An addend is any number that is added to another number. In 8 + 5 = 13, the addends are 8 and 5, and 13 is the sum. An addition can have two or more addends, and you can add them in any order. When one addend is missing, subtract the known addend from the sum to find it.
The addends are the parts and the sum is the whole. When one part is missing, take the known part away from the whole: 13 − 8 = 5.
Formal definition and notation
In an additiona1 + a2 + ⋯ + an = s, each numberak is an addend (also called a summand) and s is the sum. Because addition is commutative and associative, the sum does not depend on the order or grouping of the addends. If a + b = s, then b = s − a: an unknown addend is found by subtraction.
Symbol
Read it as
Meaning
a + b = s
a plus b equals s
a and b are the addends, s is the sum
8 + □ = 13
eight plus what equals thirteen
a missing-addend problem; the box stands for the unknown addend
Key facts
The word comes from “add”: an addend is a number that gets added.
Order does not matter: 4 + 9 and 9 + 4 both equal 13 (the commutative property).
Adding 0 leaves the other addend unchanged: 15 + 0 = 15.
An addend can be negative: in 10 + (−3) = 7, the addends are 10 and −3.
Equal addends show doubling: 6 + 6 = 12, and an even number can always be written as two equal addends.
In algebra, the addends of an expression such as 3x + 7 are called its terms.
Missing addend rule
Missing addend rule
missing addend = sum − known addend
sum
the total, after the equals sign
known addend
the part you are given
For □ + 27 = 64: 64 − 27 = 37. Check by adding: 37 + 27 = 64.
Try it: missing addend balance
Interactive
The scale shows a missing-addend equation. Subtract the known addend from both sides to find the missing addend, then press Reset and try adding instead to see why that fails.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Addend examples, step by step
Example 1: Name the addends
Warm-up
In 12 + 7 + 6 = 25, list the addends and the sum.
The numbers joined by plus signs are the addends: 12, 7 and 6.
The number after the equals sign is the total: 25.
Check: 12 + 7 = 19 and 19 + 6 = 25.
Answer: The addends are 12, 7 and 6; the sum is 25.
Example 2: Find a missing addend
Core
Find the missing addend: □ + 48 = 83.
The sum is 83 and the known addend is 48.
Missing addend = 83 − 48.
83 − 48 = 35.
Check: 35 + 48 = 83.
Answer: The missing addend is 35.
Example 3: Savings goal
Test-style
Mia wants to save 150 dollars. She has saved 64 dollars from babysitting and 27 dollars from her birthday. How much more must she save?
The goal 150 is the sum. Two addends are known: 64 and 27.
Addends are added; factors are multiplied. In 4 + 5 the 4 and 5 are addends, but in 4 × 5 they are factors.
Quick check: 3 questions
Question 1 of 3
In 17 + 26 = 43, which numbers are the addends?
Show answer and explanation
Answer: A. The addends are the numbers being added, 17 and 26. 43 is the sum, so any choice that includes 43 mixes up the parts and the total.
Question 2 of 3
What is the missing addend in 29 + □ = 71?
Show answer and explanation
Answer: C.71 − 29 = 42, and 29 + 42 = 71. 100 comes from adding 29 and 71 instead of subtracting; 52 and 58 are subtraction slips with regrouping.
Question 3 of 3
A sum is 60. One addend is 18 and another is 25. What is the third addend?
Show answer and explanation
Answer: D. The two known addends total 18 + 25 = 43, and 60 − 43 = 17. 43 is only the partial sum; 103 adds all three numbers; 35 is a subtraction error.
Addend: frequently asked questions
What is the difference between an addend and a sum?
An addend is one of the numbers you add; the sum is the result. In 7 + 8 = 15, the addends are 7 and 8 and the sum is 15. Think of addends as the parts and the sum as the whole. If you know the whole and one part, subtract to find the other part: 15 − 7 = 8.
Can there be more than two addends?
