Assignment: Equivalent Rational Numbers I Investigation
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
2. 74
3. 17.3333333…
4. π
5.
6. –18
7.
8. 87.125
9. –30
10. –8.3
11. 58.25
12. 121
13. 4.5
14. 3 7/10
To prove that each of the given numbers is rational, we need to express them as a quotient of two integers (a fraction) where the denominator is not zero. Let's go through each number:
1. 2.4 = 24/10 = 12/5
Therefore, 2.4 is a rational number.
2. 74 = 74/1
Therefore, 74 is a rational number.
3. 17.3333333... = 17 1/3 = 52/3
Therefore, 17.3333333... is a rational number.
4. π (pi) is an irrational number, as it cannot be expressed as a quotient of two integers.
5. -sqrt(2) is an irrational number, as it cannot be expressed as a quotient of two integers.
6. -18 = -18/1
Therefore, -18 is a rational number.
7. sqrt(5) is an irrational number, as it cannot be expressed as a quotient of two integers.
8. 87.125 = 87 1/8 = 699/8
Therefore, 87.125 is a rational number.
9. -30 = -30/1
Therefore, -30 is a rational number.
10. -8.3 = -83/10
Therefore, -8.3 is a rational number.
11. 58.25 = 58 1/4 = 233/4
Therefore, 58.25 is a rational number.
12. 121 = 121/1
Therefore, 121 is a rational number.
13. 4.5 = 9/2
Therefore, 4.5 is a rational number.
14. 3 7/10 = 37/10
Therefore, 3 7/10 is a rational number.