chapter 1.7 - Distributive Property

How can you solve 63 x 12 without a calculator or pencil, only your brain?

Believe it or not, we can actually solve this with the distributive property of multiplication. You might be asking "How is that possible?". All you have to do is look at the 12. What can it be broken up into? 10 + 2 is the answer. Now we take 63 (10 +2). 63 (10 + 2) => (63 x 10) + (63 x 2) => 630 + 126 => 756

What is the distributive property of division?

When a number is being divided by a set of numbers inside a set of parentheses. To solve this type of equation, take the number outside of the parentheses and divide it by all numbers inside the parentheses. (12x - 8)/2 => (12x / 2) - (8 / 2) => 6x - 4 (7x - 10)/2 => (7x / 2) - (10 / 2) => 7x/2 - 5 (5x + 9)/7 => (5x / 7) + (9 / 7) => 5x/7 + 9/7 Use division properties to see if the answer is positive or negative.

What is the distributive property of multiplication?

When a number outside a set of parentheses and is multiplied by all the numbers on the inside. To solve them, take the number outside of the parentheses and multiply it by all numbers inside the parentheses. 8 (2 + 3x) => (8 x 2) + (8 x 3x) => 16 + 24x (3x - 2) 4 => (3x x 4) - (2 x 4) => 12x - 8 -5 (8x - 2) => (-5 x 8x) + (5 x 2) => -40x + 10 (3x - 7) (-4) => (3x x -4) + (7 x 4) => -12x + 28 Use multiplication properties to see if the answer is positive or negative.