10 Questions
Which property allows us to regroup numbers in subtraction without changing the result?
Associative property
If $a \div b = c$, which of the following is true according to the multiplicative property of division?
$a \times x \div (b \times x) = c$
Which operation satisfies the property: $a \circ (b + c) = a \circ b + a \circ c$?
Multiplication
If $5 \times a = 25$, what is the value of $a$?
4
Which property allows us to change the grouping of numbers in multiplication without affecting the result?
Associative property
What is the result of 87654321 + 987654321?
1863178532
Which property states that changing the order of numbers being added does not change the sum?
Commutative property
What is the result of 11 - 5?
6
Which property ensures that when you add a number to zero, the sum remains the original number?
Identity Property
What is the result of (5 + 6) + 7 compared to 5 + (6 + 7)?
(5 + 6) + 7 = 18 and 5 + (6 + 7) = 18
Study Notes
Mathematical Operations: Addition, Subtraction, Division, Multiplication
Addition
Addition is a mathematical operation that combines two numbers into a single value. For example, 5 + 6 = 11, since when we combine 5 and 6, the result is 11. Addition can also involve larger quantities, such as 87654321 + 987654321 = 1863178532.
Properties of Addition
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Commutative Property: When adding two numbers, changing the order does not change the sum. For example, 5 + 6 = 6 + 5.
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Associative Property: Grouping 3 numbers differently will result in the same sum. For example, (5 + 6) + 7 = 5 + (6 + 7).
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Identity Property: Every number has a property called identity. If you have any number, say X, and you add it with zero, the sum will always remain the original number. X + 0 = X.
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Inverse Property: Every number has a unique property called inverse. By adding its inverse (or negative), the number becomes zero. For example, if X is a number, then X + (-X) = 0.
Subtraction
Subtraction is a mathematical operation that finds the difference between two numbers by taking away one from another. For example, 11 - 5 = 6, because we take away 5 from 11, leaving us with 6 remaining.
Properties of Subtraction
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Commutative Property: Similar to addition, the commutative property exists in subtraction as well. In this case, switching the order of the subtrahend (the number being taken away) and the minuend (the starting number) changes nothing. So, 11 - 5 = 5 - 11.
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Associative Property: As in addition, the associative property is present in subtraction. This means that grouping 3 numbers in different ways still results in the same answer. Example: ((11 - 5) - 3) = 11 - (5 - 3).
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Distributive Property: The distributive property refers to how subtraction interacts with other operations like addition and multiplication. It states that (a - b) + c = a - (b + c).
Division
Division is a mathematical operation that splits up or shares a number evenly among equal parts. For example, 10 divided by 5 equals 2 because we share 10 equally by dividing it into 5 groups of 2 each.
Properties of Division
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Commutative Property: Division follows the same commutative property as addition and subtraction. In this context, x / y = y / x.
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Multiplicative Property of Division: Division is related to multiplication through the multiplicative property. This property states that if we multiply both the divisor and dividend by the same nonzero number, the quotient remains the same.
Multiplication
Multiplication is a mathematical operation that involves combining several things together. For example, multiplying 4 times 5 gives us 20 because there are four fives combined.
Properties of Multiplication
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Commutative Property: Just like addition, multiplication also follows the commutative property. A × B = B × A.
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Associative Property: Multiplication is associative just like addition. That is, (A × B) × C = A × (B × C).
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Distributive Property: The distributive property of multiplication states that a × (b + c) = a × b + a × c.
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Multiplicative Identity Property: The multiplicative identity property states that any number multiplied by 1 remains unchanged. That is, a × 1 = a.
Solved Examples
Addition
6 + 5 = 11
Subtraction
11 - 5 = 6
Division
10 / 5 = 2
Multiplication
4 × 5 = 20
Conclusion
Mathematical operations are fundamental building blocks of mathematics and allow us to perform various calculations. Understanding addition, subtraction, division, and multiplication is essential for any mathematical endeavor.
Test your knowledge of fundamental mathematical operations including addition, subtraction, division, and multiplication. Explore properties such as commutative, associative, identity, and inverse properties associated with these operations. Solved examples included for each operation.
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