A 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.
In Spanish
fracción
Also called
part of a whole, common fraction, rational number written a over b
58 is 5 of 8 equal parts of a bar, and also the point you reach after five jumps of18 from 0 on a number line.
Formal definition and notation
A fraction is a number of the form ab, where a and b are whole numbers (or integers) and b ≠ 0. The unit fraction1b is the size of 1 part when a whole is split into b equal parts, and ab is a parts of that size. A fraction also means a division: ab = a ÷ b.
Symbol
Read it as
Meaning
ab
a over b, or a b-ths
a is the numerator, b the denominator; 34 is read three fourths
Equal parts matter. A shape cut into 4 unequal pieces does not show fourths.
Proper fraction: numerator less than denominator, so the value is less than 1, like 58. An improper fraction such as 94 is 1 or more.
equivalent fractions name the same amount: 12 = 24 = 48. Multiply or divide the top and bottom by the same number.
With the same numerator, a bigger denominator means smaller parts: 18 < 14.
Any whole number is a fraction with denominator 1: 6 = 61. A denominator of 0 is not allowed.
Fractions, decimal numbers and percent values are three ways to write the same number: 58 = 0.625 = 62.5%.
Try it: build a fraction
Interactive
Change the numerator and denominator, or tap a piece of the top bar. The bars below show equivalent fractions, and the readout gives the decimal, the percent and the simplest form.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Fraction examples, step by step
Example 1: Fraction of a whole
Warm-up
A pizza is cut into 6 equal slices and you eat 4. What fraction of the pizza did you eat? Simplify it.
The whole has 6 equal parts, so the denominator is 6.
You ate 4 parts, so the numerator is 4: 46.
Divide the top and bottom by 2: 46 = 23.
Answer: You ate 46 of the pizza, which simplifies to 2/3.
Example 2: An improper fraction on the number line
Core
Where is 74 on the number line? Write it as a mixed number.
The denominator 4 splits each whole into fourths, so each jump is 14.
Count 7 jumps from 0: four jumps reach 1, and three more pass 1.
7 ÷ 4 = 1 R 3, so 74 = 134.
The point is between 1 and 2, three fourths of the way to 2 (at 1.75).
Answer:74 = 134, the point at 1.75 between 1 and 2.
Example 3: Fraction of a number
Test-style
Maya has read 35 of a 40-page booklet. How many pages does she have left?
One fifth of 40 pages is 40 ÷ 5 = 8 pages.
Three fifths is 3 × 8 = 24 pages read.
Pages left: 40 − 24 = 16. (Or: 25 of 40 is 2 × 8 = 16.)
Answer: Maya has 16 pages left.
Common mistakes
✗ MistakeA circle cut into 4 pieces of different sizes, with 1 piece shaded, shows 14.
✓ InsteadOnly 4 equal pieces show fourths. Unequal pieces are not fractions of the whole.
The denominator counts equal parts. If the pieces differ in size, 1 piece is not 14 of the circle.
✗ Mistake18 > 14 because 8 is bigger than 4.
✓ Instead18 < 14: cutting a whole into 8 parts makes smaller parts than cutting it into 4.
A larger denominator means more pieces, so each piece is smaller.
✗ Mistake12 + 13 = 25
✓ Instead12 + 13 = 36 + 26 = 56
You can only add parts of the same size. Rewrite with a common denominator, then add the numerators and keep the denominator.
A fraction compares a part to the whole; a ratio can compare any two amounts, even part to part. With 3 red and 5 blue marbles, red is 38 of all marbles, but the ratio of red to blue is 3 : 5.
A fraction is itself a division waiting to happen; the quotient is the result. 124 is a fraction whose quotient is 3.
Quick check: 3 questions
Question 1 of 3
A bar is split into 10 equal parts and 3 are shaded. What fraction is shaded?
