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إذا كان لدينا المعادلة التالية: (a + b) + c = a + (b + c)، فهذا يُعرف بـ
إذا كان لدينا المعادلة التالية: (a + b) + c = a + (b + c)، فهذا يُعرف بـ
ما هو المفهوم الذي ينص على أن ترتيب الأرقام المضافة لا يؤثر على المجموع؟
ما هو المفهوم الذي ينص على أن ترتيب الأرقام المضافة لا يؤثر على المجموع؟
ما هي الخاصية التي تنص على أن إضافة الصفر إلى أي عدد لا تغير قيمة هذا العدد؟
ما هي الخاصية التي تنص على أن إضافة الصفر إلى أي عدد لا تغير قيمة هذا العدد؟
أي من الخصائص التالية تنص على أنه يمكن تغيير ترتيب العمليات الحسابية دون تغيير النتيجة النهائية؟
أي من الخصائص التالية تنص على أنه يمكن تغيير ترتيب العمليات الحسابية دون تغيير النتيجة النهائية؟
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ما هي الخاصية التي تُمكننا من توزيع عملية الجمع على عمليات الضرب؟
ما هي الخاصية التي تُمكننا من توزيع عملية الجمع على عمليات الضرب؟
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ما هي الخاصية التي تنص على أن $a + b = b + a$؟
ما هي الخاصية التي تنص على أن $a + b = b + a$؟
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Study Notes
Properties of Addition
Addition is one of the basic arithmetic operations, along with subtraction, multiplication, and division. It involves combining two or more numbers to produce a single sum. There are several key properties of addition that are essential to understand when working with numbers. These properties include the commutative, associative, additive identity, and distributive properties. Let's examine each property in detail.
Commutative Property
The commutative property states that the order of the numbers being added does not affect the sum. In other words, if we swap the positions of the numbers being added, the resulting sum will remain unchanged. Mathematically, this can be expressed as follows:
a + b = b + a
For example, 3 + 5 = 3, and 5 + 3 = 5.
Associative Property
The associative property refers to the ability to change the grouping of numbers without altering the sum. Specifically, it states that changing the parentheses around the numbers being added will yield the same sum. Mathematically:
(a + b) + c = a + (b + c)
For example, (3 + 5) + 2 = 3 + (5 + 2).
Additive Identity Property
The additive identity property indicates that adding zero to any number leaves the original number unchanged. Mathematically, this can be represented as:
a + 0 = a
In practical terms, this means that adding zero to a number doesn't change the value. For example, 5 + 0 = 5.
Distributive Property
The distributive property allows us to distribute a multiplication over an addition or subtraction. Specifically, it states that:
a * (b + c) = a * b + a * c
This property can be applied both left-to-right and right-to-left:
a * (b + c) = a * b + a * c
And:
a * (b + c) = a * c + a * b
For example, 3 * (5 + 2) = 3 * 5 + 3 * 2, and 3 * (5 + 2) = 3 * 2 + 3 * 5.
These properties of addition are crucial for solving various mathematical problems involving numbers. By knowing these properties, we can simplify calculations and better understand the behavior of addition.
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Description
Explore the commutative, associative, additive identity, and distributive properties of addition in mathematics. Learn how these properties affect the sum of numbers and how they can be utilized in calculations.
