Respuesta :

Step-by-step explanation:

Simplify 20/55;

[tex] \frac{20 \div 5}{55 \div 5} = \frac{4}{11} [/tex]

[tex] \frac{2}{5} \: is \: not \: equivalent \: to \: \frac{4}{11} [/tex]

In order for 2/5 to be equivalent with 20/55, it has to be an unsimplified form of the ratio 2/5. We can identify that 20/55 isn't.

Assuming 2:5 and 22:55 are equivalent. Then;

[tex]\implies 2:5 = 20:55[/tex]

This can be checked by using two methods. Listed below!

Method 1 (As stated above):

This method has been used in the above answer. The above answer has simplified the right-hand-side and verified that the ratios are not equivalent.

Obtained ratio:

[tex]2:5 = 20:55[/tex]

We can see that 20 and 55 are divisible by 5. Therefore, we can divide 5 to the numerator and the denominator to simplify the fraction.

[tex]2:5 = (20 \div 5):(55 \div 5)[/tex]

[tex]2:5 = (4):(11)[/tex]

Therefore, the given ratios are NOT equivalent.

Method 2:

To determine if the ratios are equivalent (or not);

  1. Multiply the extremes (Refer to notes) of the ratio and isolate them on one side of the equation.
  2. Multiply the middles (Refer to notes) of the ratio and isolate them on the other side of the equation.

Therefore,

[tex]\implies 2:5 = 20:55[/tex]

[tex]\implies 2 \times 55 = 5 \times 20[/tex]

Now, let's simplify both sides of the equation.

[tex]\implies 2 \times 55 = 5 \times 20[/tex]

[tex]\implies 110 = 100 \ \ \ (\text{False})[/tex]

Therefore, the given ratios are NOT equivalent, as stated in method 1.

Notes:

  • Extremes: (a : b = c : d) ⇒ "a" and "d"
  • Middles: (a : b = c : d) ⇒ "b" and "c"

Learn more about equivalent ratios: https://brainly.com/question/18835388