Common Misconceptions (Algebra)

Algebra Misconceptions


If 42>1a, \frac{4}{2} > \frac{1}{a} , is it always true that 4a>21? 4 \cdot a > 2 \cdot 1 ?

Is it always true that ab+cd=a+cb+d? \large \frac{a}{b} + \frac{c}{d} = \frac{a+c}{b+d} ?

abc=abac \frac{a}{bc} = \frac{a}{b} \cdot \frac{a}{c}

For how many different values of aa is the above statement possibly true?

HINT: You should be trying to solve for a, a , so as a first step write the equation as abc=a2bc. \frac{a}{bc} = \frac{a^2}{bc} .

Which of these statements (if any) are false \color{#D61F06} { \text{false} } ?

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

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


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