Question - Simplifying a Complex Fraction
mathmathematical expressionfraction simplificationsimplify complex fractionreciprocal multiplication
Solution:
The image presents a mathematical expression, which is a complex fraction: $$\frac{\frac{B}{3}}{B}$$To simplify this expression, you can multiply the numerator and the denominator by the reciprocal of the denominator. In simpler terms, you multiply the top and bottom by $$3/B$$:$$\frac{B}{3} \times \frac{3}{B}$$ over $$B \times \frac{3}{B}$$When we multiply the fraction $$B/3$$ by $$3/B$$, the B's cancel out in the numerator, and the 3's cancel out, leaving us with 1 since anything divided by itself is 1.When we multiply $$B$$ by $$3/B$$, the B's cancel out and we are left with 3.So we have:1 over 3The result is: $$\frac{1}{3}$$.Looking at the answer choices provided:A) $$\frac{O}{B}$$B) $$\frac{O}{3B}$$C) $$\frac{O}{3}$$D) $$\frac{3B}{B}$$Option C is equivalent to our result, $$\frac{1}{3}$$, if we assume that "O" signifies the number 1 (as it might look like a vertical line in from the fraction line and was intended to be the number 1). Therefore, C) $$\frac{O}{3}$$ is correct if "O" is misprinted and should be the number 1. If the question did not contain a misprint, none of the provided options would be equivalent to $$\frac{1}{3}$$.
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