## Latex Tester

Inline formulas:

\(\textbf{Example 2.}\)Let \(m\), \(n\neq 0\), \(k\), and \(r\neq 0\) be whole numbers. Explain why \(\frac{m(\frac{k}{r})}{n}=\frac{mk}{nr}\).

DisplayMath with inserted text:

\[ \textbf{Step 1:}\text{By Definition 1, in Module 1, }(nr)(\frac{m(\frac{k}{r})}{n})=r(n(\frac{m(\frac{k}{r})}{n}))=r({m(\frac{k}{r})})=m({r(\frac{k}{r})})=mk\]

DisplayMath with inserted text:

\[\textbf{Step 2:}\text{ By Definition 1, in Module 1, }(nr)(\frac{mk}{nr})=mk\]

Inline Formulas w/o textbf:

**Step 3:** From steps 1 and 2 we have, \((nr)(\frac{m(\frac{k}{r})}{n})=(nr)(\frac{mk}{nr})\) which can only happen if \(\frac{m(\frac{k}{r})}{n}=\frac{mk}{nr}\).

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\textbf{Exercise 1.}

Geometrically prove why $A(R(5,b))=A(R(1,5b))$.\\

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\textbf{Exercise 2.}

Geometrically prove why $A(R(7,b))=A(R(1,7b))$.\\

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\textbf{Exercise 3.}

Let $n$ be any whole number. Explain why $A(R(n,b))=A(R(1,nb))$.\\

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\textbf{Example 2.}

Geometrically prove why $A(R(\frac{1}{5},b))=A(R(1,\frac{b}{5}))$.\\

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\textbf{Step 1:} The figure below shows that $R(1,b)$ can be divided into five rectangles that are all congruent to $R(\frac{1}{5},b))$. This implies $A(R(1,b))=5A(R(\frac{1}{5},b))$.\\

Geometrically prove why $$A(R(\frac{1}{5},b))=A(R(1,\frac{b}{5}))$$

Geometrically prove why $A(R(\frac{1}{5},b))=A(R(1,\frac{b}{5}))$