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Mathematical-Sentence, Lecture notes of Mathematics

Mathematics

This is about Mathematical sentence. A mathematical sentence, also called mathematical statement, statement, or proposal, is a sentence that can be identified as either true or false.

Typology: Lecture notes

2019/2020

Uploaded on 10/16/2020

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Objective- To recognize symbols, variables,
and types of sentences used in algebra.
Equalities Inequalities
=Equals- is the
same as
Congruent- same
size and shape
Similar- same
shape
<Is less than
>Is greater than
Is less than or
equal to
Approx. equal to
=Not equal to
~
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Mathematical-Sentence and more Lecture notes Mathematics in PDF only on Docsity!

Objective- To recognize symbols, variables,

and types of sentences used in algebra.

Equalities Inequalities

= Equals- is the

same as

Congruent- same

size and shape

Similar- same

shape

< Is less than

> Is greater than

Is less than or

equal to

Approx. equal to

= Not equal to

~  

Expressions vs. Equations

Numerical Variable Expressions Equations Inequalities 2 + 3 5(8) - 4 x + 7 8 - 3y

x - 4 = 13 11= 3 + 2m

6y - 4 < 8 Sentences Open sentences Open sentences have solutions and can be solved.

Open sentences have solutions and can be solved.

Variable Equations Variable Inequalities

4 + m = 7 5 + y < 91

- 4 - 4

m = 3

- 5 - 5

y < 86

One Solution Infinite Solutions

Give three solutions to each sentence below.

    1. x >
    1. x + 3 
    1. 5 - x <
    1. 2 x  1 
    • Samples: 11, 15, - Samples: 4, -8,
      • Samples: 6, 7,
      • Samples: 3, 4,

Tricky Ones! 5 plus x 5 + x add 5 and x 5 +^ x the sum of 5 and x (^5) + x 5 increased by x (^5) + x 5 more than x (^) x + 5 5 is more than x (^5) > x

Tricky Ones! 5 minus x 5 - x 5 less x 5 -^ x the difference of 5 and x (^5) - x 5 decreased by x (^5) - x 5 is less than x (^5) < x 5 less than x (^) x - 5 5 subtracted from x (^) x - 5

Translate each phrase into a mathematical expression.

  1. six less than twice a number x
  2. five times the sum of y and 4
  3. twice the difference of m and 3
  4. the quotient of 7 and a number x less 2
  5. the difference of 6 and k divided by 9
  6. 4 times the sum of 12 and y 2x - 6 5(y + 4) 2(m - 3) (6 - k) 9 (7 x) - 2 4(12 + y)

Translate each sentence into a mathematical equation or inequality.

  1. Eight less than twice the sum of four and y is the same as 19.
  2. Six more than x is more than twice the difference of x and 7.
  3. The quotient of m and 3 is six less than the product of 10 and m.
  4. Five less than x is less than five less x. 2(4 + y) - 8 = 19 x + 6 > 2(x - 7) x - 5 < 5 - x (m 3) = 10m - 6