Hi, Justin.

We didn’t cover circle formulas very heavily in this post, did we? (Though the area formula is mentioned several times.) You can find more in Finding the Area of a Circle, where we show several ways to *derive* the area formula, and also explain the circumference. Those can provide good ways to remember the formulas, as we explained in this post, so I recommend reading that and learning the parts that work best for you.

But you can also remember the formulas by comparison. For **circumference**, just remember that it is a **multiple of the diameter**, namely pi times d. One length is a multiple of another, and that’s what circumference (or perimeter) really is. Just as the perimeter of a square is 4 times the side length, the distance around a circle is pi times the diameter. Since the diameter is twice the radius, this become 2 pi times the radius.

For **area**, remember that the area of a square is just the square of the side length. (As mentioned in this post, any area involves a **length times a length**, which is what a square number is.) For a circle, we just do the same thing, but multiply by pi. That number pi shows up everywhere circles are found!

So, perimeter of a square is \(P = 4s\), while perimeter (circumference) of a circle is \(C=2\pi r\); and area of a square is \(A=s^2\) while area of a circle is \(A=\pi r^2\). The circle formulas are nearly the same, but the 2 is moved!

]]>I wouldn’t say that the distributive property **requires** anything; it is just something you **may** do to rewrite an expression. So an expression like 2(2+2) is not a **contraction** of the larger expression; it is an expression in itself, which is equivalent to the other. Neither is “more real” than the other, though each might be more useful in particular situations.

Distributive property is an assumption nowadays?

It is implied multiplication not implied multiple operators. As such it is a part of the parentheses function signified with the absence of an operator to separate the 2 from the parentheses as the division operator separates the 8 from the 2.

Distributive property requires the 2 to be returned inside the parentheses and applied before the parentheses can be finalized.

2(2+2) is a mathematical contraction for (2Ã—2 + 2Ã—2) not two values separated by a mathematical operator such as the 8/2 is done.

I was always taught that the distribution property was the simplification of a long mathematical problem into a condensed (easier on the hands and pencils) application not dissimilar to contractions like can’t and don’t but with mathematical problems.

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