# 1.1 Real numbers: algebra essentials  (Page 7/35)

 Page 7 / 35

## Using properties of real numbers

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

1. $\text{\hspace{0.17em}}3\cdot 6+3\cdot 4$
2. $\text{\hspace{0.17em}}\left(5+8\right)+\left(-8\right)$
3. $\text{\hspace{0.17em}}6-\left(15+9\right)$
4. $\text{\hspace{0.17em}}\frac{4}{7}\cdot \left(\frac{2}{3}\cdot \frac{7}{4}\right)$
5. $\text{\hspace{0.17em}}100\cdot \left[0.75+\left(-2.38\right)\right]$

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

1. $\text{\hspace{0.17em}}\left(-\frac{23}{5}\right)\cdot \left[11\cdot \left(-\frac{5}{23}\right)\right]$
2. $\text{\hspace{0.17em}}5\cdot \left(6.2+0.4\right)$
3. $\text{\hspace{0.17em}}18-\left(7-15\right)$
4. $\text{\hspace{0.17em}}\frac{17}{18}+\cdot \left[\frac{4}{9}+\left(-\frac{17}{18}\right)\right]$
5. $\text{\hspace{0.17em}}6\cdot \left(-3\right)+6\cdot 3$
1. 11, commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;
2. 33, distributive property;
3. 26, distributive property;
4. $\text{\hspace{0.17em}}\frac{4}{9},$ commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;
5. 0, distributive property, inverse property of addition, identity property of addition

## Evaluating algebraic expressions

So far, the mathematical expressions we have seen have involved real numbers only. In mathematics, we may see expressions such as $\text{\hspace{0.17em}}x+5,\frac{4}{3}\pi {r}^{3},$ or $\text{\hspace{0.17em}}\sqrt{2{m}^{3}{n}^{2}}.\text{\hspace{0.17em}}$ In the expression $\text{\hspace{0.17em}}x+5,$ 5 is called a constant    because it does not vary and x is called a variable    because it does. (In naming the variable, ignore any exponents or radicals containing the variable.) 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.

## Describing algebraic expressions

List the constants and variables for each algebraic expression.

1. x + 5
2. $\frac{4}{3}\pi {r}^{3}$
3. $\sqrt{2{m}^{3}{n}^{2}}$
Constants Variables
a. x + 5 5 x
b. $\text{\hspace{0.17em}}\frac{4}{3}\pi {r}^{3}$ $\frac{4}{3},\pi$ $r$
c. $\text{\hspace{0.17em}}\sqrt{2{m}^{3}{n}^{2}}$ 2 $m,n$

how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Abdullahi
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of \$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation