Rational Numbers

1. Yes, this is a rational number.
2. No, this is not a rational number.
3. [latex]\frac{2}{7}[/latex]
4. [latex]\frac{33}{70}[/latex]
5. [latex]4\frac{1}{6}[/latex]
6. [latex]\frac{19}{8}[/latex]
7. [latex]0.\bar{4}[/latex]
8. [latex]0.0432[/latex]
9. [latex]\frac{23}{100}[/latex]
10. [latex]\frac{9}{10}[/latex]
11. [latex]\frac{29}{132}[/latex]
12. [latex]\frac{3}{16}[/latex]
13. [latex]\frac{8}{9}[/latex]
14. [latex]\frac{62}{147}[/latex]
15. [latex]\frac{4987}{37632}[/latex]
16. [latex]\frac{325}{552}[/latex]
17. [latex]\frac{6}{25}[/latex]
18. [latex]23\%[/latex]
19. [latex]75[/latex]
20. The total number of members in the group is [latex]164[/latex].
21. [latex]65\%[/latex]
22.  There are [latex]24[/latex] students in Professor Donaldson’s history of film class who say their favorite movie genre is comedy.
23. There are [latex]3,120[/latex] people in Tara’s town who are food insecure.
24. Maddie needs [latex]4.8[/latex] cups of mayonnaise and [latex]3.2[/latex] cups of apple cider vinegar.
25. There is [latex]41.8[/latex] liters of oxygen in [latex]200[/latex] liters of air.
26. The discount on the laptop is [latex]$140.00[/latex].
27. [latex]13[/latex] kilograms is equivalent to [latex]28.660[/latex] pounds (rounded to three decimal places).
28. [latex]10[/latex] miles is equivalent to [latex]633,600[/latex] inches.
29. For the markup question regarding Wegmans cereal:
    1. The markup in dollars is [latex]$0.79[/latex].
    2. The markup is [latex]52.7%[/latex] of the original cost (rounded to one decimal place).
30. 1. After a [latex]50\%[/latex] discount on the original price of [latex]$150.00[/latex], the price of the item becomes [latex]$75.00[/latex].
    2. [latex]25\%[/latex] of the sale price is [latex]$18.75[/latex].
    3. When an additional [latex]25\%[/latex] coupon is applied to the discounted price of [latex]$75.00[/latex], the new price becomes [latex]$56.25[/latex].
    4. The total amount saved on the item is [latex]$93.75[/latex], which is the difference between the original price and the final price paid.
    5.  The effective discount percentage is [latex]62.5\%[/latex].
    6.  The effective discount percentage is not equal to [latex]75\%[/latex]. This is because the second discount of [latex]25\%[/latex] is applied to the already discounted price, not the original price. The discounts compound rather than add directly, leading to a smaller percentage discount than simply adding the two percentages together.

Irrational Numbers

1. [latex]\sqrt{70}[/latex], [latex]5 + 9\pi[/latex]
2. [latex]2\sqrt{3}[/latex]
3. [latex]11\sqrt{5}[/latex]
4. [latex]4\sqrt{7}[/latex]
5. [latex]14\sqrt{15}[/latex]
6. [latex]18\sqrt{10}[/latex]
7. [latex]6\sqrt{3}[/latex]
8. [latex]-7\sqrt{7}[/latex]
9. This expression involves [latex]\pi[/latex] and the square root of [latex]2[/latex], which are both irrational numbers. Without a calculator, we can’t get a numerical value for this expression. It is as simplified as it can be without numeric approximation.
10. [latex]15.8\pi[/latex]
11. Since these do not have the same irrational part, the calculation can not be done.
12. [latex]6\sqrt{60}[/latex]
13. [latex]\frac{ 3\sqrt{2}}{2}[/latex]

Real Numbers

1. Rational Number, Real Number
2. Irrational number, Real Number
3. Irrational number, Real Number
4. Natural number, Integer, Rational Number, Real Number
5. Commutative Property of Addition
6. Commutative Property of Multiplication
7. Associative Property of Addition
8. Associative Property of Multiplication
9. Distributive Property
10. Multiplicative Inverse Property
11. Additive identity property
12. Additive identity property
13. Commutative Property of Addition
14. [latex]122[/latex]
15. [latex]260[/latex]
16. [latex]273[/latex]
17. [latex]1,300[/latex]
18. [latex]1,287[/latex]
19. [latex]4,343[/latex]