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Differentiating the sets of numbers

Classify each number as being a natural number ( N ), whole number ( W ), integer ( I ), rational number ( Q ), and/or irrational number ( Q′ ).

  1. 36
  2. 8 3
  3. 73
  4. −6
  5. 3.2121121112
N W I Q Q′
a. 36 = 6 X X X X
b. 8 3 = 2. 6 ¯ X
c. 73 X
d. –6 X X
e. 3.2121121112... X
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Classify each number as being a natural number ( N ), whole number ( W ), integer ( I ), rational number ( Q ), and/or irrational number ( Q′ ).

  1. 35 7
  2. 0
  3. 169
  4. 24
  5. 4.763763763
N W I Q Q'
a. 35 7 X X
b. 0 X X X
c. 169 X X X X
d. 24 X
e. 4.763763763... X
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Performing calculations using the order of operations

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

a n = a a a a n  factors

In this notation, a n is read as the n th 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 2 3 4 2 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.

Let’s take a look at the expression provided.

24 + 6 2 3 4 2

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 4 2 as 16.

24 + 6 2 3 4 2 24 + 6 2 3 16

Next, perform multiplication or division, left to right.

24 + 6 2 3 16 24 + 4 16

Lastly, perform addition or subtraction, left to right.

24 + 4 16        28 16            12

Therefore, 24 + 6 2 3 4 2 = 12.

For some complicated expressions, several passes through the order of operations will be needed. For instance, there may be a radical expression inside parentheses that must be simplified before the parentheses are evaluated. Following the order of operations ensures that anyone simplifying the same mathematical expression will get the same result.

Order of operations

Operations in mathematical expressions must be evaluated in a systematic order, which can be simplified using the acronym PEMDAS :

P (arentheses)
E (xponents)
M (ultiplication) and D (ivision)
A (ddition) and S (ubtraction)

Given a mathematical expression, simplify it using the order of operations.

  1. Simplify any expressions within grouping symbols.
  2. Simplify any expressions containing exponents or radicals.
  3. Perform any multiplication and division in order, from left to right.
  4. Perform any addition and subtraction in order, from left to right.

Questions & Answers

sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
Thanks for this helpfull app
Axmed Reply
secA+tanA=2√5,sinA=?
richa Reply
tan2a+tan2a=√3
Rahulkumar
classes of function
Yazidu
if sinx°=sin@, then @ is - ?
NAVJIT Reply
the value of tan15°•tan20°•tan70°•tan75° -
NAVJIT
0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply

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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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