# 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. $\text{\hspace{0.17em}}\frac{17}{18}+\left[\frac{4}{9}+\left(-\frac{17}{18}\right)\right]$
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 $m,n$

what are you up to?
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
state and prove Cayley hamilton therom
hello
Propessor
hi
Miranda
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.
Miranda
hi
jai
hi Miranda
jai
thanks
Propessor
welcome
jai
What is algebra
algebra is a branch of the mathematics to calculate expressions follow.
Miranda
Miranda Drice would you mind teaching me mathematics? I think you are really good at math. I'm not good at it. In fact I hate it. 😅😅😅
Jeffrey
lolll who told you I'm good at it
Miranda
something seems to wispher me to my ear that u are good at it. lol
Jeffrey
lolllll if you say so
Miranda
but seriously, Im really bad at math. And I hate it. But you see, I downloaded this app two months ago hoping to master it.
Jeffrey
which grade are you in though
Miranda
oh woww I understand
Miranda
Jeffrey
Jeffrey
Miranda
how come you finished in college and you don't like math though
Miranda
gotta practice, holmie
Steve
if you never use it you won't be able to appreciate it
Steve
I don't know why. But Im trying to like it.
Jeffrey
yes steve. you're right
Jeffrey
so you better
Miranda
what is the solution of the given equation?
which equation
Miranda
I dont know. lol
Jeffrey
Miranda
Jeffrey
answer and questions in exercise 11.2 sums
how do u calculate inequality of irrational number?
Alaba
give me an example
Chris
and I will walk you through it
Chris
cos (-z)= cos z .
cos(- z)=cos z
Mustafa
what is a algebra
(x+x)3=?
6x
Obed
what is the identity of 1-cos²5x equal to?
__john __05
Kishu
Hi
Abdel
hi
Ye
hi
Nokwanda
C'est comment
Abdel
Hi
Amanda
hello
SORIE
Hiiii
Chinni
hello
Ranjay
hi
ANSHU
hiiii
Chinni
h r u friends
Chinni
yes
Hassan
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
I speak French
Abdel
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
it's 12
what is the function of sine with respect of cosine , graphically
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
sinx sin2x is linearly dependent
what is a reciprocal
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls
How look for the general solution of a trig function