## Easy Mathematics Step-by-Step (2012)

### Answer Key

**Chapter 1 Numbers and OperationsExercise 1**

__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.

__10.__ Undefined

__11.__ 0

__12.__ Undefined

__13.__ Distributive property

__14.__ Zero factor property

__15.__ Associative property of multiplication

**Chapter 2 IntegersExercise 2**

__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.”

__18.__

__19.__

__20.__

**Chapter 3 ExponentsExercise 3**

__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 OperationsExercise 4**

**Chapter 5 FractionsExercise 5**

**Chapter 6 DecimalsExercise 6**

__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 PercentsExercise 7**

**Chapter 8 Units of MeasurementExercise 8**

__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 ft^{2}. 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 ProportionsExercise 9**

__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 RadicalsExercise 10**

__1.__ and

Thus, 12 and –12 are the two square roots of 144.

__2.__ and

Thus, and are the two square roots of .

__3.__ and

Thus, 0.8 and –0.8 are the two square roots of 0.64.

__4.__ and

Thus, 20 and –20 are the two square roots of 400.

__5.__ , so 6 is the positive square root of 36.

Thus,

__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 .

Thus,

**Chapter 11 Algebraic ExpressionsExercise 11**

__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 FormulasExercise 12**

**Chapter 13 PolynomialsExercise 13**

__1.__ is a trinomial.

__2.__ is a binomial.

__3.__ 2*x*^{2} + 7*x* – 4 is a trinomial.

__4.__ is a monomial.

__5.__ is a polynomial.

__6.__ –15*x* + 17*x* = 2*x*

__7.__ is simplified.

**Chapter 14 Solving EquationsExercise 14**

__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 GeometryExercise 15**

__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°

__12.__ Intersecting

__13.__ Parallel

__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 VolumeExercise 16**

__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.

__8.__

__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 TheoremExercise 17**

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 ProbabilityExercise 18**

__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 RangeExercise 19**

__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