Algebra Review Packet 1 The Real Number System

Real Number System Worksheets

Real Number System Worksheets kids will be learning about rational numbers and irrational numbers, Non-Integer Fractions, Integers, Whole Numbers, and Natural Numbers. Real numbers are the set of all numbers that can be expressed as a or that are on the number line. Real numbers have certain properties and different classifications, including natural, whole, integers, rational and irrational.

Properties Of Real Numbers

When we multiply a number by itself, we square it or raise it to a power of 2. For example, ^=4\cdot 4=16. We can raise any number to any power. In general, the exponential notation ^ means that the number or variable a is used as a factor n times.

In this notation, ^ is read as the nth power of a, where a is called the base and n is called the exponent. A term in exponential notation may be part of a mathematical expression, which is a combination of numbers and operations. For example, 24+6\cdot \frac-^ is a mathematical expression.

To evaluate a mathematical expression, we perform the various operations. However, we do not perform them in any random order. We use the order of operations. This is a sequence of rules for evaluating such expressions.

Recall that in mathematics we use parentheses , brackets , and braces to group numbers and expressions so that anything appearing within the symbols is treated as a unit. Additionally, fraction bars, radicals, and absolute value bars are treated as grouping symbols. When evaluating a mathematical expression, begin by simplifying expressions within grouping symbols.

The next step is to address any exponents or radicals. Afterward, perform multiplication and division from left to right and finally addition and subtraction from left to right.

Lets take a look at the expression provided.

There are no grouping symbols, so we move on to exponents or radicals. The number 4 is raised to a power of 2, so simplify ^ as 16.

Example: Using The Order Of Operations

Use the order of operations to evaluate each of the following expressions.

\begin\left^ & =\left^-4\left & & \text \\ & =36-4\left & & \text \\ & =36-32 & & \text \\ & =4 & & \text\end

\begin\frac-4}-\sqrt & =\frac-4}-\sqrt & & \text \\ & =\frac-4}-3 & & \text \\ & =\frac-3 & & \text \\ & =\frac-3 & & \text \\ & =3-3 & & \text \\ & =0 & & \text\end

Note that in the first step, the radical is treated as a grouping symbol, like parentheses. Also, in the third step, the fraction bar is considered a grouping symbol so the numerator is considered to be grouped.

\begin6-|5-8|+3\left & =6-|-3|+3\left & & \text \\ & =6-3+3\left & & \text \\ & =6-3+9 & & \text \\ & =3+9 & & \text \\ & =12 & & \text\end

\begin\frac} & =\frac & & \text \\ & =\frac & & \text \\ & =\frac & & \text \\ & =8 & & \text\endIn this example, the fraction bar separates the numerator and denominator, which we simplify separately until the last step.

\begin7\left-2+1 & =7\left-2+1 & & \text \\ & 7\left-2\left+1 & & \text \\ & =7\left-2\left+1 & & \text \\ & =105+26+1 & & \text \\ & =132 & & \text\end

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Algebra 1 Quarter 1 Benchmark Review Packet

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Key Algebra 1 Review Packets Ivy Hawn

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• Descriptions: NATURAL NUMBERS : 1, 2, 3, 4, Name all sets to which each number belongs. Topic #3: Square & Cube Roots Give the value of each expression. Gina Wilson (All
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Printable Pdfs For Real Number System Worksheets

Real Number System Worksheets helps kids with understanding the whole concept of the real number system. These worksheets are a helpful guide for kids as well as their parents to see and review their answer sheets. Children can download the pdf format of these easily accessible Real Number System Worksheets to practice and solve questions for free.

Algebra 1 Review Packets Teaching Resources

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Algebra I Summer Review Packet

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Practice Problems On How To Classify Real Numbers

Example 1: Tell if the statement is true or false. Every whole number is a natural number.

Solution: The set of whole numbers includes all natural or counting numbers and the number zero . Since zero is a whole number that is NOT a natural number, therefore the statement is FALSE.

Example 2: Tell if the statement is true or false. All integers are whole numbers.

Solution: The number -1 is an integer that is NOT a whole number. This makes the statement FALSE.

Example 3: Tell if the statement is true or false. The number zero is a rational number.

Solution: The number zero can be written as a ratio of two integers, thus it is indeed a rational number. This statement is TRUE.

Example 4: Name the set or sets of numbers to which each real number belongs.

1) 7

It belongs to the sets of natural numbers, . It is a whole number because the set of whole numbers includes the natural numbers plus zero. It is an integer since it is both a natural and a whole number. Finally, since 7 can be written as a fraction with a denominator of 1, 7/1, then it is also a rational number.

2) 0

This is not a natural number because it cannot be found in the set . This is definitely a whole number, an integer, and a rational number. It is rational since 0 can be expressed as fractions such as 0/3, 0/16, and 0/45.

3) 0.3\overline

4) \sqrt 5

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Benefits Of Real Number System Worksheets

Real Number System Worksheets helps kids to understand the whole concept of real numbers and they can know the properties and operations of numbers which are very important in our daily lives. Real Number System Worksheets helps kids to know about the whole numbers and the fundamental operations on them. And study on the integers, rationals, decimals, fractions and powers in this section.

