A proper fraction is a fraction whose numerator is smaller than its denominator, such as 34 or 29. Because fewer parts are taken than make one whole, a positive proper fraction is always less than 1. If the numerator is equal to or greater than the denominator, the fraction is improper instead.
In Spanish
fracción propia
Also called
common fraction less than 1, fraction less than one
Grade level
K-5
Grade 3Grade 4Grade 5GEDTABEACCUPLACER
Proper Fraction in a picture
A fraction is proper when it takes fewer parts than make a whole. That is why every positive proper fraction sits between 0 and 1 on the number line.
Formal definition and notation
A fraction ab with whole numbersa and b, b ≠ 0, is proper when a < b. Then 0 ≤ ab < 1. The fraction ab is an improper fraction when a ≥ b. For signed fractions, ab is called proper when |a| < |b|, so −25 is also a proper fraction.
Symbol
Read it as
Meaning
ab, a < b
a over b, where a is less than b
the test for a proper fraction: top smaller than bottom
0 < ab < 1
a over b is between 0 and 1
where every positive proper fraction sits on a number line
55 is not proper: when the top and bottom are equal, the fraction equals 1 and counts as improper.
A mixed number such as 234 has a proper fraction as its fraction part.
Multiplying a positive number by a proper fraction makes it smaller: 23 × 12 = 8.
Simplifying never changes the type: 68 = 34 is still proper.
Proper fraction test
Proper fraction test
ab is proper when a < b
a
the numerator: how many parts are taken
b
the denominator: how many equal parts make one whole
Only compare the two numbers. The size of the numbers does not matter: 9899 is proper, but 32 is not.
Try it: proper or improper?
Interactive
Drag the point along the line in fifths. While it stays left of 1, the fraction is proper; at 1 or beyond, the numerator catches up with the denominator.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Proper Fraction examples, step by step
Example 1: Sorting fractions
Warm-up
Which of these are proper fractions: 47, 98, 66, 1112?
Compare each numerator with its denominator.
4 < 7 and 11 < 12: proper. 9 > 8 and 6 = 6: not proper.
Answer: The proper fractions are 47 and 1112.
Example 2: The fraction part of a mixed number
Core
Write 235 as a mixed number. What proper fraction is in it?
A mixed number is a whole number plus a proper fraction, like 312. It is more than 1.
Quick check: 3 questions
Question 1 of 3
Which fraction is proper?
Show answer and explanation
Answer: C. 12 < 13, so 1213 is proper and less than 1. 85 and 94 are greater than 1, and 1010 equals 1, so all three are improper.
Question 2 of 3
What is the fraction part of 173 written as a mixed number?
Show answer and explanation
Answer: A.17 ÷ 3 = 5 remainder 2, so 173 = 523. The fraction part 23 is proper. 53 uses the quotient as the numerator, and 317 flips the fraction.
Question 3 of 3
Which statement about every positive proper fraction is true?
Show answer and explanation
Answer: C. The numerator is smaller than the denominator, so the value is more than 0 and less than 1. It cannot be greater than 1, its reciprocal is improper, and the numerator can be odd, as in 34.
Proper Fraction: frequently asked questions
Is 1/1 a proper fraction?
No. In 11 the numerator equals the denominator, so the fraction equals 1, not less than 1. A proper fraction needs a numerator strictly smaller than its denominator, which makes it less than 1. Fractions equal to 1, like 44 or 99, are grouped with the improper fractions.
Can a proper fraction be negative?
Yes. When signs are involved, a fraction is called proper if the numerator’s absolute value is smaller than the denominator’s. So −38 is a proper fraction; its value is between −1 and 0. In elementary school, proper fractions are usually positive and lie between 0 and 1.
How do you turn an improper fraction into a proper fraction?
You cannot make it proper without changing its value, but you can split off the wholes. Divide the numerator by the denominator: 114 is 2 remainder 3, so it equals 234. The leftover part, 34, is a proper fraction, and the 2 counts the full wholes.
Updated November 2026·Reviewed by the Effortless Math team·Standards: n/a
Cite this entry
Effortless Math Team. “Proper Fraction.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/proper-fraction/
Flashcard
TermProper Fractiontop smaller than bottom
DefinitionA fraction whose numerator is less than its denominator, so its value is less than 1. Example: 3/4 is proper; 5/4 and 4/4 are not.
Whole 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 5Improper 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 6Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6NumeratorThe 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 5DenominatorThe 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 5Mixed 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 6NumberA 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 2RemainderA 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 6Simplest FormSimplest 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.Number System · Grade 4, Grade 5, Grade 6Equal ToEqual to means having exactly the same value or amount, and it is written with the symbol =. Numbers that look different can still be equal to each other: 12 is equal to 0.5. When two amounts are not the same, one is greater than or less than the other.Symbols and Notation · Kindergarten, Grade 1, Grade 2Absolute ValueThe absolute value of a number is its distance from zero on the number line, so it is never negative. It is written with two vertical bars: |−6| = 6 and |6| = 6. A positive number and 0 keep their value; a negative number loses its minus sign.Number System · Grade 6, Grade 7, Grade 8FractionA 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 5Equivalent 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 5ReciprocalThe reciprocal of a number is 1 divided by that number, so the two multiply to 1. For a fraction, swap the numerator and denominator: the reciprocal of 34 is 43, and the reciprocal of 5 is 15. Zero has no reciprocal. Dividing by a fraction is the same as multiplying by its reciprocal.Number System · Grade 5, Grade 6, Grade 7Unit FractionA unit fraction is a fraction with a numerator of 1, such as 12, 15 or 112. It names one equal part of a whole split into that many parts. The bigger the denominator, the smaller the unit fraction, and every fraction ab is a copies of 1b.Number System · Grade 3, Grade 4, Grade 5