The Distributive Property states that when multiplying a number by an addition or subtraction expression inside parentheses, each term inside the parentheses can be multiplied by the number outside, and then the results can be added or subtracted. The Distributive Property can be used in conjunction with the Break Apart method to simplify complex multiplication and division equations.
To apply the Distributive Property to a multiplication equation:
- Identify one number to break apart so that the product of the first part of that number with the other number is a more convenient value.
- Multiply the other number by the first part of the number broken apart.
- Multiply the other number by the second part of the number broken apart.
- Add the results of the two products.
For example, let's consider the expression 7 × 14 :
- Since 14 is a 2-digit number, let's break that apart into 10 and 4, so the resulting equation is 7 x (10 + 4).
- Apply the Distributive Property, so 7 × (10 + 4) becomes 7 × 10 + 7 × 4.
- Multiply each term: 7 × 10 = 70 and 7 × 4 = 28.
- Add the results: 70 + 28 = 98, which is the final product.