Evaluate And Simplify Algebraic Expressions

So far, the mathematical expressions we have seen have involved real numbers only. In mathematics, we may see expressions such as x+5,\frac\pi ^, or \sqrt^^}. In the expression x+5, 5 is called a constant because it does not vary and x is called a variable because it does. An algebraic expression is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division.

We have already seen some real number examples of exponential notation, a shorthand method of writing products of the same factor. When variables are used, the constants and variables are treated the same way.

In each case, the exponent tells us how many factors of the base to use, whether the base consists of constants or variables.

Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value, then simplify the resulting expression using the order of operations. If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.

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Example: Describing Algebraic Expressions

Using Properties Of Real Numbers

For some activities we perform, the order of certain operations does not matter, but the order of other operations does. For example, it does not make a difference if we put on the right shoe before the left or vice-versa. However, it does matter whether we put on shoes or socks first. The same thing is true for operations in mathematics.

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Algebra 1 Summer Review Packet Cotter Schools

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Five Subsets Of Real Numbers

1) The Set of Natural or Counting Numbers

The set of the natural numbers contains the elements

The ellipsis signifies that the numbers go on forever in that pattern.

2) The Set of Whole Numbers

The set of whole numbers includes all the elements of the natural numbers plus the number zero .

The slight addition of the element zero to the set of natural numbers generates the new set of whole numbers. Simple as that!

3) The Set of Integers

The set of integers includes all the elements of the set of whole numbers and the opposites or negatives of all the elements of the set of counting numbers.

4) The Set of Rational Numbers

The set of rational numbers includes all numbers that can be written as a fraction or as a ratio of integers. However, the denominator cannot be equal to zero.

A rational number may also appear in the form of a decimal. If a decimal number is repeating or terminating, it can be written as a fraction, therefore, it must be a rational number.

Examples of terminating decimals:

Examples of repeating decimals:

5) The Set of Irrational Numbers

The set of irrational numbers can be described in many ways. These are the common ones.

• Irrational numbers are numbers that cannot be written as a ratio of two integers. This description is exactly the opposite of that of rational numbers.

• Irrational numbers are the leftover numbers after all rational numbers are removed from the set of the real numbers. You may think of it as,

Examples:

c) The square root of 2

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Algebra 1 Review Packets & Quizzes

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Example: Using Properties Of Real Numbers

Use the properties of real numbers to rewrite and simplify each expression. State which properties apply.

\begin3\cdot6+3\cdot4 & =3\cdot\left & & \text \\ & =3\cdot10 & & \text \\ & =30 & & \text\end

\begin\left+\left & =5+\left & & \text \\ & =5+0 & & \text \\ & =5 & & \text\end

\begin6-\left & =6+ & & \text \\ & =6+\left & & \text \\ & =-18 & & \text\end

\begin\frac\cdot\left & =\frac \cdot\left & & \text \\ & =\left\cdot\frac & & \text \\ & =1\cdot\frac & & \text \\ & =\frac & & \text\end

\begin100\cdot & =100\cdot0.75+100\cdot\left & & \text \\ & =75+\left & & \text \\ & =-163 & & \text\end

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Algebra 1 Summer Review Packet 2005

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Math 10005 Review Of The Real Number System Ksu

Definitions:

• Rational Numbers: Any number that can be written as a fraction or whose decimal expansion either terminates or repeats.

• Irrational Numbers:Any number that cannot be written as a fraction or whose decimal expansion does not terminate nor repeat.

• Real Numbers:The collection of all rational and irrational numbers.

• Absolute Value:The absolute value of a real numbern, denoted|n|, is the distance betweennand 0 on the number line.

• Exponents:An exponent is a number that tells how many times a factor is repeated in a product. For example, 24 = 2· 2 · 2 · 2 4 times

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Summer Math Review Algebra Packet

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Example: Using A Formula

A right circular cylinder with radius r and height h has the surface area S given by the formula S=2\pi r\left. Find the surface area of a cylinder with radius 6 in. and height 9 in. Leave the answer in terms of \pi.

Right circular cylinder

Evaluate the expression 2\pi r\left for r=6 and h=9.

The surface area is 180\pi square inches.

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Algebra 1 Review Packet Teaching Resources

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Classify A Real Number

The numbers we use for counting, or enumerating items, are the natural numbers: 1, 2, 3, 4, 5, and so on. We describe them in set notation as where the ellipsis indicates that the numbers continue to infinity. The natural numbers are, of course, also called the counting numbers. Any time we enumerate the members of a team, count the coins in a collection, or tally the trees in a grove, we are using the set of natural numbers. The set of whole numbers is the set of natural numbers plus zero: .

The set of integers adds the opposites of the natural numbers to the set of whole numbers: . It is useful to note that the set of integers is made up of three distinct subsets: negative integers, zero, and positive integers. In this sense, the positive integers are just the natural numbers. Another way to think about it is that the natural numbers are a subset of the integers.

The set of rational numbers is written as \left\|m\text\text\ne\right\}. Notice from the definition that rational numbers are fractions containing integers in both the numerator and the denominator, and the denominator is never 0. We can also see that every natural number, whole number, and integer is a rational number with a denominator of 1.

Because they are fractions, any rational number can also be expressed in decimal form. Any rational number can be represented as either:

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Review Of Algebra 1 * Placement Test Review

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Key To Algebra 1 Semester 1 Review Packet

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