Whether you are here to learn about reducing fractions for a class, prepare for a test, or simply want to refresh your memory, you're in the right place!
In this middle-school-friendly guide, we'll show you what it means to reduce a fraction, how to do it, and give you practice questions to test your skills.
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Fractions are numbers that aren’t whole. They are called “fractions” because they represent parts of a whole number or object.
Fractions consist of two parts:
Fractions are used in everyday life, such as baking, measuring, and understanding time. For example, if you cut a pizza into 8 slices, and you eat 2 slices, you’ll have \( \Large \frac{6}{8}\)of the pizza left. If you cut a pizza into 4 slices and you eat 1 slice, you’ll have \( \Large \frac{3}{4}\) of the pizza left.
We can simplify many, if not most fractions, by reducing them to their smallest numerator and denominator with equivalent value.
Let's explore how!
Reducing a fraction means simplifying the numerator (top number) and denominator (bottom number) to the smallest possible numbers while keeping the fraction equal to the original value.
For example, fractions like \( \Large \frac{11}{28}\) and \( \Large \frac{2}{3}\) are already in their simplest form. There is no single number, i.e. greatest common factor, we can use to reduce both the numerator and the denominator to smaller numbers.
But let’s take fractions like \( \Large \frac{3}{6}\) and \( \Large \frac{2}{8}\)
Do you see their greatest common factors?
In the first example, \( \Large \frac{3}{6}\), we can see that both numbers, the numerator and denominator, are divisible by 3, correct?
In the second, \( \Large \frac{2}{8}\), both numbers are divisible by 2.
This means that both fractions, \( \Large \frac{3}{6}\) and \( \Large \frac{2}{8}\), can be reduced to smaller numbers.
Let's see how!
We reduce fractions by finding factors. Let’s refresh our memory:
Factor is a number that divides evenly into another number without leaving a remainder.
For example, 5 is a factor of 10, 15, and 20 because it divides each of these numbers evenly.
To reduce a fraction to its simplest form, we need to find the greatest common factor (GCF) of both the numerator and denominator. The GCF is the largest number that divides evenly into both numbers.
Let's try an example together!
The fraction we want to reduce is \( \Large \frac{3}{6}\)
Find the GCF: List the factors of both the numerator and denominator and find the largest number that appears in both lists.
Based on our lists, 3 is our greatest common factor (GCF)!
Now that we have our GCF, divide both the numerator and denominator by 3.
The final step is putting it together!
The result you get after dividing both the numerator and denominator by their greatest common factor is the reduced fraction, i.e. a simplified fraction.
The reduced fraction of \( \Large \frac{3}{6}\), therefore, is \( \Large \frac{1}{2}\).
Let’s look at some more worked-out examples of how to reduce fractions:
Fraction 1:
\( \Large \frac{4}{8}\)
Fraction 2:
\( \Large \frac{6}{9}\)
Fraction 3:
\( \Large \frac{8}{12}\)
Fraction 4:
\( \Large \frac{10}{15}\)
Fraction 5:
\( \Large \frac{12}{18}\)
Try to reduce these fractions on your own!
Remember the goal is to find the greatest common factor (GCF) of both the numerator and denominator and then divide both by it.
Solve these problems then scroll to the bottom of the page to check your answers.
Fraction 1: \( \Large \frac{4}{8}\)
Fraction 2: \( \Large \frac{6}{9}\)
Fraction 3: \( \Large \frac{10}{15}\)
Fraction 4: \( \Large \frac{12}{18}\)
Fraction 5: \( \Large \frac{14}{21}\)
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Here are the answers to the 5 exercise problems, let’s see how you did!
Fraction 1: \( \Large \frac{1}{2}\)
Fraction 2: \( \Large \frac{2}{3}\)
Fraction 3: \( \Large \frac{2}{3}\)
Fraction 4: \( \Large \frac{2}{3}\)
Fraction 5: \( \Large \frac{2}{3}\)
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