Yes. An addition can have any number of addends: 3 + 4 + 5 + 6 = 18 has four. Because you can regroup and reorder addends freely, a handy trick is to pair numbers that make 10 or 100 first, as in 3 + 7 + 6 + 4 = 10 + 10 = 20.
What is a missing addend?
A missing addend is an unknown part in an addition equation, such as □ + 6 = 14. Find it by subtracting the known addend from the sum: 14 − 6 = 8. This is how first graders learn that subtraction answers the question “what do I add?” and it is the first step toward solving equations like x + 6 = 14.
SumA sum is the result you get when you add two or more numbers. In 8 + 5 = 13, the numbers 8 and 5 are the addends and 13 is the sum. The order does not change it: 5 + 8 is also 13. Word problems ask for a sum with words like total, in all and altogether.Operations · Grade 1, Grade 2, Grade 3AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2NumberA 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 2SubtractionSubtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.Operations · Grade 1, Grade 2, Grade 3Commutative PropertyThe commutative property says that changing the order of the numbers does not change the result of adding or multiplying them: a + b = b + a and a × b = b × a. For example, 4 + 9 = 9 + 4 and 3 × 5 = 5 × 3. Subtraction and division are not commutative.Operations · Grade 1, Grade 3, Grade 6Even NumberAn even number is an integer that can be divided by 2 with no remainder, so it can be split into two equal groups or into pairs. Even numbers end in 0, 2, 4, 6 or 8, such as 14, 236 and −10. Zero is even. Every even number can be written as 2n for some integer n.Number System · Grade 2, Grade 3, Grade 4ExpressionAn expression is a number, variable, or combination of numbers and variables joined by operations, without an equal sign. Examples are 7, 4x + 9 and 3(a − 2). Expressions can be simplified, but they are not solved unless they are part of an equation. You evaluate one by replacing each variable with a number.Algebra · Grade 6, Grade 7, Grade 8TermA term is a single number, a variable, or numbers and variables multiplied together, such as 7, x or −4xy2. In an expression, terms are the parts separated by plus and minus signs, so 5x2 − 3x + 8 has three terms. The sign in front of a term belongs to it.Algebra · Grade 6, Grade 7, Algebra 1MinuendThe minuend is the number you subtract from: the first number in a subtraction. In 17 − 6 = 11, the minuend is 17, the subtrahend is 6 and the difference is 11. The minuend is the whole you start with, so it equals the difference plus the subtrahend.Operations · Grade 1, Grade 2, Grade 3SubtrahendThe subtrahend is the number being subtracted: the number written after the minus sign. In 12 − 5 = 7, the subtrahend is 5. It is taken away from the minuend (12) to leave the difference (7). To find a missing subtrahend, subtract the difference from the minuend: 12 − 7 = 5.Operations · Grade 1, Grade 2, Grade 3FactorA 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 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 5Associative PropertyThe associative property says that when you add or multiply three or more numbers, the way you group them does not change the result: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). It lets you pick the easiest pair first. It does not work for subtraction or division.Operations · Grade 1, Grade 3, Grade 6Fact FamilyA fact family is a group of related math facts that use the same three numbers. With 6, 9 and 15 you get 6 + 9 = 15, 9 + 6 = 15, 15 − 6 = 9 and 15 − 9 = 6. Multiplication and division make fact families too, such as 4, 7 and 28. They show that operations undo each other.Operations · Grade 1, Grade 2, Grade 3Inverse 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 6EquationAn equation is a statement that two expressions are equal. It always has an equal sign, such as x + 5 = 12 or 3a = 18. Solving an equation means finding the value of the variable that makes it true: here x = 7 and a = 6. An expression like 4x + 7 has no equal sign, so it is not an equation.Algebra · Grade 6, Grade 7, Grade 8DifferenceA difference is the result of subtracting one number from another. In 12 − 7 = 5, the difference is 5. It tells how much bigger one number is than another, or how far apart they are on a number line. “The difference of a and b” means a − b, in that order.Operations · Grade 1, Grade 2, Grade 3