Jeremy is playing a game called “Rational Round Up” where he has to collect all the numbers in a maze that are rational and then get to the end of the maze. When he collects a number, he must prove it is rational by writing it as a quotient of two integers. Help him determine how to prove that each of the following numbers is rational.
1. 2.4 = 12/5
2. 74 = 74/1 rational
3. 17.3333333… = 52/3 rational
4. π pi cant be expressed as a fraction so irrational.
5. 61/11 rational
6. –18 = -18/1 rational
7. = 6/10 rational
8. 87.125
9. –30 = -30/1 rational
10. –8.3
11. 58.25 = 58 ¼ rational
12. 121
13. 4.5
14. = 71/10 rational
I have completed a few i just need help on the rest.
ummmm? hello?
Looks like you handled it pretty well.
.125 = 125/1000 = 1/8
So, 87.125 = 87 1/8 rational
All terminating decimals work this way
you got -30, but can't figure 121???
Sure, I can help you with the remaining questions:
8. To prove that 87.125 is rational, we need to express it as a quotient of two integers. Since it is a terminating decimal, we can write it as 87.125 = 87125/1000.
10. To prove that -8.3 is rational, we need to express it as a quotient of two integers. Note that -8.3 can be written as -83/10.
12. To prove that 121 is rational, we can write it as 121 = 121/1.
13. To prove that 4.5 is rational, we can write it as 4.5 = 9/2.
Please let me know if you need help with anything else!
Sure! I can help you prove that each of the remaining numbers is rational. Let's go through them one by one:
8. 87.125: To prove that 87.125 is rational, you need to write it as a quotient of two integers. Notice that 87.125 can be written as 87125/1000. Since both the numerator and denominator are integers, 87.125 is rational.
10. -8.3: To prove that -8.3 is rational, we need to write it as a quotient of two integers. -8.3 can be written as -83/10. Again, both the numerator and denominator are integers, so -8.3 is rational.
12. 121: To prove that 121 is rational, we need to write it as a quotient of two integers. In this case, 121 is already an integer, so we can express it as 121/1. Since both the numerator and denominator are integers, 121 is rational.
13. 4.5: To prove that 4.5 is rational, we need to write it as a quotient of two integers. Notice that 4.5 can be written as 9/2. Again, both the numerator and denominator are integers, so 4.5 is rational.
I hope that helps! Let me know if you have any other questions.