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Using properties of real numbers

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

  1. 3 6 + 3 4
  2. ( 5 + 8 ) + ( −8 )
  3. 6 ( 15 + 9 )
  4. 4 7 ( 2 3 7 4 )
  5. 100 [ 0.75 + ( −2.38 ) ]

  1. 3 6 + 3 4 = 3 ( 6 + 4 ) Distributive property = 3 10 Simplify = 30 Simplify

  2. ( 5 + 8 ) + ( −8 ) = 5 + [ 8 + ( −8 ) ] Associative property of addition = 5 + 0 Inverse property of addition = 5 Identity property of addition

  3. 6 ( 15 + 9 ) = 6 + [ ( −15 ) + ( −9 ) ] Distributive property = 6 + ( −24 ) Simplify = −18 Simplify

  4. 4 7 ( 2 3 7 4 ) = 4 7 ( 7 4 2 3 ) Commutative property of multiplication = ( 4 7 7 4 ) 2 3 Associative property of multiplication = 1 2 3 Inverse property of multiplication = 2 3 Identity property of multiplication

  5. 100 [ 0.75 + ( 2.38 ) ] = 100 0.75 + 100 ( −2.38 ) Distributive property = 75 + ( −238 ) Simplify = −163 Simplify
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Use the properties of real numbers to rewrite and simplify each expression. State which properties apply.

  1. ( 23 5 ) [ 11 ( 5 23 ) ]
  2. 5 ( 6.2 + 0.4 )
  3. 18 ( 7 −15 )
  4. 17 18 + [ 4 9 + ( 17 18 ) ]
  5. 6 ( −3 ) + 6 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. 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
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Evaluating 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 , 4 3 π r 3 , or 2 m 3 n 2 . In the expression 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.

( −3 ) 5 = ( −3 ) ( −3 ) ( −3 ) ( −3 ) ( −3 ) x 5 = x x x x x ( 2 7 ) 3 = ( 2 7 ) ( 2 7 ) ( 2 7 )   ( y z ) 3 = ( y z ) ( y z ) ( y z )

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. 4 3 π r 3
  3. 2 m 3 n 2
Constants Variables
a. x + 5 5 x
b. 4 3 π r 3 4 3 , π r
c. 2 m 3 n 2 2 m , n
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Questions & Answers

the third and the seventh terms of a G.P are 81 and 16, find the first and fifth terms.
Suleiman Reply
if a=3, b =4 and c=5 find the six trigonometric value sin
Martin Reply
pls how do I factorize x⁴+x³-7x²-x+6=0
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in a function the input value is called
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if a=4 b=4 then a+b=
Rimsha Reply
a+b+2ab
Kin
commulative principle
DIOSDADO
a+b= 4+4=8
Mimi
If a=4 and b=4 then we add the value of a and b i.e a+b=4+4=8.
Tariq
what are examples of natural number
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an equation for the line that goes through the point (-1,12) and has a slope of 2,3
Katheryn Reply
3y=-9x+25
Ishaq
show that the set of natural numberdoes not from agroup with addition or multiplication butit forms aseni group with respect toaaddition as well as multiplication
Komal Reply
x^20+x^15+x^10+x^5/x^2+1
Urmila Reply
evaluate each algebraic expression. 2x+×_2 if ×=5
Sarch Reply
if the ratio of the root of ax+bx+c =0, show that (m+1)^2 ac =b^2m
Awe Reply
By the definition, is such that 0!=1.why?
Unikpel Reply
(1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin$)
Ajay Reply
hatdog
Mark
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Ryan
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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