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Fractions, Decimals and Percentages Explained: The Connection Every Student Needs to Understand





Fractions, decimals and percentages are some of the most important concepts students learn in primary school. They appear throughout Maths and continue to be used in high school topics such as algebra, probability, measurement and financial mathematics.


However, many students struggle because they learn fractions, decimals and percentages as separate topics rather than understanding that they are different ways of representing the same value.


A strong understanding of number relationships, including factors and multiples, can make these concepts much easier. When students understand why the methods work, they are less reliant on memorising rules and become more confident solving problems.


Fractions: Understanding Parts of a Whole

A fraction shows how many parts of something we have compared to the total number of equal parts.


For example:

1/2 means we have 1 part out of 2 equal parts.

3/4 means we have 3 parts out of 4 equal parts.

Fractions are also closely connected to division:

3 ÷ 4 = 3/4

This connection is important because fractions are not just numbers to memorise, they represent a relationship between two numbers.


How Factors Help Students Simplify Fractions


One of the most important skills when working with fractions is simplifying them.

To simplify a fraction, students need to understand common factors. A factor is a number that divides exactly into another number.


For example:

12/18


The factors of 12 include: 1, 2, 3, 4, 6 and 12

The factors of 18 include: 1, 2, 3, 6, 9 and 18


The highest common factor (HCF) is 6, meaning both numbers can be divided by 6:

12 ÷ 6 / 18 ÷ 6 = 2/3

The value has not changed, the fraction has simply been written in its simplest form.

Understanding factors helps students recognise equivalent fractions and makes later work with decimals and percentages much easier.



Decimals: Another Way to Write Fractions


Decimals are another way of representing fractions, especially when the denominator is 10, 100 or 1000.


For example:

1/10 = 0.1

25/100 = 0.25


The decimal system is based on place value, which is why understanding tenths, hundredths and thousandths is essential.


Decimals are commonly used in everyday situations, including:

  • money

  • measurements

  • calculations involving numbers that are not whole

Students who understand fractions often find decimals much easier because they can see that both represent parts of a whole.



Percentages: Fractions Out of 100


Percentages are another way of showing fractions, but they always represent a value out of 100. The word "percent" means "per hundred".

For example:

50% = 50/100 = 1/2 = 0.5

25% = 25/100 = 1/4 = 0.25

This means that percentages are not a separate topic — they are another way of expressing fractions and decimals.



How Multiples Help When Working With Fractions


While factors help students simplify fractions, multiples help when adding, subtracting or comparing fractions with different denominators.


For example:

1/4 + 1/6

The denominators are different, so we need to find a common denominator.

Multiples of 4: 4, 8, 12, 16...

Multiples of 6: 6, 12, 18...

The lowest common multiple (LCM) is 12.

This allows us to convert both fractions:

1/4 = 3/12

1/6 = 2/12

Now they can be added:

3/12 + 2/12 = 5/12

Understanding multiples helps students see why fractions need a common denominator rather than simply memorising a rule.



Seeing the Connection Between Fractions, Decimals and Percentages


These are not different numbers. They are different ways of describing the same amount.

Fraction

Decimal

Percentage

1/2

0.5

50%

1/4

0.25

25%

3/4

0.75

75%

1/10

0.1

10%

When students understand the connections between these forms, they can easily move between them with confidence.


Why Students Often Find These Topics Difficult

Many students can follow a method but struggle when they need to apply their knowledge to a new problem.

Common challenges include:

  • memorising conversions without understanding the meaning

  • struggling to simplify fractions

  • not recognising equivalent values

  • confusing when to multiply or divide

  • finding it difficult to apply skills to word problems

Building a strong foundation in factors, multiples, fractions, decimals and percentages helps students approach Maths with greater confidence.



Why This Skill Matters Beyond Primary School


Fractions, decimals and percentages continue to appear throughout high school Maths, including:

  • ratios and rates

  • probability

  • algebra

  • equations

  • financial mathematics


Students who develop a strong understanding of these concepts early often find later Maths topics much easier.


At Primo Tutoring, we help students build strong Maths foundations through personalised lessons designed around their individual needs. By focusing on understanding rather than memorising formulas, students can develop the confidence and skills needed to succeed.



Want personalised support for Mathematics in 2026?


Primo Tutoring offers Maths lessons for students from years 3 - 8. These personalised lessons help students gain greater confidence and understanding of the wide variety of concepts they will encounter in the subject.


Want patient and personalised tutoring? Feel free to reach out by emailing us at info@primotutoring.com.au.


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