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Which operation is distributive over both addition and subtraction?
- a)Multiplication
- b)Division
- c)Exponentiation
- d)Square root
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Which operation is distributive over both addition and subtraction?a)M...
Multiplication is distributive over both addition and subtraction. This means that multiplying a number by the sum or difference of two other numbers is equivalent to multiplying each number individually and then performing the corresponding operation on the results.
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Which operation is distributive over both addition and subtraction?a)M...
Understanding the Distributive Property
The distributive property is a fundamental principle in mathematics that explains how multiplication interacts with addition and subtraction.
Distributive Property Explained
- The distributive property states that for any numbers \( a, b, \) and \( c \):
\[
a \times (b + c) = (a \times b) + (a \times c)
\]
and
\[
a \times (b - c) = (a \times b) - (a \times c)
\]
- This means that when you multiply a number by a sum or difference, you can distribute the multiplication across each term inside the parentheses.
Examples of Multiplication's Distributive Nature
- Addition Example:
- If \( a = 3 \), \( b = 4 \), and \( c = 2 \):
\[
3 \times (4 + 2) = 3 \times 6 = 18
\]
- Using distribution:
\[
(3 \times 4) + (3 \times 2) = 12 + 6 = 18
\]
- Subtraction Example:
- If \( a = 5 \), \( b = 10 \), and \( c = 3 \):
\[
5 \times (10 - 3) = 5 \times 7 = 35
\]
- Using distribution:
\[
(5 \times 10) - (5 \times 3) = 50 - 15 = 35
\]
Why Other Options Do Not Apply
- Division: Does not distribute over addition or subtraction.
- Exponentiation: Also does not distribute over addition or subtraction.
- Square Root: Does not distribute over addition or subtraction.
Conclusion
Thus, multiplication (option A) is the only operation that is distributive over both addition and subtraction, making it a powerful tool in simplifying expressions and solving equations.
The distributive property is a fundamental principle in mathematics that explains how multiplication interacts with addition and subtraction.
Distributive Property Explained
- The distributive property states that for any numbers \( a, b, \) and \( c \):
\[
a \times (b + c) = (a \times b) + (a \times c)
\]
and
\[
a \times (b - c) = (a \times b) - (a \times c)
\]
- This means that when you multiply a number by a sum or difference, you can distribute the multiplication across each term inside the parentheses.
Examples of Multiplication's Distributive Nature
- Addition Example:
- If \( a = 3 \), \( b = 4 \), and \( c = 2 \):
\[
3 \times (4 + 2) = 3 \times 6 = 18
\]
- Using distribution:
\[
(3 \times 4) + (3 \times 2) = 12 + 6 = 18
\]
- Subtraction Example:
- If \( a = 5 \), \( b = 10 \), and \( c = 3 \):
\[
5 \times (10 - 3) = 5 \times 7 = 35
\]
- Using distribution:
\[
(5 \times 10) - (5 \times 3) = 50 - 15 = 35
\]
Why Other Options Do Not Apply
- Division: Does not distribute over addition or subtraction.
- Exponentiation: Also does not distribute over addition or subtraction.
- Square Root: Does not distribute over addition or subtraction.
Conclusion
Thus, multiplication (option A) is the only operation that is distributive over both addition and subtraction, making it a powerful tool in simplifying expressions and solving equations.
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Which operation is distributive over both addition and subtraction?a)Multiplicationb)Divisionc)Exponentiationd)Square rootCorrect answer is option 'A'. Can you explain this answer?
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Which operation is distributive over both addition and subtraction?a)Multiplicationb)Divisionc)Exponentiationd)Square rootCorrect answer is option 'A'. Can you explain this answer? for Class 4 2024 is part of Class 4 preparation. The Question and answers have been prepared according to the Class 4 exam syllabus. Information about Which operation is distributive over both addition and subtraction?a)Multiplicationb)Divisionc)Exponentiationd)Square rootCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 4 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which operation is distributive over both addition and subtraction?a)Multiplicationb)Divisionc)Exponentiationd)Square rootCorrect answer is option 'A'. Can you explain this answer?.
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