Trace Mcintyre

2022-04-25

Simplifying compound fraction: $\frac{3}{\frac{\sqrt{5}}{5}}$

I'm trying to simplify the following:$\frac{3}{\text{}\frac{\sqrt{5}}{5}}$

I know it is a very simple question but I am stuck. I followed through some instructions on Wolfram which suggests that I multiply the numerator by the reciprocal of the denominator.

The problem is I interpreted that as:

$\frac{3}{\text{}\frac{\sqrt{5}}{5}\text{}}\times \frac{5}{\sqrt{5}},$

Which I believe is:

$\frac{15}{\text{}\frac{5}{5}\text{}}=\frac{15}{1}.$

What am I doing wrong?

I'm trying to simplify the following:

I know it is a very simple question but I am stuck. I followed through some instructions on Wolfram which suggests that I multiply the numerator by the reciprocal of the denominator.

The problem is I interpreted that as:

Which I believe is:

What am I doing wrong?

tswe0uk

Beginner2022-04-26Added 19 answers

Giovanny Howe

Beginner2022-04-27Added 18 answers

This means

$3\xb7\frac{5}{\sqrt{5}}=3\xb7\frac{(\sqrt{5}{)}^{2}}{\sqrt{5}}=3\sqrt{5}$

You're multiplying twice for the reciprocal of the denominator.

Another way to see it is multiplying numerator and denominator by the same number:

$\frac{3}{\frac{\sqrt{5}}{5}}=\frac{3\sqrt{5}}{\frac{\sqrt{5}}{5}\xb7\sqrt{5}}=\frac{3\sqrt{5}}{1}$

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