Simplifying fractions
Simplifying does not change the amount. It changes how we describe that amount, using larger pieces and fewer of them.
Same amount, fewer pieces
Start with 812. Eight of twelve equal pieces are shaded.
Now take the same 12 equal pieces and place them into 3 groups of 4. The pieces themselves have not changed size — we are only showing which small pieces belong together.
The shaded amount never changed. We only changed the size of the pieces used to describe it.
Equivalent fractions multiply; simplifying divides
What number can divide both?
To simplify a fraction, look for a number that divides the numerator and denominator exactly.
Any common factor greater than 1 will simplify the fraction. The largest one makes the biggest jump.
Simplify in stages
If you spot a smaller common factor first, use it. Then look again.
Cross out and write what is left
Divide the top and bottom by the same number. Watch the picture regroup into fewer, larger pieces.
Start with 12/18. The rectangle has 6 columns and 3 rows: 18 equal pieces, with 12 shaded.
Cancel before you multiply
When fractions are multiplied, the whole numerator is one product and the whole denominator is another. That means we can simplify common factors before doing the multiplication.
Change division to multiplication first
Do not cancel across a division sign. First use the rule from the previous lesson: multiply by the reciprocal. Then simplify the multiplication.
Cancellation works with factors, not terms
You may cancel when numbers are factors in a product. You cannot simply cross out numbers across addition or subtraction.
Choose a common factor
Pick any factor greater than 1 that divides both numbers.
The greatest common divisor
The greatest common divisor (GCD) is simply the largest number that divides both numerator and denominator. Dividing by the GCD simplifies a fraction in one step.
You do not need the GCD method to simplify fractions now. We will return to a systematic GCD method in a later extension.
Simplify the fraction fully
Try five fresh questions. Choose guided working or type your final answer. Results feed into your Practice Lab log on this browser/device.
You have learned
Simplifying keeps the value of a fraction the same while using fewer, larger pieces.
Divide numerator and denominator by the same common factor.
The fraction is fully simplified when numerator and denominator have no common factor greater than 1.