Simplifying Fractions

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Simplifying Fractions

Simplifying fractions is a fundamental skill in mathematics. This concept helps in understanding fractions better and preparing you for more advanced mathematical operations involving fractions, such as when adding and subtracting fractions with unlike denominators.

Fraction simplification is when we reduce fractions into their simplest form.

Let’s learn how to create simplified fractions!

Simplifying Fractions – Rules

Simplifying fractions involves reducing them to their simplest form. This process makes fractions easier to understand and work with. We can refer to these fractions as simplest form fractions. Below, you will find the fraction simplification rules.

Rule Description
Identify the HCF Find the highest common factor of the numerator and denominator.
Divide by HCF Divide both the numerator and the denominator by the HCF.
Write simplified fraction Write the new values as the simplified fraction.
Check if already simplest form If there are no common factors, the fraction is already in its simplest form.

Definition: Simplifying fractions is the process of reducing the numerator and denominator of a fraction to their smallest possible values while keeping the fraction equivalent to the original.

Simplifying Fractions – Example

Let's simplify the fraction $\frac{9}{12}$.

• First, list the factors of both the numerator, 9, and the denominator, 12.

• The factors of 9 are 1, 3 and 9. The factors of 12 are 1, 2, 3, 4, 6 and 12.

• Then find the highest common factor (HCF) they both share. In this case, it is 3.

• Divide both the numerator and the denominator by 3.

• This means that $\frac{9}{12}$ simplifies to $\frac{3}{4}$.

Before moving ahead, check your understanding of the learning so far by using the following questions:

Is $\frac{4}{6}$ in its simplest form? If not, what is its simplest form?
What is the simplest form of $\frac{10}{15}$?

Simplifying Fractions – Guided Practice

Let’s work through the following question together. Let’s simplify $\frac{16}{24}$.

Check if it is already in the simplest form.

Simplifying Fractions – Exercises

Here are some simplifying fractions practice questions for you to have a go at yourself. Review the steps in the rules table if you need to!

Here's a fraction to simplify: $\frac{18}{27}$. Try simplifying it before checking the solution.
What is the simplest form of the fraction $\frac{20}{25}$?
How can you simplify the fraction $\frac{14}{21}$?

Simplifying Fractions – Summary

• Simplifying fractions makes them easier to understand and work with.
• The process involves finding the highest common factor of the numerator and denominator and dividing both by this number.
• Simplified fractions are equivalent to the original fraction but in their simplest form.

Explore more about fractions and other maths concepts through our interactive tools, videos and printable worksheets to enhance your learning journey!

If you need some extra support with this topic, why not check out the learning text on Equivalent Fractions.

If you’re feeling confident and ready for some practicing using you new fraction skills, then check out the learning text on Comparing Fractions.

Frequently Asked Questions – Simplifying Fractions

What does it mean to simplify a fraction?
Is a fraction in its simplest form when the numerator is 1?
How do you know if a fraction is fully simplified?
Can simplifying fractions change the value of the fraction?
Can all fractions be simplified?
Can simplifying fractions help in solving mathematical problems?
Is it necessary to always simplify fractions in maths problems?
What is a real-life application of simplifying fractions?
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