This document provides objectives and instructions for translating mathematical phrases to rational algebraic expressions. It begins by reviewing polynomials and defining the symbols, variables, and operations used in algebraic expressions like numbers, parentheses, brackets, braces, and variables to represent values. It then discusses how multiplication, division, addition and subtraction can be represented and notes there are additional terms for these operations. The document provides an activity for students to practice the translations and closes with a reminder of key points to remember and a biblical verse.
This presentation is based on CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product
This presentation is based on CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product
I am kind of confused about quantifiers. I am not sure how to transl.pdfAMITPANCHAL154
I am kind of confused about quantifiers. I am not sure how to translate them into english
correctly so a quick Guide to how or the answer will work. Thanks!
***** (A = universal) , (E = existential), (V = or), (^ = and) I do not know how to input the real
symbol)
1.) AxAyAz([x+y]+z = x+([y+z])
2.) Here x, y are students C(x) is having a computer and F(x,y) indicates that x and y are friends.
Ax(C(x) vEy[C(y)^F(x,y)]
3.) Suppose that x and y are real numbers
a. AxAy([x>0 ^ y>0] ------> [x+y>0])
b. AxAy([x<0 ^ 4<0] [x(y)>0])
Solution
There are several logical symbols in the alphabet, which vary by author but usually
include: The quantifier symbols and The logical connectives: for conjunction, for disjunction, for
implication, for biconditional, for negation. Occasionally other logical connective symbols are
included. Some authors use , or Cpq, instead of , and , or Epq, instead of , especially in contexts
where is used for other purposes. Moreover, the horseshoe may replace ; the triple-bar may
replace , and a tilde (~), Np, or Fpq, may replace ; ||, or Apq may replace ; and &, or Kpq, may
replace , especially if these symbols are not available for technical reasons. Parentheses,
brackets, and other punctuation symbols. The choice of such symbols varies depending on
context. An infinite set of variables, often denoted by lowercase letters at the end of the alphabet
x, y, z, … . Subscripts are often used to distinguish variables: x0, x1, x2, … . An equality symbol
(sometimes, identity symbol) =; see the section on equality below. It should be noted that not all
of these symbols are required - only one of the quantifiers, negation and conjunction, variables,
brackets and equality suffice. There are numerous minor variations that may define additional
logical symbols: Sometimes the truth constants T, Vpq, or , for \"true\" and F, Opq, or , for
\"false\" are included. Without any such logical operators of valence 0, these two constants can
only be expressed using quantifiers. Sometimes additional logical connectives are included, such
as the Sheffer stroke, Dpq (NAND), and exclusive or, Jpq. [edit]Non-logical symbols The non-
logical symbols represent predicates (relations), functions and constants on the domain of
discourse. It used to be standard practice to use a fixed, infinite set of non-logical symbols for all
purposes. A more recent practice is to use different non-logical symbols according to the
application one has in mind. Therefore it has become necessary to name the set of all non-logical
symbols used in a particular application. This choice is made via a signature.[2] The traditional
approach is to have only one, infinite, set of non-logical symbols (one signature) for all
applications. Consequently, under the traditional approach there is only one language of first-
order logic.[3] This approach is still common, especially in philosophically oriented books. For
every integer n = 0 there is a collection of n-ary, or n-place, predicate .
Making Sense of Rational ExpressionsA rational expression .docxtienboileau
Making Sense of Rational Expressions
A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions. The last one may look a little strange since it is more commonly written. Simplifying rational expressions requires good factoring skills. The twist now is that you are looking for factors that are common to both the numerator and the denominator of the rational expression.
This unit emphasizes performing mathematical operations on rational expressions and using these operations to solve equations and inequalities.
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Add, subtract, multiply, and divide real numbers, including square roots and exponents, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator. Describe, analyze and generalize relationships, patterns, and functions using words, symbols, variables, tables, and graphs. Determine the impact when changing the parameters of given functions.
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
2. At the end of this lesson, you are expected to:
determine the symbols, variables, and operations
in translating verbal phrases to algebraic
expressions; and
Objectives
translate mathematical phrases to rational
algebraic expressions.
3. Let’s start this lesson by recalling your knowledge about
polynomials.
Review
7. What is it Translating Mathematical phrases to
Rational Algebraic Expressions
In translating verbal phrases to algebraic
expressions, we need to use numbers, the common
symbols of operations such as +, -, x, ÷, the symbols
for grouping like the parentheses ( ), brackets [ ],
or braces { }, and variables which means any letter
of the English alphabet which is use to represent a
number or several numbers. If a variable stands only
for one specific value, it is called a constant.
8. The operation of multiplication can be represented by
the symbol (×), by ( ) or we can also use dot (.) which is
written halfway up the factors. Division can be
represented by the symbol (÷) or /.
In addition to the words add, subtract, multiply and
divide, there are other terms that also corresponds to
these mathematical operations.
15. -Proverbs 3:5-6
“Delight yourself in the LORD, and he will give
you the desires of your heart. Commit your way
to the LORD; trust in him, and he will act.”