The dividend is the number being divided in a division problem. In 56 ÷ 8 = 7, the dividend is 56, the divisor is 8 and the quotient is 7. It is the total you start with before splitting it into equal groups. In a fraction such as 568, the dividend is the numerator.
The dividend is the whole amount being shared. Divide 15 by 3 and each share is 5; multiply back, 3 × 5 = 15, to get the dividend.
Formal definition and notation
In a divisiona ÷ b = q with b ≠ 0, the numbera is the dividend. Exact division means a = b × q. In whole-number division with remainder, the dividend satisfies a = b × q + r with 0 ≤ r < b. Written as a fraction ab, the dividend is the numerator; in long division it goes inside the division bracket.
Symbol
Read it as
Meaning
a ÷ b
a divided by b
a, before the sign, is the dividend
ab
a over b
the dividend a is on top
Key facts
The dividend comes first in a ÷ b, on top in ab, and inside the bracket in long division.
“Divide 40 by 5” and “40 divided by 5” both have dividend 40. In “5 divided into 40”, the dividend is still 40.
A dividend of 0 gives a quotient of 0: 0 ÷ 9 = 0.
When the dividend is smaller than the divisor, the quotient is less than 1: 3 ÷ 4 = 0.75.
Multiplying both the dividend and divisor by the same number keeps the quotient: 56 ÷ 8 = 560 ÷ 80 = 7.
In money, a “dividend” is also a payment a company makes to its shareholders; in math class it always means the number being divided.
Rebuilding the dividend
Rebuilding the dividend
dividend = divisor × quotient + remainder
divisor
the number you divide by
quotient
the answer
remainder
what is left over, 0 for exact division
For □ ÷ 6 = 14 R 5: dividend = 6 × 14 + 5 = 89.
Dividend examples, step by step
Example 1: Name the dividend
Warm-up
In 9015 = 6, which number is the dividend?
A fraction bar means divide: top divided by bottom.
The top number, 90, is being divided.
Answer: The dividend is 90.
Example 2: Find a missing dividend
Core
Find the dividend: □ ÷ 7 = 23 R 4.
Use dividend = divisor × quotient + remainder.
7 × 23 = 161.
161 + 4 = 165.
Check: 165 ÷ 7 = 23 R 4, since 7 × 23 = 161 and 165 − 161 = 4.
Answer: The dividend is 165.
Example 3: Words in a different order
Test-style
A ribbon is cut into 12 equal pieces, each 35 cm long. How long was the ribbon, and which number is the dividend in the division that describes the cut?
The quotient is the result: in 30 ÷ 6 = 5, the quotient is 5, the dividend 30.
Quick check: 3 questions
Question 1 of 3
In 144 ÷ 12 = 12, what is the dividend?
Show answer and explanation
Answer: B. 144 is the number being divided. The 12 before the equals sign is the divisor and the 12 after it is the quotient; 156 adds 144 and 12.
Question 2 of 3
What dividend makes □ ÷ 9 = 15 R 3 true?
Show answer and explanation
Answer: C.9 × 15 + 3 = 138. 135 forgets the remainder, 132 subtracts it, and 27 adds instead of multiplying.
Question 3 of 3
Which expression has a dividend of 8?
Show answer and explanation
Answer: D. In 8 ÷ 32, 8 is being divided, so it is the dividend (the quotient is 0.25). In the other three, 8 is the divisor.
Dividend: frequently asked questions
What is the difference between a dividend and a divisor?
The dividend is the number being divided, and the divisor is the number you divide by. In 35 ÷ 7 = 5, the dividend 35 is the total and the divisor 7 tells how many groups (or how big each group is). A memory trick: the dividend gets divided, the divisor does the dividing.
Can the dividend be smaller than the divisor?
Yes. Then the quotient is less than 1: 2 ÷ 5 = 0.4, or 25. In whole-number division with remainders, 2 ÷ 5 = 0 R 2: no full group of 5 fits, so all 2 are left over. Every proper fraction is a division whose dividend is smaller than its divisor.
DivisorA divisor is the number you divide by. In 56 ÷ 8 = 7, the divisor is 8: it tells how many equal groups to make, or how big each group is. The divisor can never be 0. A divisor of a whole number is also one of its factors, because it divides that number with no remainder.Operations · 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 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 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 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 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 5Long DivisionLong division is a step-by-step written method for dividing large numbers. You work through the dividend one digit at a time from the left, repeating four steps: divide, multiply, subtract, bring down. For 872 ÷ 4, the steps give the quotient 218 with a remainder of 0.Operations · Grade 4, Grade 5, Grade 6LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3Proper 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 5MultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4FractionA 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 5Inverse OperationsInverse operations are operations that undo each other. Addition and subtraction are inverses: 9 + 6 − 6 = 9. Multiplication and division are inverses: 7 × 4 ÷ 4 = 7. You use them to check answers and to solve equations, undoing each step in reverse order until the variable is alone.Operations · Grade 1, Grade 3, Grade 6