Sonia Ayers

Answered

2022-07-03

Is there an example to demonstrate why $\frac{1}{(1/2)}$ equals 2?

Answer & Explanation

SweallySnicles3

Expert

2022-07-04Added 21 answers

I know you are looking for something about pizzas but I think fractions in general work better if you work with a definition more akin to the axiomatic definition.

I mean what is $\frac{1}{\pi}$ in terms of pizzas?

I would define $\frac{1}{x}$ as the number, which when multiplied by x, gives me 1. This works fine for pizzas because, e.g. $2\times \frac{1}{2}=1$ two half slices is the whole.

Now whatever $\frac{1}{\frac{1}{2}}$ is, if I multiply it by $\frac{1}{2}$ I get one so that

$\frac{1}{\frac{1}{2}}\cdot \frac{1}{2}=\mathrm{1...}$

but this is nothing other than two... (or multiply both sides of the equation on the left by two).

I mean what is $\frac{1}{\pi}$ in terms of pizzas?

I would define $\frac{1}{x}$ as the number, which when multiplied by x, gives me 1. This works fine for pizzas because, e.g. $2\times \frac{1}{2}=1$ two half slices is the whole.

Now whatever $\frac{1}{\frac{1}{2}}$ is, if I multiply it by $\frac{1}{2}$ I get one so that

$\frac{1}{\frac{1}{2}}\cdot \frac{1}{2}=\mathrm{1...}$

but this is nothing other than two... (or multiply both sides of the equation on the left by two).

invioor

Expert

2022-07-05Added 3 answers

Use ratios.

Pizza will be consumed at a rate of one person per one-half pizza.

$\frac{dP}{d\mathrm{\Pi}}=\frac{1\text{}\text{person}}{\frac{1}{2}\text{}\text{pizza}}.$

Pizza is delivered at a rate of 1 pizza per day

$\frac{d\mathrm{\Pi}}{dt}=\frac{1\text{}\text{pizza}}{1\text{}\text{day}}.$

To avoid an excess of pizza, we require at least

$\frac{dP}{d\mathrm{\Pi}}\frac{d\mathrm{\Pi}}{dt}=\frac{1\text{}\text{person}}{\frac{1}{2}\text{}\text{pizza}}\cdot \frac{1\text{}\text{pizza}}{1\text{}\text{day}}=2\frac{\text{person}}{\text{day}}.$

Pizza will be consumed at a rate of one person per one-half pizza.

$\frac{dP}{d\mathrm{\Pi}}=\frac{1\text{}\text{person}}{\frac{1}{2}\text{}\text{pizza}}.$

Pizza is delivered at a rate of 1 pizza per day

$\frac{d\mathrm{\Pi}}{dt}=\frac{1\text{}\text{pizza}}{1\text{}\text{day}}.$

To avoid an excess of pizza, we require at least

$\frac{dP}{d\mathrm{\Pi}}\frac{d\mathrm{\Pi}}{dt}=\frac{1\text{}\text{person}}{\frac{1}{2}\text{}\text{pizza}}\cdot \frac{1\text{}\text{pizza}}{1\text{}\text{day}}=2\frac{\text{person}}{\text{day}}.$

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