Show answer and explanation
Answer: B. 3 shaded parts out of 10 equal parts is 310. 37 compares shaded to unshaded, 710 is the unshaded part, and 103 is upside down.
Question 2 of 3
Which fraction is greater than 12?
Show answer and explanation
Answer: D. Half of 9 is 4.5, and 5 is more than 4.5, so 59 > 12. The others are less than half: 3 is less than half of 8, 4 is less than half of 10, and 2 is less than half of 5.
Question 3 of 3
What is 1216 in simplest form?
Show answer and explanation
Answer: B. The greatest common factor of 12 and 16 is 4, and 12 ÷ 416 ÷ 4 = 34. 68 is equivalent but not simplest; the others change the value.
Fraction: frequently asked questions
Is a fraction a number?
Yes. A fraction is a number with its own place on the number line, not just a picture of shaded pieces. 34 sits between 0 and 1, three fourths of the way to 1. You can add, compare and multiply fractions like any other numbers, and every fraction can also be written as a decimal.
What are the parts of a fraction called?
The top number is the numerator and the bottom number is the denominator; the line between them is the fraction bar. In 27, 7 says the whole is cut into 7 equal parts and 2 says how many of them you have. The fraction bar also means division: 27 = 2 ÷ 7.
Can the numerator be bigger than the denominator?
Yes. That is an improper fraction, and its value is 1 or more. 94 means nine fourths: two whole units and one fourth more, so 94 = 214. The denominator, though, can never be 0, because a whole cannot be split into zero parts.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 3.NF.A.1, CCSS 3.NF.A.2, CCSS 4.NF.A.1
Cite this entry
Effortless Math Team. “Fraction.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/fraction/
Flashcard
TermFractionab
DefinitionA number naming equal parts of a whole: the denominator counts the parts in the whole, the numerator counts the parts you have. 34 is 3 of 4.
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 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 2Whole 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 5Unit 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 5DivisionDivision is the operation of splitting a number into equal groups. In 12 ÷ 3 = 4, the dividend 12 is shared into 3 equal groups (the divisor), and each group gets 4 (the quotient). Division undoes multiplication, because 3 × 4 = 12. If the groups do not come out even, the amount left over is the remainder.Operations · 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 6Proper FractionA 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.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 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 5DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6PercentA percent is a number out of 100. Percent means per hundred, so 25% means 25 out of 100, or 25100 = 0.25. To find a percent of a quantity, change the percent to a decimal and multiply: 20% of 80 is 0.20 × 80 = 16. The symbol for percent is %.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 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 6CircleA circle is the set of all points in a flat plane that are the same distance from one fixed point, the center. That distance is the radius. A segment through the center from edge to edge is the diameter, twice the radius. The distance around is the circumference, 2π r, and the area inside is π r2.Geometry · Kindergarten, Grade 1, Grade 7Common DenominatorA common denominator is a number that can be used as the denominator of two or more fractions at once. It is any common multiple of the denominators. For 13 and 14, 12 works: 412 and 312. You need one to add, subtract or compare fractions with different denominators.Number System · Grade 4, Grade 5, Grade 6RatioA 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 8Place ValuePlace value is the value of a digit based on its position in a number. In 3,507 the 5 is worth 500, because it sits in the hundreds place. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and after the decimal point, tenths and hundredths.Number System · Grade 3, Grade 4, Grade 5QuotientA quotient is the answer you get when you divide one number by another. In 20 ÷ 4 = 5, the quotient is 5. The number being divided is the dividend and the number you divide by is the divisor. When the division is not exact, the quotient comes with a remainder, or as a decimal or fraction.Operations · Grade 3, Grade 4, Grade 5Rational NumberA rational number is any number that can be written as a fraction of two integers, ab, where b is not 0. Fractions, integers, terminating decimals, and repeating decimals are rational numbers: 34, −5 = −51, 1.6 and 0.333… all qualify. Numbers such as √2 and π are irrational.Number System · Grade 7, Grade 8, Algebra 1