Question

the product \[7 \times 317\] is equal to
A) \[7\]
B) \[317 \times 7\]
C) \[317\]
D) \[317\]\[ + \] \[7\]

Answer 1

Hint: As we know multiplication is commutative we can swap the two numbers, giving us the required answer.

Complete step by step solution: Given: \[7 \times 317\]
As multiplication is commutative we have \[a \times b = b \times a\],
So let a=7 and b=317
Hence \[a \times b = 7 \times 317\]
And \[b \times a = 317 \times 7\]
So we have,\[7 \times 317 = 317 \times 7\]

Hence, option (B) \[317 \times 7\] is the correct answer.

Note: Properties of multiplication:-
Commutative property: you can multiply in any order.
i.e. \[a \times b = b \times a\]
\[Example:3 \times 4 = 12 = 4 \times 3\]
Identity property: the product of any number with one(1) is that number.
i.e. \[a \times 1 = a = 1 \times a\]
Example: \[3 \times 1 = 3 = 1 \times 3\]
Zero property: the product of any number with zero(0) is zero.
i.e. \[a \times 0 = 0 = 0 \times a\]
\[Example:3 \times 0 = 0 = 0 \times 3\]
Associative property: you can group factors and still get the same answer.
i.e.\[a \times \left( {b \times c} \right) = \left( {a \times b} \right) \times c\]
\[Example:3 \times \left( {2 \times 4} \right) = 24 = \left( {3 \times 2} \right) \times 4\]