Question

On the first math test, Keiko answered 19 out of 25 questions correctly. On the

second 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 1

Keiko got a better answer on the test on her second test, and you could compare these two ratios as they are written.

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
`(19)/(25)`, and 17 out of 20 will become
`(17)/(20)`. To convert a fraction to a percentage:

• Divide the numerator by the denominator:

19 ÷ 25 = 0.76 AND 17 ÷ 20 = 0.85

• Multiply your quotient by 100

0.76 x 100 = 76 AND 0.85 x 100 = 85

• Add the percent sign

76% 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 = 6

20 - 17 = 3

Since 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