" denominators. Different denominators, or different "things," can't be added together, so we create equivalent fractions where the denominators are the same.

More explanation of common denominators.

Now the example of how to change fractions with different denominators into fractions with the same denominator.

Subtracting fractions that require "regrouping."

Just like when subtracting numbers written as whole numbers or decimals, sometimes a fraction subtraction problem requires "regrouping."

Here is an example of how to "regroup" to provide the fractional parts that are needed to subtract.

A common mistake or "sticking point"

When using base-ten whole numbers and decimals, regrouping always involves subtracting "1" from a number and adding "10" to the place to the right. That is because each "place" is always equal to 10 of whatever the place to the right is:

• 10 "ones" equals 1 "ten"

• 10 "tens" equals 1 "hundred"

• 10 "hundreds equals 1 "thousand"

And with decimals:

• 10 "hundredths" equals 1 "tenth"

• 10 "tenths" equals 1 "one"

When regrouping fractions, "ten" is no longer the important number to remember.

What is "regrouped" is always a fraction that is equivalent to "1".