How do you simplify a fraction to simplest form?

To simplify a fraction, divide the numerator and the denominator by the same number, and repeat until 1 is the only number that divides both. For 18/24, both parts divide by 6, so 18/24 = 3/4. Dividing by the greatest common factor gets there in one step, and the simplified fraction is still the same amount.

What does simplest form mean for a fraction?

Simplest form means that the numerator and the denominator of a fraction have no common factor other than 1. The fraction 3/4 is in simplest form because no whole number above 1 divides both 3 and 4, while 6/8 is not, because 2 divides both. Simplest form is also called lowest terms or a reduced fraction.

How do you simplify a fraction quickly?

The quickest way to simplify a fraction is to divide the numerator and the denominator by their greatest common factor in one step. For 24/36 the greatest common factor is 12, so 24 ÷ 12 = 2 and 36 ÷ 12 = 3, and the answer is 2/3. If the greatest common factor is not obvious, divide by any common factor you see and repeat.

How do you simplify an improper fraction?

An improper fraction is simplified the same way as any other fraction: divide the top and the bottom by a common factor until only 1 divides both. For 20/6, dividing by 2 gives 10/3. If the answer should be a mixed number, divide 10 by 3 to get 3 with remainder 1, so 10/3 = 3 1/3.

Is reducing a fraction the same as simplifying it?

Reducing a fraction and simplifying a fraction are two names for the same process. Both mean dividing the numerator and the denominator by a common factor until the fraction is in lowest terms. The word "reduce" can mislead children, because the value of the fraction stays the same and only the numbers get smaller.

Does a fraction have to be simplified to be correct?

A fraction does not have to be simplified to be mathematically correct, because 6/8 and 3/4 are equal. Many teachers and tests still ask for answers in simplest form, so a child can lose marks for 6/8. Check the instructions on the worksheet, and when in doubt, simplify the final answer.

How to Simplify Fractions to Simplest Form

Your child brings home a worksheet that says "write each answer in simplest form", and the first answer is 6/8. You remember that 6/8 is somehow the same as 3/4, but not how to explain it. This guide shows how to simplify fractions step by step, why simplifying fractions never changes the amount, and the shortcuts that make it quick at the kitchen table.

What does simplifying fractions mean?

Simplifying a fraction means writing the same amount with smaller numbers, so the pieces get bigger and fewer. A pizza cut into 8 slices with 6 eaten and a pizza cut into 4 slices with 3 eaten show the same amount of pizza gone, so 6/8 = 3/4.

Fractions that name the same amount are called equivalent fractions. Common Core standard 4.NF.A.1 asks fourth graders to "explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size."

Simplifying runs that rule backwards. Multiplying the top and bottom by 2 turns 3/4 into 6/8, so dividing the top and bottom by 2 turns 6/8 back into 3/4.

Three equal bars split into 16, 8 and 4 parts, with 12, 6 and 3 parts shaded, so the shaded length is the same and 12/16 = 6/8 = 3/4.

Why simplest form is taught

Simplest form is taught because it gives every amount one standard name, which makes answers easy to compare and check. A fraction is in simplest form when 1 is the only whole number that divides both the numerator and the denominator; the Wikipedia entry on irreducible fractions lists "lowest terms" and "reduced fraction" as other names for it.

The national curriculum in England sets the same skill in Year 6: pupils should "use common factors to simplify fractions". The What Works Clearinghouse practice guide on fractions recommends teaching that fractions are numbers with magnitudes "that can be either ordered or considered equivalent", which is the idea behind simplifying.

How to simplify fractions, step by step

The method for how to simplify fractions has one rule: divide the top and the bottom by the same number. These steps reduce 18/24.

Look for a number that divides both parts. Both 18 and 24 are even, so 2 divides both.
Divide the numerator and the denominator by it. 18 ÷ 2 = 9 and 24 ÷ 2 = 12, so 18/24 becomes 9/12.
Repeat with the new fraction. Both 9 and 12 divide by 3, and 9 ÷ 3 = 3 and 12 ÷ 3 = 4, so 9/12 becomes 3/4.
Stop when only 1 divides both. No whole number above 1 divides both 3 and 4, so 3/4 is in simplest form.
Check by multiplying back. 3 × 6 = 18 and 4 × 6 = 24, so 3/4 and 18/24 are the same amount.

Play free in your browserFactor PairsGrade 3–5

Dividing by the GCF in one step

Dividing by the greatest common factor (GCF) simplifies a fraction in one step instead of several. For 18/24, the GCF is 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4, and the answer is 3/4 at once.

The two routes always agree. For 36/48, halving twice and then dividing by 3 uses 2 × 2 × 3 = 12, which is the GCF of 36 and 48. Standard 6.NS.B.4 asks sixth graders to "find the greatest common factor of two whole numbers less than or equal to 100", and the guide to GCF and LCM shows how to find it.

A division ladder for 36/48: divide by 2 to get 18/24, by 2 to get 9/12 and by 3 to get 3/4, beside a single step dividing 36/48 by 12 to get 3/4.

Four ways to reduce fractions compared

Four methods answer how to reduce fractions, and each suits a different child and a different fraction. The step-by-step route is safest for beginners, and the GCF route is fastest once factors are familiar.

