Why Cancel Common Factors?

When we learn canceling fractions, canceling common factors can seem like a random procedure that is allowed only in certain types of problems. Instead, when used consistently, canceling common factors becomes a tool for students to use with confidence in many problems.

Canceling fractions:

How To Cancel Out A Fraction? 

1824 can be simplified to 34 by dividing the numerator and denominator by 6. But another way to think about this is that because there is a factor of 6 in the numerator and denominator, that factor can be canceled out.

3646 which is the same as 3466 which is the same as 341. Since the product of any number and 1 is that number, we can essentially cancel out the 6s.

Multiplying Fractions

Canceling common factors when multiplying fractions eliminates the need for simplifying at the end. In this example, after successfully multiplying, students must think about a common factor for 140 and 105.

Most likely they will not immediately think to divide each value by 35, and simplifying will take several steps. 

1071415=140105

Instead, students can cancel common factors first. To do this, the larger numbers are broken down into smaller factors. For example, 10 is rewritten as 2 times 5.

1071415=2572735=2527735=2235577=4311=43

Understanding How To Simplify Algebraic Fractions

Canceling common factors should feel like a familiar tool when it is time to simplify algebraic fractions.

Introducing the concept of simplifying algebraic expressions using this familiar method helps to explain the rules of exponents.

Look at all of the pairs of values equivalent to one here:

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When they are all canceled out, we are left with

Multiplying Algebraic Fractions

Cancelling the values that are equal to one leaves us with 2w5y.

Also read: How To Divide Fractions Using Area Models

Frequently Asked Questions On Canceling Fractions