TRUE or FALSE
1. (2×b)×c=a×(b×c)It is commutative property.
2. a÷0is not defined or infinity.
3. Sum of two whole numbers is a again a whole number.
4. -53 +0=- 53
5. The most common representative value of group of data is the arithmetic mean.
6. A bar graph is a representation of numbers using bars of uniform widths.
7. A line segment has one end points
8. The place value of 2 in 5. 32 is 0.02
9. The measure of the complement of the angle 30° is 60°
Answers
Answer:
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Step-by-step explanation:
The word number typically refers to a quantity, which may be definite as in ``the number of people in line'', indefinite as in ``a number of students took the class''; the dictionary definition typically lists over a dozen common meanings. In this course, a variety of types of numbers will be studied, including the numbers in each of the following sets:
The positive integers or natural numbers images/num1.png : 1, 2, 3, ....
The integers images/num2.png which includes the positive integers, zero, and the negative integers: -1, -2, -3, ....
The rational numbers images/num3.png is the set of numbers which can be written as m/n where m and n are integers with n non-zero. Rational numbers can be expressed as finite or repeating decimals.
The real numbers images/num4.png include the rational numbers as well as irrational numbers such as images/num5.png and images/num6.png . Every real number has a possibly infinite decimal expansion.
The complex numbers images/num7.png which include the real numbers as well as the images/num8.png . Every complex number can be expressed in the form images/num9.png where images/num10.png and images/num11.png are real numbers.
On each of these sets, is defined the binary operations addition and multiplication. For each ordered pair images/num12.png of numbers from one of these sets, there are well defined numbers images/num13.png and images/num14.png called the sum and the product of images/num15.png and images/num16.png in the same set. One expresses this property by saying that the sets are closed under addition and multiplication.
These operations have simple geometric interpretations. For example, if two line segments are of length x and y respectively, then connecting the two together end-to-end yields a line segment of length x + y. Similarly, the area of a rectangle with length x and width y is precisely xy.
By repeatedly combining numbers via addition and multiplication, one can make complicated expressions such as images/num17.png . By substituting various values of x and y into this expression, one gets numerical values for the expression. One finds that regardless of which values of x and y you use, the numerical value is the same as that obtained by the expression images/num18.png . The process of verifying this is one of the skills that you have already mastered in earlier algebra courses. The idea is that you can use a number of properties of numbers to successively simplify the first expression until you get to the second one. Amongst these properties are:
Addition and Multiplication are commutative: a + b = b + a and ab = ba.
Addition and Multiplication are associative: (a + b) + c = a + (b + c) and (ab)c = a(bc).
Multiplication distributes over addition: a(b + c) = ab + ac.
These properties are referred to as the commutative, associative, and distributive laws.
Before going on, we should clear up some ambiguity. We said that images/num19.png was obtained by a succession of additions and multiplications. This is true, but there are many different ways of doing this, e.g. after one gets the value of images/num20.png , images/num21.png , and images/num22.png , one could add the third to the sum of the first two or add the first to the sum of the last two. Of course, the result would be the same, and it is the associative law for addition that guarantees this. For this reason, one typically does not even bother to specify the order by adding in parentheses. Similarly, one didn't put parentheses to indicate the order of evaluation of the product of the three factors in images/num23.png . Another ambiguity occurs in the expression images/num24.png . Does this mean add the product of 4 and x to y or does it mean multiply 4 times the sum of x and y? This is more serious because the two ways of evaluating the expression give different answers. This is resolved by the rules for order of evaluation of expressions. In this case, the rules say that you evaluate multiplications before additions. So, the meaning of the expression images/num25.png is images/num26.png and not images/num27.png . The rules for order of evaluation will be stated in detail at the end of the next section.