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Common Misconceptions (Algebra)

Algebra Misconceptions

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

Yes No

by Brilliant Staff

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

Yes No

by Brilliant Staff

$\frac{a}{bc} = \frac{a}{b} \cdot \frac{a}{c}$

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 $\frac{a}{bc} = \frac{a^2}{bc} .$

0 1 2 3

by Brilliant Staff

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

\sqrt{5} \cdot \sqrt{3} = \sqrt{5 \cdot 3}

\sqrt{-5} \cdot \sqrt{3} = \sqrt{-5 \cdot 3}

\sqrt{-5} \cdot \sqrt{-3} = \sqrt{-5 \cdot -3}

All of them are true

by Brilliant Staff

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?

a \cdot 1 = a

a (b + c) = ab + ac

(a\cdot b) \cdot c = a \cdot (b \cdot c)

a \cdot b = b \cdot a

by Brilliant Staff

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