Method	How it works	Example	Best for	Speed
Repeated halving	Divide both parts by 2 while both are even	16/24 → 8/12 → 4/6 → 2/3	Grade 4, even numbers	Slow, needs a final check for 3, 5 or 7
Divide by small primes	Try 2, 3, 5 and 7 in turn	30/42 → 15/21 → 5/7	Grades 4 and 5	Medium
GCF in one step	Find the GCF, divide once	18/24 ÷ 6 = 3/4	Grade 6 and adults	Fast when the GCF is known
Prime factorization	Write both parts as primes and cancel the shared ones	12/18 = (2 × 2 × 3)/(2 × 3 × 3) = 2/3	Large numbers	Slow to write, never misses a factor

Divisibility shortcuts

Divisibility rules show which numbers divide both parts without any long division. Five rules cover most homework fractions:

By 2: the last digit is even, as in 14 and 38.
By 3: the digits add to a multiple of 3, as in 51, where 5 + 1 = 6.
By 5: the last digit is 0 or 5, as in 45 and 60.
By 9: the digits add to a multiple of 9, as in 27 and 63.
By 10: the last digit is 0, as in 30 and 70.

Take 45/60. Both numbers end in 5 or 0, so divide by 5 to get 9/12; 9 is a multiple of 3 and the digits of 12 add to 3, so divide by 3 to get 3/4. For 27/63, both digit sums are 9, so one division by 9 gives 3/7.

The prime-factor method relies on knowing which numbers are prime, and the explainer on prime numbers lists them. Quick division facts carry every shortcut, and the division worksheet for 4th graders gives printable practice with an answer key.

Play free in your browserDivision FactsGrade 3+

How to simplify improper fractions and mixed numbers

An improper fraction is simplified exactly like a proper one, by dividing the top and bottom by a common factor. For 14/4, both parts are even, so 14 ÷ 2 = 7 and 4 ÷ 2 = 2, giving 7/2.

Turning the result into a mixed number is a second, separate step. Divide 7 by 2 to get 3 with remainder 1, so 7/2 = 3 1/2. Converting first and simplifying the fraction part gives the same answer, 14/4 = 3 2/4 = 3 1/2, but simplifying first keeps the numbers small.

How to simplify mixed fractions

A mixed number is simplified by leaving the whole number alone and reducing only the fraction part. For 2 6/9, the fraction 6/9 divides by 3 to give 2/3, so 2 6/9 = 2 2/3.

A mixed number whose fraction part is improper needs one more move. In 1 9/6, the 9/6 simplifies to 3/2, which is 1 1/2, so 1 9/6 = 1 + 1 1/2 = 2 1/2. The same skills reappear when your child learns how to divide fractions, where answers are usually given in simplest form.

How to check your child can simplify fractions

Five short questions show whether simplifying fractions has landed. Ask for the working, because a right answer from a guess teaches you nothing.

One common factor: Simplify 10/15. The answer is 2/3, found by dividing both parts by 5.
A hidden factor: Simplify 21/28. The answer is 3/4, found by dividing by 7.
More than one step: Simplify 24/36. The answer is 2/3, by 12 in one step or by 2, 2 and 3 in turn.
Already simplest: Ask whether 9/15 is in simplest form. It is not, because 3 divides both, and the answer is 3/5.
Improper: Simplify 18/4 and write it as a mixed number. The answer is 9/2, which is 4 1/2.

A five-minute test

A five-minute test of three mixed fractions, one easy, one with a hidden factor and one improper, tells you more than a page of one type. Repeat it once a week with new numbers, and move on when your child gets all three right two weeks in a row.

The guide to fractions explained for parents covers the earlier ideas (numerator, denominator, comparing fractions) if one of these checks shows a gap.

Common mistakes when simplifying fractions

Three mistakes cause most wrong answers, and each has a one-line fix.

Subtracting instead of dividing: Taking 4 from the top and bottom of 5/10 gives 1/6, but 5/10 is one half. Divide both parts by the same number: 5/10 ÷ 5 = 1/2.
Cancelling digits: Crossing out the 2s in 12/24 gives 1/4, but 12/24 is 1/2. The trick looks right on 16/64 = 1/4 only by luck, so divide whole numbers and never strike out single digits.
Stopping too early: Halving 8/12 gives 4/6, and both 4 and 6 are still even. Keep going to 2/3, or divide by the GCF of 4 at the start.

Edge case: fractions that are already in simplest form

A fraction is already in simplest form when its parts share no factor above 1, even when the numbers look large. In 7/12, 7 is prime and does not divide 12, so 7/12 cannot be simplified.

Two consecutive numbers such as 8/9 or 15/16 never share a factor above 1, and neither does any fraction with 1 on top. A fraction whose numerator equals its denominator, such as 6/6, simplifies to 1.

Your simplest form checklist and next steps

Same number: divide the top and the bottom by the same number, never subtract.
Shortcuts: test 2, 3, 5, 9 and 10 with the divisibility rules first.
GCF: divide by the greatest common factor to finish in one step.
Stop rule: stop only when 1 is the only number that divides both parts.
Mixed numbers: keep the whole number and simplify the fraction part.
Check: multiply your answer back and compare it with the starting fraction.

Factor facts make every one of these steps faster. The math game for 5th graders page collects grade-level practice for the year when fraction work picks up speed.

MathIt is a free app for iOS and Android with about 90 game types, adaptive difficulty and daily practice in 33 languages, plus 2–5 player real-time battles for the whole family. Twenty-two of its games play free in the browser with no sign-up, and 30 printable worksheets come with answer keys.