Simplest form is the way of writing a fraction so its numerator and denominator have no common factor other than 1. To get there, divide the top and bottom by their greatest common factor: 68 = 6 ÷ 28 ÷ 2 = 34. The value stays the same; only the numbers get smaller. It is also called lowest terms.
In Spanish
forma más simple
Also called
lowest terms, reduced form, simplified fraction, reduce a fraction
Simplifying merges equal pieces: two eighths make one fourth, so the shaded amount never changes.
Formal definition and notation
A fraction ab with integers a and b ≠ 0 is in simplest form (lowest terms) when gcd (a, b) = 1, that is, when a and b are relatively prime. Every fraction has exactly one equivalent fraction in simplest form with a positive denominator, found by dividing the numerator and denominator by gcd (a, b). The idea extends to ratios (12 : 18 = 2 : 3) and, in algebra, to rational expressions with no common factor left in the numerator and denominator.
A fraction in simplest form names the same amount as the original. It is one of its equivalent fractions.
Test: if the only number that divides both the top and the bottom is 1, the fraction is already in simplest form, like 815.
If one of the two numbers is prime, check only that prime: 721 simplifies because 7 divides 21, so it becomes 13.
An improper fraction can be in simplest form: 94 is simplest. Some teachers also want it written as the mixed number214.
Most tests expect fraction answers in simplest form, and answer choices are usually written that way.
Simplifying rule
Simplifying rule
ab = a ÷ gb ÷ g, where g = GCF(a, b)
a, b
the numerator and denominator
g
their greatest common factor
Dividing by any common factor works, but you may need to repeat it: 3648 → 1824 → 912 → 34. Dividing by the GCF, 12, does it in one step.
Try it: see equal fractions
Interactive
Change the numerator and denominator and read the simplest form in the result box. Start at 6/8, then try 9/12, 10/12 and 7/12.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Simplest Form examples, step by step
Example 1: Use the GCF
Warm-up
Write 1015 in simplest form.
Factors of 10: 1, 2, 5, 10. Factors of 15: 1, 3, 5, 15.
The greatest common factor is 5.
Divide both by 5: 10 ÷ 515 ÷ 5 = 23.
Answer:1015 = 23 in simplest form.
Example 2: Larger numbers
Core
Write 3648 in simplest form.
Find the GCF: 36 = 22 × 32 and 48 = 24 × 3, so the GCF is 22 × 3 = 12.
Divide: 36 ÷ 12 = 3 and 48 ÷ 12 = 4.
Check: 3 and 4 share no factor except 1, so 34 is simplest.
Answer:3648 = 34.
Example 3: Simplify an improper fraction
Test-style
A recipe uses 42 tablespoons of flour, and 18 tablespoons fill one cup. How many cups is that? Give the answer as a fraction in simplest form and as a mixed number.
Equivalent fractions are all the fractions with the same value, such as 34, 68 and 912. Simplest form is the one member of that family with the smallest whole numbers.
Simplest form is about common factors; a mixed number is about whole parts. 94 is simplest form, and 214 is the same value as a mixed number.
Simplest Formvs.Simplify an expression
In algebra, “simplest form” can also mean combining like terms, as in 3x + 2x = 5x. For a fraction it means no common factor in the top and bottom.
Quick check: 3 questions
Question 1 of 3
What is 2436 in simplest form?
Show answer and explanation
Answer: A. The GCF of 24 and 36 is 12, so 2436 = 23. The other choices are equal to it but still share a factor: 6, 2 and 3.
Question 2 of 3
Which fraction is already in simplest form?
Show answer and explanation
Answer: C.16 = 24 and 27 = 33 share no prime factor, so the GCF is 1. The others share 3, 7 and 11.
Question 3 of 3
Write 4510 in simplest form.
Show answer and explanation
Answer: D. The GCF of 45 and 10 is 5: 45 ÷ 510 ÷ 5 = 92, which is 412. 910 divides only the top, 152 divides the top by 3 and the bottom by 5, and 184 still shares 2.
Simplest Form: frequently asked questions
How do you know if a fraction is in simplest form?
