Minuend, Subtrahend and Difference in Subtraction

What are the minuend, subtrahend and difference?

Every subtraction sentence is made up of three specific parts. The minuend is the total amount you start with. It is always the first number in a horizontal subtraction equation.

The subtrahend is the amount you are subtracting or taking away from the minuend. It is the second number in the equation, written immediately after the minus sign.

The difference is the final answer. It tells you exactly how much is left over or how far apart the two numbers are on a number line.

Parts of a subtraction sentence

When we calculate with larger numbers, we usually stack the numbers vertically in a column format. The vocabulary remains exactly the same, but the positions change.

In a column subtraction, the minuend is always the top number. The subtrahend is always the bottom number being subtracted. The difference is written below the equals line at the very bottom.

How the order changes the difference

In addition, you can add two numbers in any order and get the same total. Subtraction does not work this way. The order of the minuend and the subtrahend is strictly fixed.

If you start with $10$ items and take away $4$, you have $6$ items left. The equation is $10-4=6$.

If you try to swap the numbers to $4-10$, the meaning completely changes. You cannot take $10$ whole items away from $4$ items without going into negative numbers. Swapping the minuend and subtrahend changes the difference.

How to find a missing part

We can use a part-whole model to see how the three subtraction terms connect. The minuend is the whole block. The subtrahend and the difference are the two smaller pieces that make up that whole.

Because the pieces fit perfectly together, you can use inverse operations to find any missing number.

If the minuend is missing, you know the two parts but not the whole. Add the subtrahend and the difference together to find the starting number.

If the subtrahend is missing, you know the whole and one part. Subtract the difference from the minuend to find the missing part.

Worked examples

Practicing with missing-number equations and subtraction word problems will build your confidence in identifying each part.

Example 1: Identifying the parts of a subtraction equation

Question: In the equation $45-12=33$, what is the subtrahend?

Method:

1. Remember that the subtrahend is the amount being taken away.
2. Look for the number immediately following the minus sign.

Answer: The subtrahend is $12$.

Check: The starting number (minuend) is $45$. The answer (difference) is $33$. This confirms $12$ is the subtrahend.

Example 2: Finding a missing minuend

Question: Solve for the missing number: $\square -24=51$.

Given: A subtraction equation where the first number (minuend) is missing. The subtrahend is $24$ and the difference is $51$.

Method:

1. Identify which part of the whole-part model is missing. The missing minuend is the whole amount.
2. Use the inverse operation to add the two parts together.
3. Calculate $24+51=75$.

Answer: The missing minuend is $75$.

Check: Use checking subtraction by replacing the box with your answer: $75-24=51$. The equation is correct.

Example 3: Finding a missing subtrahend in a word problem

Question: A baker starts the day with $60$ muffins. After selling some, there are $15$ muffins left. How many muffins did the baker sell?

Given: The starting amount (minuend) is $60$. The amount taken away (subtrahend) is unknown. The amount left (difference) is $15$. The equation is $60-\square =15$.

Method:

1. Identify that a part is missing.
2. Subtract the known difference from the minuend to find the missing part.
3. Calculate $60-15=45$.

Answer: The baker sold $45$ muffins. The subtrahend is $45$.

Check: $60-45=15$.

Common mistakes

A very common mistake in column subtraction happens when a digit in the subtrahend is larger than the digit above it in the minuend.

Instead of regrouping from the next place value column, some learners simply subtract the smaller digit from the larger digit, ignoring which number is on top. You must always subtract the subtrahend digit from the minuend digit, never the other way around.

Frequently asked questions

What happens if the subtrahend is zero?

When the subtrahend is zero, you are taking nothing away. The difference will be exactly the same as the minuend. For example, $18-0=18$.

Can the difference be zero?

Yes. If the minuend and the subtrahend are the exact same number, taking one away from the other leaves nothing. The difference is zero. For example, $25-25=0$.