The 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.
In Spanish
sustraendo
Also called
number being subtracted, second number in a subtraction
The subtrahend is how many you take away. With the minuend fixed at 12, subtrahends of 5, 9 and 12 leave 7, 3 and 0.
Formal definition and notation
In a subtractiona − b = c, the numberb is the subtrahend. It is the unique number for which c + b = a, so b = a − c. Subtracting b is the same as adding its opposite: a − b = a + (−b). For a fixed minuend, a larger subtrahend gives a smaller difference.
Symbol
Read it as
Meaning
a − b
a minus b
b, after the minus sign, is the subtrahend
a + (−b)
a plus the opposite of b
the same value: subtracting a subtrahend equals adding its opposite
Key facts
The name comes from Latin and means “the thing to be subtracted”.
The subtrahend sits right after the minus sign: in 45 − 18, it is 18.
A subtrahend of 0 changes nothing: 37 − 0 = 37.
In word problems, “take away”, “less than” and “subtract … from” point to the subtrahend: “6 less than 20” is 20 − 6, with subtrahend 6.
A negative subtrahend increases the result: 9 − (−4) = 9 + 4 = 13.
Put the green point on the minuend and the blue point on the difference. The distance between them is the subtrahend. Try a minuend of 15 and a difference of 6.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Subtrahend examples, step by step
Example 1: Name the subtrahend
Warm-up
What is the subtrahend in 73 − 28 = 45?
The subtrahend is the number right after the minus sign: 28.
Check: 73 − 45 = 28.
Answer: The subtrahend is 28.
Example 2: Find a missing subtrahend
Core
Solve 140 − □ = 86.
The box is the subtrahend; 140 is the minuend and 86 is the difference.
Subtrahend = 140 − 86.
140 − 86 = 54.
Check: 140 − 54 = 86.
Answer: The missing subtrahend is 54.
Example 3: A negative subtrahend
Test-style
The temperature at noon was 5 degrees C. At midnight it was −8 degrees C. Write the change from midnight to noon as a subtraction and evaluate it.
Change = later value − earlier value = 5 − (−8). The subtrahend is −8.
Subtracting a negative is adding its opposite: 5 + 8.
5 + 8 = 13.
Answer: The temperature rose 13 degrees Celsius.
Common mistakes
✗ Mistake“7 less than 30” means 7 − 30.
✓ InsteadIt means 30 − 7 = 23. The 7 is the subtrahend.
“Less than” reverses the spoken order: the number before “less than” is the one taken away.
The difference is the answer, not the amount removed. In 30 − 12 = 18, the subtrahend is 12 and the difference is 18.
Quick check: 3 questions
Question 1 of 3
In 250 − 75 = 175, which number is the subtrahend?
Show answer and explanation
Answer: D. 75 is after the minus sign, so it is the subtrahend. 250 is the minuend, 175 is the difference, and 325 adds the first two numbers.
Question 2 of 3
Find the subtrahend: 64 − □ = 39.
Show answer and explanation
Answer: A.64 − 39 = 25, and 64 − 25 = 39. 103 adds the numbers; 35 and 15 are regrouping slips.
Question 3 of 3
Which phrase has a subtrahend of 9?
Show answer and explanation
Answer: C. “9 fewer than 31” means 31 − 9, so 9 is taken away. In the other three phrases 9 is the starting number (the minuend): 9 − 4, 9 − 2, 9 − 1.
Subtrahend: frequently asked questions
How do you remember minuend and subtrahend?
The subtrahend shares its start with “subtract”: it is the number that gets subtracted, after the minus sign. The minuend is the number before it, the one that is made smaller. In 9 − 2 = 7, 9 is the minuend, 2 is the subtrahend and 7 is the difference. Saying “minuend minus subtrahend equals difference” keeps the order.
What happens when the subtrahend is bigger than the minuend?
The difference is negative. For example, 8 − 13 = −5: you go 13 steps left from 8 on a number line and land 5 below zero. In grades 1 to 5, problems usually keep the subtrahend smaller, but with integers any subtrahend is allowed.
MinuendThe 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 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 2DegreeA degree is the standard unit for measuring an angle, written with the symbol °. One degree is 1360 of a full turn, so a full turn is 360°, a straight angle is 180° and a right angle is 90°. An angle that turns through 25 one-degree angles measures 25°.Geometry · Grade 4, Grade 5, Grade 7EvaluateEvaluate means to find the single number value of an expression. Replace each variable with the number you are given, then calculate using the order of operations. For example, 2x + 7 evaluated at x = 3 is 2(3) + 7 = 13. The result is one number, not a new expression.Algebra · Grade 6, Grade 7, Algebra 1Number 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 6Negative 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 7Additive InverseThe additive inverse of a number is the value that adds to it to give zero. The additive inverse of 9 is −9, because 9 + (−9) = 0, so it is the same thing as its opposite. To find it, change the sign: the additive inverse of −14 is 14, and 0 is its own.Number System · Grade 6, Grade 7, Grade 8Fact 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 3AddendAn 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