List or test the common factors of the numerator and denominator. If the only one is 1, the fraction is in simplest form. For 1528: 15 = 3 × 5 and 28 = 2 × 2 × 7 share no prime, so it is simplest. For 1527, both divide by 3, so it is not.
Is simplest form the same as lowest terms?
Yes. Simplest form, lowest terms and reduced form all mean the numerator and denominator have no common factor except 1. “Reducing” a fraction does not make it smaller in value: 68 and 34 are the same amount, written with smaller numbers.
Do improper fractions need to be changed to mixed numbers for simplest form?
Not by the math definition: 73 is already in simplest form because 7 and 3 share no factor. Many elementary classes ask for mixed numbers, 213, and algebra classes usually prefer improper fractions. Follow the directions in the problem. If no directions are given, either form is correct.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.NF.A.1
Cite this entry
Effortless Math Team. “Simplest Form.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/simplest-form/
Flashcard
TermSimplest Formno common factor but 1
DefinitionNumerator and denominator share no factor except 1. Divide both by the GCF: 3648 = 34.
DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5NumeratorThe numerator is the top number in a fraction. It tells how many parts are being counted, while the denominator below the fraction bar tells how many equal parts make one whole. In 35, the numerator is 3: three of five equal parts are taken.Number System · Grade 3, Grade 4, Grade 5RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8Rational ExpressionA rational expression is a fraction whose numerator and denominator are polynomials, such as x + 3x − 2 or 5x2. The denominator cannot equal 0, so values that make it 0 are excluded. You simplify, add, subtract, multiply and divide rational expressions the same way you work with numerical fractions.Functions · Algebra 1, Algebra 2Greatest Common FactorThe greatest common factor (GCF) is the largest factor shared by two or more numbers: the largest number that divides into both without a remainder. The GCF of 18 and 24 is 6. Find it by listing factors or by multiplying the prime factors the numbers share. The GCF is how you simplify fractions in one step.Number System · Grade 5, Grade 6, Grade 7SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6Equivalent FractionsEquivalent fractions are fractions that name the same value, like 12, 24 and 36. To make one, multiply or divide the numerator and denominator by the same nonzero number. That multiplies the fraction by 1, so its value does not change, and the fractions land on the same point of a number line.Number System · Grade 3, Grade 4, Grade 5NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Improper FractionAn improper fraction has a numerator that is greater than or equal to its denominator, so its value is 1 or more. Examples are 74, 92 and 55. Every improper fraction can be rewritten as a whole number or a mixed number: 74 = 134. Improper does not mean wrong.Number System · Grade 4, Grade 5, Grade 6Mixed NumberA mixed number has a whole number and a fraction together, such as 234, which means 2 + 34. It represents a value greater than one whole when the whole-number part is positive. Every mixed number can be rewritten as an improper fraction, and back: 234 = 114.Number System · Grade 4, Grade 5, Grade 6RemainderA remainder is the amount left over when one whole number does not divide another evenly. In 23 ÷ 5, four groups of 5 make 20 and 3 are left, so 23 ÷ 5 = 4 R 3. The remainder is always smaller than the divisor. A remainder of 0 means the division is exact.Operations · Grade 4, Grade 5, Grade 6Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5Combining Like TermsCombining like terms is simplifying an expression by adding or subtracting the terms that have exactly the same variable part. You add their coefficients and keep the variable part: 3x + 2x = 5x. Constants combine with constants. So 3x + 5 + 2x − 1 simplifies to 5x + 4.Algebra · Grade 6, Grade 7, Algebra 1FractionA fraction is a number that names equal parts of a whole, written ab. The bottom number, the denominator, tells how many equal parts make one whole; the top number, the numerator, tells how many of those parts you have. So 34 means 3 of 4 equal parts. Every fraction is also a point on the number line.Number System · Grade 3, Grade 4, Grade 5FactorA factor is a number or expression that divides another number or expression evenly, with no remainder. Factors multiply together to make a product: 4 × 6 = 24, so 4 and 6 are factors of 24. Every whole number greater than 1 has at least two factors, 1 and itself.Number System · Grade 4, Grade 5, Grade 6