Question

Multiplication is distributive over which arithmetic operations?

• A. Only Addition
• B. Only Subtraction
• C. Both Addition and Subtraction
• D. Neither Addition nor Subtraction

Answer 1

The correct option is C Both Addition and Subtraction

Multiplication is distributive over addition:
$a(b+c)=a\times b+a\times c=ab+ac$

For example, $2(4+3)$
$\underset{–}{\text{Applying Property}:}$
$2(4+3)=2\times 4+2\times 3=8+6=14$

$\underset{–}{\text{Normal Way}:}$
$2(4+3)=2\left(7\right)=2\times 7=14$

Multiplication is distributive over subtraction:
$p(q-r)=p\times q-p\times r=pq-pr$

For example, $3(5-2)$
$\underset{–}{\text{Applying Property}:}$
$3(5-2)=3\times 5-3\times 2=15-6=15$

$\underset{–}{\text{Normal Way}:}$
$3(5-2)=3\left(3\right)=3\times 3=9$

Multiplication is distributive over both the arithmetic operations of Addition and Subtraction.

Therefore, option (c.) is the correct answer.