Multiplication is distributive over ____ for whole numbers.
Addition
Idea in words: When we multiply a number by a sum, we can multiply it with each part and then add.
Property (step by step):
Take any whole numbers \(a\), \(b\), and \(c\).
Start with the sum: \(b + c\)
Multiply by \(a\): \(a\times(b + c)\)
Distribute \(a\) to each term:
\(a\times b\)
\(+\)
\(a\times c\)
So,
\(a\times(b + c) = (a\times b) + (a\times c).\)
Example:
Let \(a=3\), \(b=4\), \(c=5\).
Left side:
\(3\times(4 + 5)\)
\(= 3\times 9\)
\(= 27\)
Right side:
\((3\times 4) + (3\times 5)\)
\(= 12 + 15\)
\(= 27\)
Both sides are equal, so the property works.
Conclusion: Multiplication is distributive over addition.
Note: This question asks only about addition. (For subtraction, it is not asked here.)