On the first math test, Keiko answered 19 out of 25 questions correctly. On thesecond test she got 17 out of 20 correct. On which test did she get a better grade? Can you compare these two ratios as they are written? Explain why or why not.

Answer:Keiko got a better answer on the test on her second test, and you could compare these two ratios as they are written.Step-by-step explanation:First: Convert each of the scores into percentages:How do you convert ratios to percentages? Well, first we have to convert the ratio to a decimal or a fraction. Let's convert it to a fraction. So, 19 out of 25 will become [tex]\frac{19}{25}[/tex], and 17 out of 20 will become [tex]\frac{17}{20}[/tex]. To convert a fraction to a percentage:Divide the numerator by the denominator:19 ÷ 25 = 0.76                                        AND                                    17 ÷ 20 = 0.85Multiply your quotient by 1000.76 x 100 = 76                                      AND                                 0.85 x 100 = 85Add the percent sign76%                                                          AND                                                   85%Now the two quantities are easier to compare. We can obviously see that 85% is bigger [and better] than 76%. So, the ratio that equals 85% - 17 out of 20 - is a better grade.The second question was: Can you compare these two ratios as they are written? Explain why or why not.Yes, you can compare these two ratios, just find the [positive] difference between the amount that she scored and the total number of scores that could be gained.25 - 19 = 620 - 17 = 3Since the equation with 20 and 17 in it has a smaller difference, it is most likely to have a greater value [because that means that Keiko got more right and less wrong, which means a greater mark which is also a greater quantity].Thanks, Topic: Quantity Relationships, Quantity Conversions