Is simplifying fractions the same as reducing fractions?

Yes. Simplifying, reducing and writing in lowest terms all mean the same thing: dividing the top and bottom by a common factor until only 1 divides both.

How do you know a fraction is in simplest form?

When the numerator and denominator have no common factor except 1. For example, 5/8 is in simplest form, but 6/8 is not, because 2 divides both.

Do you always have to simplify fractions?

A fraction that isn't simplified is still correct, but final answers are usually expected in simplest form unless the question says otherwise.

How do you simplify an improper fraction?

The same way: divide the top and bottom by their greatest common factor. 18/4 becomes 9/2, which you can also write as the mixed number 4 1/2.

What is the fastest way to find the greatest common factor?

List the factors of the smaller number, then test them from the biggest down. The first one that also divides the larger number is the GCF.

Can a fraction with a prime denominator be simplified?

Not if it is less than 1. A proper fraction with a prime denominator, like 4/7 or 10/13, is already in simplest form.

Grades 4 to 6 (Years 5 to 7 in England)

How to simplify fractions

Simplifying, or reducing, a fraction means writing the same amount with the smallest possible numbers, so 18/24 becomes 3/4. Learn how to simplify fractions in a few steps, then try the free simplifying fractions practice below or print a fresh worksheet with an answer key.

The method, step by step

List the factors of the numerator and of the denominator.
Find the greatest common factor (GCF), the biggest number that divides both exactly.
Divide the numerator and the denominator by the GCF.
Check that the new numerator and denominator share no common factor except 1.
If you can't spot the GCF, divide by any common factor, such as 2, and repeat until nothing but 1 divides both.

CCSS 4.NF.A.1CCSS 3.NF.A.3.BEngland: Y4 FractionsEngland: Y5 Fractions

Worked example

Simplify 18/24 to its simplest form.

Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
The greatest common factor is 6.
Divide both by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
3 and 4 share no common factor except 1, so 18/24 = 3/4.

Practice now

Question 1 of 100 correct

Simplify 5/20 to its simplest form.

Print a worksheet with answers Share to Google ClassroomFree, no sign-up. Nothing you type is saved.

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Free printables, made fresh each time you open one. Print as many as you like, or do them on a tablet or computer with a finger, stylus or mouse.

Practice worksheetFresh questions every time, with an answer key you can turn on or off.
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Riddle puzzleSolve the questions to crack the code and answer a math joke.
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FlashcardsCut, fold and quiz: question on the front, answer on the back.
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Fraction wallEvery fraction from wholes to twelfths, to compare, color and cut out.
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What simplest form means

A fraction is in simplest form when its numerator and denominator have no common factor except 1. 3/4 is in simplest form; 6/8 is not, because 6 and 8 can both be divided by 2. Simplifying is equivalent fractions in reverse: instead of multiplying the top and bottom by the same number, you divide them.

Simplifying does not make the fraction smaller. Picture a bar cut into 8 equal parts with 6 shaded. Join the parts in pairs and you have 4 bigger parts with 3 shaded. The shaded length has not changed, so 6/8 = 3/4. Reducing a fraction only means describing the same amount with fewer, bigger pieces. Every fraction has exactly one simplest form, which is why teachers like answers written that way: two correct answers then look the same.

How to simplify fractions: two ways

The quickest way is to divide by the greatest common factor in one step. For 24/36, the GCF of 24 and 36 is 12. Since 24 ÷ 12 = 2 and 36 ÷ 12 = 3, 24/36 = 2/3.

If the GCF isn't obvious, divide by any common factor and repeat. Dividing 24/36 by 2 gives 12/18, by 2 again gives 6/9, and by 3 gives 2/3. It takes longer but always gets there, as long as you stop only when nothing but 1 divides both numbers.

These divisibility checks help you spot common factors fast:

Both numbers are even: divide by 2.
The digits of each number add up to a multiple of 3: divide by 3. For 27/45, 2 + 7 = 9 and 4 + 5 = 9, so 3 works, and so does 9, giving 3/5.
Both numbers end in 0 or 5: divide by 5.
Both numbers end in 0: divide by 10.

Simplifying fractions practice: examples

4/8 = 1/2 (GCF 4)
9/12 = 3/4 (GCF 3)
10/25 = 2/5 (GCF 5)
16/40 = 2/5 (GCF 8)
30/48 = 5/8 (GCF 6)
7/9 is already in simplest form, because 7 and 9 share no factor except 1.
14/4 = 7/2 (GCF 2), which is 3 1/2 as a mixed number.

The practice set below gives you fractions like these to reduce, with denominators up to 48. Each answer is checked as soon as you enter it, with a hint and the worked steps if you get stuck.

Why simplest form matters

Teachers and tests usually expect final answers in simplest form, so simplifying becomes the last step of almost every fraction calculation. After 1/6 + 1/3 = 3/6, the answer is written as 1/2. After 3/4 × 2/3 = 6/12, it is also written as 1/2. Simplified fractions are easier to compare and to picture, too: most people can see 2/3 more easily than 16/24.

How it is taught in school

Common Core does not list simplifying as a standard on its own. It grows out of equivalent fractions in grade 4 (4.NF.A.1), and in grade 6 students find the greatest common factor of two whole numbers up to 100 (6.NS.B.4). In England, the national curriculum expects Year 6 pupils to use common factors to simplify fractions.

How parents can help

Check times tables first. Spotting that 8 and 12 are both in the 4 times table is most of the work.
Ask "Can you go any further?" after every simplification, until your child can say why not.
Use real things. 6 eggs out of a box of 12 is half the box, so 6/12 = 1/2.
Turn it into a game: write a fraction like 20/30 and see who can reach simplest form in the fewest steps. Dividing by 10 gets to 2/3 in one.
Print a fresh simplifying fractions worksheet with an answer key, and choose the version with worked steps if your child wants to see where a mistake crept in.

Common mistakes

Dividing the top and bottom by different numbers, which changes the amount.
Stopping too early: 12/16 divided by 2 is 6/8, but 6 and 8 still share a factor of 2, so keep going to 3/4.
Subtracting instead of dividing: taking 3 from both parts of 6/9 gives 3/6, which is 1/2, but 6/9 is really 2/3.
Crossing out matching digits. It looks like 12/24 becomes 1/4 by crossing out the 2s, but 12/24 is 1/2.
Trying to simplify a fraction that is already in simplest form, such as 9/14. 9 = 3 × 3 and 14 = 2 × 7, so they share no factor except 1.

Questions people ask

Is simplifying fractions the same as reducing fractions?: Yes. Simplifying, reducing and writing in lowest terms all mean the same thing: dividing the top and bottom by a common factor until only 1 divides both.
How do you know a fraction is in simplest form?: When the numerator and denominator have no common factor except 1. For example, 5/8 is in simplest form, but 6/8 is not, because 2 divides both.
Do you always have to simplify fractions?: A fraction that isn't simplified is still correct, but final answers are usually expected in simplest form unless the question says otherwise.
How do you simplify an improper fraction?: The same way: divide the top and bottom by their greatest common factor. 18/4 becomes 9/2, which you can also write as the mixed number 4 1/2.
What is the fastest way to find the greatest common factor?: List the factors of the smaller number, then test them from the biggest down. The first one that also divides the larger number is the GCF.
Can a fraction with a prime denominator be simplified?: Not if it is less than 1. A proper fraction with a prime denominator, like 4/7 or 10/13, is already in simplest form.

Updated November 1, 2026.

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