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Subtraction

Subtraction is a fundamental arithmetic operation that finds the difference between two quantities, represented by the minuend and subtrahend. It is non-commutative and non-associative, with various methods for performing subtraction, including the standard algorithm and counting up. Subtraction has practical applications in finance, measurement, and time calculation.

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88 views3 pages

Subtraction

Subtraction is a fundamental arithmetic operation that finds the difference between two quantities, represented by the minuend and subtrahend. It is non-commutative and non-associative, with various methods for performing subtraction, including the standard algorithm and counting up. Subtraction has practical applications in finance, measurement, and time calculation.

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limboalena18
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### Notes on Subtraction

Subtraction is one of the fundamental operations in arithmetic,


representing the process of taking one quantity away from another.

**1. Basic Concepts**

- **Definition:** Subtraction is the operation of finding the difference


between two numbers or quantities. It involves taking away one
number (the subtrahend) from another (the minuend) to get the
result (the difference). citeturn0search0

- **Notation:** The subtraction operation is denoted by the minus sign


(−). For example, in the expression 8 – 3 = 5:

- **Minuend:** 8

- **Subtrahend:** 3

- **Difference:** 5

**2. Properties of Subtraction**

- **Non-Commutative:** Unlike addition, subtraction is not


commutative, meaning that changing the order of the numbers
changes the result. For example, 10 – 5 ≠ 5 – 10.

- **Non-Associative:** Subtraction is also non-associative, which


means that the grouping of numbers affects the outcome. For
instance, (20 – 5) – 3 ≠ 20 – (5 – 3).

**3. Subtraction Methods**

- **Standard Algorithm (Borrowing/Regrouping):** This traditional


method involves aligning numbers by place value and subtracting
each column, borrowing from the next column to the left when
necessary.

- **Counting Up:** Instead of subtracting, one can count up from the


subtrahend to the minuend to find the difference. This method is
often used in making change.

- **Partial Differences:** Subtract each place value separately and then


combine the results. For example, to subtract 652 from 478:

- Subtract hundreds: 600 – 400 = 200

- Subtract tens: 50 – 70 = -20

- Subtract units: 2 – 8 = -6

- Combine: 200 – 20 – 6 = 174

**4. Subtraction of Negative Numbers**

- Subtracting a negative number is equivalent to adding its positive


counterpart. For example, 7 – (−3) = 7 + 3 = 10.

**5. Real-Life Applications**

- **Financial Transactions:** Calculating expenses, determining


change, and balancing accounts.

- **Measurement:** Finding the difference between two


measurements, such as lengths, weights, or temperatures.

- **Time Calculation:** Determining the duration between two time


points.
**6. Practice Problems**

1. Subtract 456 from 789.

2. What is the result of 1000 – 587?

3. If you have $50 and spend $23.75, how much money remains?

For a visual explanation and more examples, you might find this video
helpful:

videoSubtraction – Math | Basic Introductionturn0search2 

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