Why does [tex] \frac{2\pi}{\frac{1}{3}} [/tex] equal [tex] 6\pi [/tex]?
Answer (3)
2 π : 3 1 = 2 π ⋅ 1 3 = 2 π ⋅ 3 = 6 π
The expression 2 pi divided by 1/3 equals 6 pi because dividing by a fraction is the same as multiplying by its reciprocal. Therefore, 2 pi divided by 1/3 is equivalent to 2 pi multiplied by 3, resulting in 6 pi.
The question asks why 2 pi divided by 1/3 equals 6 pi. This can be understood by performing the division, which in mathematics is the same as multiplying by the reciprocal. Here's the step-by-step explanation:
Start with the original expression: 2 pi / (1/3).
Recall that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/3 is 3/1, or simply 3.
So, multiply 2 pi by 3: (2 pi) * 3 = 6 pi.
This relationship is fundamental in mathematics, especially when dealing with fractions and proportionalities.
The expression 3 1 2 π simplifies to 6 π by multiplying 2 π by the reciprocal of 3 1 , which is 3 . Thus, it results in 2 π × 3 = 6 π . Understanding how to manipulate fractions is key in various mathematical calculations.
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