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);
- Multiply the extremes (Refer to notes) of the ratio and isolate them on one side of the equation.
- 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