6. Explain how you would respond to the following:
a. A student claims that 9443/9444 and 9444/ 9445 are equal because both display 0.9998941 on his scientific calculator when the divisions are performed.
b. Another student claims that the fractions are not equal and wants to know if there is any way the same calculator can determine which is greater.
My calculator goes out one more decimal place to show the difference. I do not know any way your calculator could show it. Sorry.
Calculators usually store more numbers internally than on the screen.
Since you get 0.9998941, ask the student to subtract 1 from ANS. (If you don't have an ANS button, you can press the subtraction sign after pressing equal sign for the same effect as pressing "ANS" and "-" )
Then times it by 10 using the same method to move all the digits to the left. Then continue this process until you got the precision you wanted.
So for 9444/ 9445, the buttons I would press would be:
9444
/
9445
=
-
.9
=
*
10
=
This will move all the digits one spot to the left
Dang I was not even born when this happened 2010 i was born in 2011
a. To respond to the first student's claim, you can explain that although their calculator displays the decimal approximation 0.9998941 for both divisions, it does not necessarily mean that the fractions 9443/9444 and 9444/9445 are equal. Scientific calculators often display decimal approximations, which can have rounding errors.
To verify if the fractions are truly equal, you should explain that you can find their exact values by simplifying each fraction. For the first fraction, 9443/9444, you can divide both the numerator and denominator by their greatest common divisor (GCD), which is 1. In this case, since 9443 and 9444 are relatively prime (they have no common factors except 1), the fraction cannot be simplified further.
For the second fraction, 9444/9445, you can again divide both the numerator and denominator by their GCD, which is also 1. Similarly, since 9444 and 9445 are relatively prime, this fraction cannot be simplified further.
By simplifying the fractions, you can determine that both 9443/9444 and 9444/9445 are already in their simplest form. Therefore, they are not equal.
b. To respond to the second student's question about determining which fraction is greater using the same calculator, you can explain that scientific calculators usually cannot directly compare fractions. However, you can use the scientific calculator to convert each fraction into decimal form, and then compare the decimals to determine which fraction is larger.
To convert the fractions to decimals, you can instruct the student to divide the numerator by the denominator using the calculator. For example, to convert 9443/9444 to a decimal, the student should input 9443 ÷ 9444 into the calculator. Similarly, to convert 9444/9445 to a decimal, the student should input 9444 ÷ 9445.
After obtaining the decimal approximations for both fractions, the student can compare the decimals. If one decimal is larger than the other, then the corresponding fraction is greater.
In this case, the student can compare the decimals 0.9998941 (from 9443/9444) and 0.9998940 (from 9444/9445). By comparing these decimals, the student can determine that 9443/9444 is greater than 9444/9445.