# 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 $m,n$

#### Questions & Answers

The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply

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