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Distributive Property, a la Shmoop.

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King Moneylust values gold and jewels above all else. [King Moneylust sat on a throne]

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One day, the king’s first steward brought him 5 gold bars and 1 precious diamond. [Steward drops 5 gold bars and a diamond for the King]

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His second steward entered the court, also bringing the king 5 gold bars and 1 precious diamond.

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Moneylust’s third steward, never one to be a trailblazer, followed suit. [Third steward drops gold bars and diamond on the floor]

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In he came with 5 gold bars and 1 precious diamond.

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Because Moneylust is a busy guy and hardly has time to sit around and count all of his riches…[The King reading a piece of paper]

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…is there a shortcut he can use to determine how many he has of each item?

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You betcha.

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Because we are dealing with three occurrences of the same data, we can write it this way: [3 lots of gold bars and diamonds]

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Three times 5g plus d… where “g” stands for a gold bars, the 5 that multiplies the

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“g” stands for the amount of gold total and the “d” stands for a diamond.

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The stuff in parentheses represents what each steward presented to the king… [Stewards holding their gold bars and diamond]

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5 gold bars and a diamond…

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…and because there were three of them, we can multiply the whole thing by “3.”

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To simplify this expression, we can use distributive property. [maths formula scribbled under distributive property]

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In other words, whatever is on the outside of the parentheses, we can multiply by each

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term on the inside of the parentheses. Three times 5g equals 15g…

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…and three times 1d equals 3d. [King wearing 3D glasses]

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So we can rewrite the expression as “15g plus 3d.”

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Moneylust was a tad displeased when he realized that his stewards had only brought him 15 [The King looking unhappy with 15 gold bars and 3 diamonds]

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gold bars and 3 precious diamonds.

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He punished them by forcing them to solve this problem. [Stewards solving maths problem as King watches]

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