K-12 – Addition, Subtraction, Multiplication, Division

Contents

The four basic mathematical operations are:

+ Addition
− Subtraction
× Multiplication
÷ Division

It is important to learn the various parts of an equation, particularly when the equations are relatively simple, to form a basis for learning more complex mathematical concepts. Knowing the vocabulary used to reference the various parts of the equation allows us to more exactly define new concepts while efficiently referencing others. [1]

Addition

Adding two (or more) numbers means to find their sum (or total).

An addition statement can be split into the following parts. [4]

Addend (Summand): The numbers that are added are known as the addends.
Addition Symbol: There is the addition symbol (+) which is placed in between the addends. If the statement is written horizontally as shown below, then we place an equal to sign (=) just before the sum is written.
Sum: The final result obtained after adding the addends is known as the sum.

An addend together with an operation and equality symbol (in this case addition (+) and equals (=)) they form an addition sentence, or even more generally, an equation, as shown below.

9 (addend) + 7 (addend) = 2 (sum)

Using this basic concept of addition let us learn how to solve addition problems.

Adding Fractions

TBD

Lesson

TBD

Tricks

TBD

Subtraction

Subtracting one number from another number is to find the difference between them.

When we subtract two numbers, we use some terms which are used in the subtraction expression:

Minuend: The number from which the other number is subtracted.
Subtrahend: The number which is to be subtracted from the minuend.
Difference: The final result after subtracting the subtrahend from the minuend.

The subtraction formula is written as: Minuend – Subtrahend = Difference

Let us understand the subtraction formula or the mathematical equation of subtraction with an example.

9 (minuend) – 7 (subtrahend) = 2 (difference) [2]

Using this basic concept of subtraction let us learn how to solve subtraction problems.

Lesson

TBD

Tricks

TBD

Multiplication

Multiplication means times (or repeated addition).

The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:

Multiplicand: The first number (factor).
Multiplier: The second number (factor).
Product: The final result after multiplying the multiplicand and multiplier.
Multiplication symbol: ‘×’ (which connects the entire expression)

Let us understand the multiplication formula with the help of the following expression.

7 (multiplicand) × 5 (multiplier) = 35 (product)

Using this basic concept of multiplication let us learn how to solve multiplication problems. [3]

Lesson

TBD

Tricks

TBD

Division

Division ‘undoes’ multiplication and involves a number called the dividend being ‘divided’ by another number called the divisor.

Parts of division mean the name of the terms associated with the division process. There are four parts of the division, which are dividend, divisor, quotient, and remainder. Let us look at an example of division given below and understand the meanings of these four parts of the division.

Here, when we divide 105 by 8, we get the values of a divisor, dividend, quotient, and remainder.

The division formula is expressed as, Dividend ÷ Divisor = Quotient + Remainder; where:

Dividend: The number that is to be divided.
Divisor: The number of equal groups that are to be made, or the number by which we divide the dividend.
Quotient: The value/answer obtained after performing the division.
Remainder: The remaining or left out value that is not a part of any group.

Let us understand the division formula with the help of the following expression.

105 (dividend) ÷ 8 (divisor) = 35 (quotient) + 1 (remainder)

Using this basic concept of division let us learn how to solve division problems.

Dividing Fractions

Note
See K-12 – Division for additional information on dividing fractions.

Dividing Decimals

TBD

Lesson

TBD

Tricks

TBD

References

[1] “Addend.” 2023. math.net. Accessed October 29. https://www.math.net/addend.

[2] “Subtraction – Definition, Examples: Subtraction on Number Line.” 2023. CUEMATH. Accessed October 29. https://www.cuemath.com/numbers/subtraction/.

[3] “Multiplication – Definition, Formula, Examples.” 2023. CUEMATH. Accessed October 29. https://www.cuemath.com/numbers/multiplication/.

[4] “Addition – Meaning: Definition: Examples: What Is Addition?” 2023. CUEMATH. Accessed October 29. https://www.cuemath.com/numbers/addition/.

[5] “Division – Meaning, Steps, Algorithm, Examples.” 2023. CUEMATH. Accessed October 29. https://www.cuemath.com/numbers/division/.

Additional Reading

⭐ “Addition and Subtraction (Definition, Rules and Examples).” 2022. BYJUS. BYJU’S. July 11. https://byjus.com/maths/addition-and-subtraction/.

“Difference.” 2023. math.net. Accessed October 29. https://www.math.net/difference.

“Dividend.” 2023. math.net. Accessed October 29. https://www.math.net/dividend.

“Divisor.” 2023. math.net. Accessed October 29. https://www.math.net/divisor.

“Multiplicand and Multiplier: Learn and Solve Questions.” 2023. VEDANTU. Vedantu. August 11. https://www.vedantu.com/maths/multiplicand-and-multiplier.

⭐ “Multiplication and Division: Rules and Examples Multiplication and Division.” 2021. BYJUS. BYJU’S. September 30. https://byjus.com/maths/multiplication-and-division/.

“Quotient.” 2023. math.net. Accessed October 29. https://www.math.net/quotient.

⭐ Remick, Karen. 2023. “Teaching Math: Tools VS Methods.” Medium. Medium. October 23. https://karenremick.medium.com/teaching-math-tools-vs-methods-9767e59c35e0.

Imagine a carpenter. If he built things like we teach math, he’d need a different set of instructions for each thing he built. A wooden box has one set, a table has another, a roof has a third, a door frame a 4th, a shed a 5th, etc. What actual carpenters do is have a good understanding of what their tools can do and apply them as needed. This gives them flexibility and allows them to build things they don’t have specific instructions on how to make. This is what we need to do with math education; teach the tools and then show the student how to use the tools in different applications. Let’s look at three of my favorite tools.

“Subtrahend and Minuend: Learn Definition, Facts & Examples.” 2023. VEDANTU. Vedantu. August 11. https://www.vedantu.com/maths/subtrahend-and-minuend.

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.

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