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# Common Misconceptions (Algebra)

Arm yourself with the tools to be the king or queen of heady mathematical debates, like the age old question of whether 0.999.... = 1.

If \( \frac{4}{2} > \frac{1}{a} ,\) is it always true that \( 4 \cdot a > 2 \cdot 1 ?\)

Is it always true that \( \large \frac{a}{b} + \frac{c}{d} = \frac{a+c}{b+d} ?\)

\[ \frac{a}{bc} = \frac{a}{b} \cdot \frac{a}{c} \]

For how many different values of \(a\) is the above statement possibly true?

**HINT:** You should be trying to solve for \( a ,\) so as a first step write the equation as \( \frac{a}{bc} = \frac{a^2}{bc} .\)

Which of these statements (if any) are \( \color{red} { \text{false} } \)?

Suppose you changed the rules of math so a negative times a negative was negative. So for instance \( -3 \times -2 = -6 \) instead of 6.

Which of these properties of arithmetic would no longer be true?

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