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2 years ago

20:4 in simplest form

Mathematics

2 answers:

MaRussiya [10]2 years ago

8 0

Answer:

5:1

Step-by-step explanation:

20:4 is the same thing is 10:2, because what you do to one side you must do to the other, so I divided each side by 2. Then I do it again to get 5:1 which is the unit rate therefore simplest form. To check my work I can do 4x5 = 20.

kenny6666 [7]2 years ago

7 0

ANSWER: 20:4 in simplest form is 5:1

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Ierofanga [76]

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1. Let us proof that √3 is an irrational number, using reductio ad absurdum. Assume that $\sqrt{3}=\frac{m}{n}$ where $m$ and $n$ are non negative integers, and the fraction $\frac{m}{n}$ is irreducible, i.e., the numbers $m$ and $n$ have no common factors.

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Thus, 3 divides $n^2$ and necessarily 3 must divide $n$ . Hence, $n=3q$ where $q$ is a non negative integer.

Notice that

$\frac{m}{n} = \frac{3p}{3q} = \frac{p}{q}$ .

The above equality means that the fraction $\frac{m}{n}$ is reducible, what contradicts our initial assumption. So, $\sqrt{3}$ is irrational.

2. Let us prove now that the multiplication of an integer and a rational number is a rational number. So, $r\in\mathbb{Q}$ , which is equivalent to say that $r=\frac{m}{n}$ where $m$ and $n$ are non negative integers. Also, assume that $k\in\mathbb{Z}$ . So, we want to prove that $k\cdot r\in\mathbb{Z}$ . Recall that an integer $k$ can be written as

$k=\frac{k}{1}$ .

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$k\cdot r = \frac{k}{1}\frac{m}{n} = \frac{mk}{n}$ .

Notice that the product $mk$ is an integer. Thus, the fraction $\frac{mk}{n}$ is a rational number. Therefore, $k\cdot r\in\mathbb{Q}$ .

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Write $q=x+p$ and let us suppose that $q$ is a rational number. So, we get that

$x=q-p$ .

But the subtraction or addition of two rational numbers is rational too. Then, the number $x$ must be rational too, which is a clear contradiction with our hypothesis. Therefore, $x+p$ is irrational.

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3 years ago

Initially, the ratio of Ed’s toy cars to Pete’s toy cars was 5:2. After Ed gave 30 toy cars to Pete, they each had an equal numb

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So here is the answer. Initially, Ed's toy cars compared to Pete's toy cars was 5:2. So for every 5 cars that Ed has, Pete has 2. Now that Ed gave 30 cars to Pete. So here it goes. The total number of ratio units is 5+2=7, so each will have an equal number if they both have 3.5 ratio units. That is, if Ed transfers to Pete 1.5 ratio units, their car counts will be equal. Thus 1.5 ratio units = 30 cars, or 1 ratio unit = 20 cars. Therefore, this makes 7*20 cars = 140 cars.
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