How to Use Distributive Property in Math

The Distributive Property in mathematics is a fundamental property that allows us to simplify expressions and equations by distributing a number or variable across terms within parentheses. In basic terms, the Distributive Property states that for any numbers a, b, and c:

Distributive Property:

a * (b + c) = a * b + a * c

This means that we can multiply a number outside the parentheses with each term inside the parentheses and then add the results together.

When it comes to finding quotients, the Distributive Property can be used to simplify division problems. By understanding how to apply the Distributive Property, we can break down a division problem into smaller, more manageable parts.

Example:

Let's say we have the division problem 7 ÷ 1421 and we want to find the quotient. To use the Distributive Property in this case, we can rewrite the division problem as:

7 = 1 + 1 + 1 + 1 + 1 + 1 + 1

1421 = 1000 + 400 + 20 + 1

Now, we can distribute the 7 (dividend) across each digit of 1421 (divisor) and calculate the partial quotients:

7 * 1000 = 7000

7 * 400 = 2800

7 * 20 = 140

7 * 1 = 7

Finally, we add up the partial quotients to find the overall quotient:

7000 + 2800 + 140 + 7 = 9947

Therefore, the quotient of 7 ÷ 1421 is 9947, which we obtained by using the Distributive Property to simplify the division process.