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# What does distributive property mean?

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The distributive property is a mathematical and algebraic property that says that multiplying two numbers is the same as multiplying one of those numbers by the sum of the other number's parts. In arithmetic, 50 x 45 is equal to (50 x 40) + (50 x 5). In algebra, the property is shown as x(y + z) = xy + xz.

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Using the distributive property in this way helps such number problems to be solved quickly and often without pen and paper. In using the distributive property algebraically, the number on the outside of the parentheses applies to all numbers inside the parentheses.

In the above example, x(y + z) = xy + xz, the variable x is multiplied by both variables in the parentheses, which are y and z. The sign inside the parentheses indicates whether addition or subtraction then occurs. If the equation reads, x(y - z), then the distributive property indicates the equivalent is xy - xz.

If x equals 2, y equals 7 and z equals 5, then:

2(7 + 5) = (2 x 7) + (2 x 5) = 14 + 10 = 24

and

2(7 -5) = (2 x 7) - (2 x 5) = 14 - 10 = 4

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## Related Questions

• A:

The sum of the first 100 odd numbers is 10,000. There are 100 odd numbers between 1 and 199, and each pair from the start and end of the sequence (e.g. 1 and 199, 3 and 197, etc.) adds up to 200. Multiplying 50 times 200 equals 10,000.

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• A:

The sum of the first 100 even numbers is 10,100. This is calculated by taking the sum of the first 100 numbers, which is 5,050, and multiplying by 2. To find the total of the first 100 numbers, multiply 50 by 101.

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• A:

In mathematics, adding numbers, items or amounts produces a sum. The word also refers to a group of arithmetic problems given as a classroom assignment. As a verb, to sum is to find the total of added amounts.