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Algebra

# Algebra Misconceptions

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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