Easy Mathematics Step-by-Step (2012)
Chapter 1 Numbers and Operations
1. 10 is a natural number, a whole number, an integer, a rational number, and a real number.
2. –7.3 is a rational number and a real number.
3. –74 is an integer, a rational number, and a real number.
4. –1000 is an integer, a rational number, and a real number.
5. 0.555 … is a rational number and a real number.
6. is a rational number and a real number.
7. is a rational number and a real number.
8. 0 is a whole number, an integer, a rational number, and a real number.
9. is an irrational number and a real number.
13. Distributive property
14. Zero factor property
15. Associative property of multiplication
Chapter 2 Integers
4. “Negative nine plus the opposite of negative four equals negative nine plus four.”
5. “Negative nine minus negative four equals negative nine plus four.”
Chapter 3 Exponents
1. “six to the fifth”
2. “negative five to the fourth”
3. “four to the zero”
4. “negative nine squared”
12. 0–4 is the notation for or , which is undefined.
Chapter 4 Order of Operations
Chapter 5 Fractions
Chapter 6 Decimals
3. Prediction: Five places
4. Prediction: Six places
7. Divide 2.917 by 0.37 and round to three places
8. Multiply 6.678 by 0.37 and round to two places
Answer: 2.47 (using a calculator)
9. Divide 3.977 by 0.0372 and round to three places
10. Multiply 45.67892 by 0.0374583 and round to four places
Answer: 1.7111 (using a calculator)
Chapter 7 Percents
Chapter 8 Units of Measurement
15. Which is a better buy for shelled peanuts, 8 oz for $4.50 or 9 oz for $4.99?
16. A runner ran 250 m. How many kilometers did the runner run?
17. First-class postage is charged by the ounce. A package weighs 3 lb 12 oz. How many ounces does the package weigh?
18. Carpet is sold by the square yard. The surface of the floor of a 9 ft by 12 ft room is 108 ft2. How many square yards of carpet are needed to cover the floor?
19. A recipe calls for 3 tbsp of oil. How many fluid ounces is 3 tbsp?
20. A large container holds 5 gal of water. How many cups of water does the container hold?
Chapter 9 Ratios and Proportions
9. You will earn only one-half of a year’s interest.
amount of interest you will earn in 6 months.
Chapter 10 Roots and Radicals
Thus, 12 and –12 are the two square roots of 144.
Thus, and are the two square roots of .
Thus, 0.8 and –0.8 are the two square roots of 0.64.
Thus, 20 and –20 are the two square roots of 400.
5. , so 6 is the positive square root of 36.
6. –9 is a negative number; square roots of negative numbers are not real numbers.
Thus, is undefined for the set of real numbers.
7. , so is the positive square root of .
Chapter 11 Algebraic Expressions
1. The variable is s, and the constant is 4.
2. The numerical coefficient is –12.
3. The numerical coefficient is 1.
4. The numerical coefficient is .
Chapter 12 Formulas
Chapter 13 Polynomials
1. is a trinomial.
2. is a binomial.
3. 2x2 + 7x – 4 is a trinomial.
4. is a monomial.
5. is a polynomial.
6. –15x + 17x = 2x
7. is simplified.
Chapter 14 Solving Equations
5. Two more than three times a number x is four less than six times the number x.
The student’s percent grade is 87.5%.
The regular price of the shirt is $95.
Chapter 15 Informal Geometry
1. Yes, the size and shape appear to be the same.
2. No, the size is about the same but the shape is different.
3. No, the size is different.
4. Yes, the shape is the same.
5. Yes, the shape is the same.
6. No, the shape is different.
Dashed lines are lines of symmetry
8. The figure is not symmetric.
9. Acute, because 50° is between 0° and 90°
10. Right, because the angle is exactly 90°
11. Obtuse, because 130° is between 0° and 180°
14. Hexagon, because it has exactly six sides
15. Heptagon, because it has exactly seven sides
16. Isosceles, because it has two congruent sides
17. Equilateral, because it has three congruent sides
18. Acute triangle, because it has three acute angles
19. Obtuse triangle, because it has one obtuse angle
20. Right triangle, because it has one right angle
21. Parallelogram, because opposite sides are congruent and parallel
22. Rectangle, because it is a parallelogram that has four right angles
23. Trapezoid, because it has exactly one pair of parallel sides
24. The length of the diameter is
25. Rectangular prism, because it has two parallel and congruent rectangular bases and rectangles for sides
26. Cylinder, because it has two parallel congruent bases, which are circles, and it has one rectangular side that wraps around
27. A square or rectangular pyramid, because it is a solid with exactly one base, triangular sides, and a square base
28. Sphere, because it is a three-dimensional solid that is shaped like a ball
29. Triangular pyramid, because it is a solid with exactly one base, triangular sides, and a triangular base
30. Pentagonal prism, because it has two parallel and congruent pentagonal bases and rectangles for sides
Chapter 16 Perimeter, Area, and Volume
2. The area of the floor is . Because the tiles are each of size , 600 tiles are needed.
The size of the complete region is by , so the area
4. The area of the rectangle is . Because the square has the same area, the side of the square is
The perimeter . Dividing 102 ft by 3 ft between each post gives 34. Thus, 34 posts are needed.
b. The number of bushels is bushels.
c. The value of the wheat in the full silo is
11. Find the surface area of the box.
Sum the areas of the faces.
Chapter 17 Pythagorean Theorem
The triangle is not a right triangle.
6. The required area is the area of the semicircle minus the area of the triangle. Let A be the area of the semicircle and let T be the area of the triangle. Then, to find the area of the semicircle, the radius length must be known. The diameter and thus the radius can be found by using the Pythagorean theorem on the right triangle. Let d be the length of the diameter.
The radius is
The required area is square units.
(The triangle in this figure is the special 3-4-5 triangle. Any triangle similar to this triangle has proportional side lengths, such as the 27-36-45 triangle of problem 1 above.)
8. The length of the sides of the square is needed for the perimeter. You can use the Pythagorean theorem to find the side length. Let s be the side length and let P be the perimeter.
9. Because 4 is the largest number, the question is
The triangle is a right triangle.
The ladder will reach up on the wall approximately 3.92 m.
Chapter 18 Counting and Probability
1. no. of ways to select one door and one curtain =
(no. of ways to select a door) ×(no. of ways to select a curtain) = 3 × 4 = 12 different ways
2. no. of codes possible =
(no. of ways to select first letter) × (no. of ways to select second letter) × (no. of ways to select third letter) = 15 × 15 × 15 = 3375 different codes
3. no. of ways to select one bread, one sandwich filling, one bag of chips, and one drink =
(no. of ways to select a bread) × (no. of ways to select a sandwich filling) × (no. of ways to select a bag of chips) × (no. of ways to select a drink) = 3 × 4 × 2 × 3 = 72 different lunches
9. The events are independent, so
10. The events are independent, so
Chapter 19 Mean, Median, Mode, and Range
10. median = 4
11. no mode
12. mode is –4; unimodal
13. modes are 4.7 and 5.6; bimodal
14. mode is 3; unimodal
15. modes are 4, and 10; bimodal