Equivalent definition math


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The term “equivalent” in math refers to two meanings, numbers, or quantities that are the same. The equivalence of two such quantities shall be denoted by a bar over an equivalent symbol or Equivalent Sign. It also means a logical equivalence between two values or a set of quantities.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s). Examples.

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Answer

What does the word equivalent mean?

Equivalent: one that is equal to another in status, achievement, or value. Synonyms: coequal, compeer, coordinate… Find the right word.

What does equivalently mean?

a. having a particular property in common; equal. b. (of two equations or inequalities) having the same set of solutions. c. (of two sets) having the same cardinal number. 4. (Logic) maths logic (of two propositions) having an equivalence between them. n. 5. something that is equivalent. 6.

What is an example of equivalent?

Equivalent Expressions. Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. For example, let’s solve the following numerical expressions: 25 × 5 = 125. Also, 10 2 + 5 2 = 100 + 25 =125. Thus, the above two expressions are equivalent and can be written as: 25 × 5 = 10 2 + 5 2

What is the definition of equivalent equations?

Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class but also in everyday life. Take a look at examples of equivalent equations, how to solve them for one or more variables, and how you might use this skill outside a classroom.

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What is a equivalent in math example?

Equivalent Expressions Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. Similarly, the two math expressions 2 × (10 – 8) and 4 ÷ 4 are also equivalent as both can be simplified to 4.


What is the the equivalent?

Effective dose equivalent (HE) is the sum of the products of the dose equivalent to the organ or tissue (HT) and the weighting factors (wT) applicable to each of the body organs or tissues that are irradiated (HE = wT HT).


How do you do equivalent in math?

Solution: In Equivalent Calculations Maths, any equivalent fraction can be obtained by multiplying and dividing the same number into the fraction. Therefore let us multiply 2 to both numerator and denominator. On multiplying 2 to both numerator and denominator, we get, (7 × 2)/(9 × 2) = 14/18.


What is an equivalent math problem?

A division problem can be changed into an equivalent problem by dividing both numbers by the same number, thus maintaining the quotient between them.


What does equivalent mean in fractions?

the same valueEquivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake.


What is difference between equal and equivalent?

Equal and equivalent are terms that are used frequently in mathematics. The main difference between equal and equivalent is that the term equal refers to things that are similar in all aspects, whereas the term equivalent refers to things that are similar in a particular aspect.


What is equivalent value?

The value of an original amount at any particular time is called equivalent value or dated value. The equivalent payment combines the original sum with the interest earned up to the dated value date. When sums of money fall due or are payable at different time, they are not directly comparable.


What is the equivalent of 8 12?

2/32/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.


What is the equivalent of 2 12?

1/6Equivalent fractions of 1/6 : 2/12 , 3/18 , 4/24 , 5/ Equivalent fractions of 5/6 : 10/12 , 15/18 , 20/24 , 25/


How do you determine if a function is equivalent?

We say two functions f and g are equal if they have the same domain and the same codomain, and if for every a in the domain, f(a)=g(a).


How do you find an equivalent fraction?

To find the equivalent fractions for any given fraction, multiply the numerator and the denominator by the same number. For example, to find an equivalent fraction of 3/4, multiply the numerator 3 and the denominator 4 by the same number, say, 2. Thus, 6/8 is an equivalent fraction of 3/4.


What is the equivalent symbol?

≡Equivalent Symbol (≡)


What is equivalent formula?

The equivalent of any substance is given by the charge it carries on itself. