Which Multiplication Expression is Equivalent To: 4 x (2 + 3) or 4 x 2 + 4 x 3?

When multiplying a number by a quantity in parentheses, you can either distribute the number to each term within the parentheses or multiply the number by the entire quantity in parentheses. In this case, both 4 x (2 + 3) and 4 x 2 + 4 x 3 are equivalent expressions.

Understanding the Distributive Property

The distributive property of multiplication over addition states that a(b + c) = ab + ac. This means that when multiplying a number by a sum, you can distribute the number to each term in the sum.

For example, 4 x (2 + 3) can be rewritten as 4 x 2 + 4 x 3 using the distributive property.

Simplifying the Expressions

To simplify 4 x (2 + 3), we can use the order of operations:

1. Perform the operation inside the parentheses: 2 + 3 = 5.
2. Multiply the result by the number outside the parentheses: 4 x 5 = 20.

Therefore, 4 x (2 + 3) = 20.

To simplify 4 x 2 + 4 x 3, we can simply multiply each term by 4:

4 x 2 = 8
4 x 3 = 12

Therefore, 4 x 2 + 4 x 3 = 8 + 12 = 20.

Conclusion

As you can see, both 4 x (2 + 3) and 4 x 2 + 4 x 3 evaluate to the same value, which is 20. Therefore, they are equivalent expressions.

Additional Examples

Here are some additional examples of equivalent multiplication expressions:

• 3 x (4 + 5) = 3 x 4 + 3 x 5
• 2 x (6 – 2) = 2 x 6 – 2 x 2
• 5 x (3 + 7 + 1) = 5 x 3 + 5 x 7 + 5 x 1

Practice Questions

1. Simplify 6 x (2 + 4).
2. Simplify 3 x 5 + 3 x 2.
3. Are the following expressions equivalent: 4 x (3 + 6) and 4 x 3 + 4 x 6?

Answers

1. 6 x (2 + 4) = 6 x 6 = 36
2. 3 x 5 + 3 x 2 = 15 + 6 = 21
3. Yes, the expressions are equivalent.