The 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.
In Spanish
minuendo
Also called
first number in a subtraction, number you subtract from
The minuend is where you start. Taking away the subtrahend leaves the difference, so the minuend is always the difference plus the subtrahend: 11 + 6 = 17.
Formal definition and notation
In a subtractiona − b = c, the numbera is the minuend, b is the subtrahend and c is the difference. Subtraction is defined through addition: a − b is the unique number c with c + b = a. So the minuend always satisfies a = c + b. With whole numbers, c is a whole number only when a ≥ b; with integers any minuend works.
Symbol
Read it as
Meaning
a − b = c
a minus b equals c
a is the minuend, b the subtrahend, c the difference
Key facts
The name comes from the Latin for “to be made smaller”: the minuend is the number that gets reduced.
Order matters in subtraction: 12 − 5 = 7 but 5 − 12 = −7. Swapping the minuend and subtrahend changes the answer.
If the minuend equals the subtrahend, the difference is 0: 9 − 9 = 0.
If the minuend is smaller than the subtrahend, the difference is negative: 4 − 10 = −6.
In “subtract 8 from 30”, the minuend is 30, even though 8 is said first.
Minuend from the other parts
Minuend from the other parts
minuend = difference + subtrahend
difference
the answer to the subtraction
subtrahend
the amount taken away
For □ − 25 = 38: the minuend is 38 + 25 = 63. Check: 63 − 25 = 38.
Minuend examples, step by step
Example 1: Spot the minuend
Warm-up
Name the minuend in 64 − 29 = 35.
The minuend is the number before the minus sign: 64.
Check it equals difference plus subtrahend: 35 + 29 = 64.
Answer: The minuend is 64.
Example 2: Find a missing minuend
Core
Find the missing number: □ − 47 = 85.
The box is the minuend. The subtrahend is 47 and the difference is 85.
Minuend = difference + subtrahend = 85 + 47.
85 + 47 = 132.
Check: 132 − 47 = 85.
Answer: The missing minuend is 132.
Example 3: Words in reverse order
Test-style
A tank held some water. After 18 liters leaked out, 56 liters were left. How many liters were in the tank at first? Write the subtraction and name its minuend.
The starting amount is unknown, so it is the minuend: □ − 18 = 56.
Minuend = 56 + 18 = 74.
Check: 74 − 18 = 56.
Answer: The tank held 74 liters at first; the subtraction is 74 − 18 = 56, with minuend 74.
Common mistakes
✗ Mistake“Subtract 8 from 30” means 8 − 30.
✓ InsteadIt means 30 − 8 = 22. The number after “from” is the minuend.
“From” names the starting amount. The phrase lists the subtrahend first, so the written order flips.
✗ MistakeFor □ − 15 = 40, subtract: 40 − 15 = 25.
✓ InsteadThe missing number is the minuend, so add: 40 + 15 = 55. Check: 55 − 15 = 40.
A missing minuend is the whole, and you rebuild a whole by adding its parts.
✗ MistakeIn 52 − 38, take the smaller digit from the larger in each column: 8 − 2 = 6, 5 − 3 = 2, giving 26.
✓ InsteadRegroup from the minuend: 52 becomes 4 tens and 12 ones, 12 − 8 = 4, 4 − 3 = 1, so 52 − 38 = 14.
Each column must subtract the subtrahend digit from the minuend digit. When the minuend digit is smaller, regroup.
The difference is the result. In 20 − 7 = 13, 13 is the difference, not the minuend.
Quick check: 3 questions
Question 1 of 3
In 91 − 37 = 54, what is the minuend?
Show answer and explanation
Answer: C. The minuend is the number you subtract from, 91. 37 is the subtrahend, 54 is the difference, and 128 adds the two numbers instead.
Question 2 of 3
What number completes □ − 26 = 49?
Show answer and explanation
Answer: B. The missing number is the minuend: 49 + 26 = 75, and 75 − 26 = 49. 23 subtracts instead of adding; 65 and 85 are addition slips.
Question 3 of 3
Which expression has a minuend of 40?
Show answer and explanation
Answer: C. “The difference of 40 and 12” means 40 − 12, so 40 is the minuend. “Subtract 40 from 90” and “40 less than 75” both take 40 away, so 40 is the subtrahend there; “12 minus 40” starts at 12.
Minuend: frequently asked questions
What are the three parts of a subtraction problem?
A subtraction has a minuend, a subtrahend and a difference. In 15 − 4 = 11, the minuend 15 is the starting amount, the subtrahend 4 is the amount taken away, and the difference 11 is what remains. A helpful memory aid: the minuend comes first and gets made smaller, and the subtrahend is subtracted from it.
Can the minuend be smaller than the subtrahend?
Yes, once you use negative numbers. 6 − 10 = −4, so the difference is negative. In early grades, problems keep the minuend at least as big as the subtrahend so the answer stays a whole number, but in grade 7 and beyond any two numbers can be subtracted in either order.
SubtrahendThe 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 3DifferenceA 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 3SubtractionSubtraction 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 3NumberA 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 2AdditionAddition 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 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 5Negative NumberA negative number is a number less than zero, written with a minus sign, such as −3, −0.5 or −23. On a number line, negative numbers sit to the left of 0. They describe amounts below a starting point: temperatures below zero, depths below sea level, or money owed. Zero itself is neither negative nor positive.Number System · Grade 6, Grade 7Number 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 6Inverse 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 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 3Standard AlgorithmThe standard algorithm is the usual written column method for adding, subtracting, multiplying or dividing multi-digit numbers. You line up digits by place value, work one place at a time, and regroup (carry or borrow) when a place overflows or runs short. For 478 + 365 it gives 843 in three short steps.Operations · Grade 4, Grade 5, Grade 6AddendAn 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.Operations · Grade 1, Grade 2, Grade 3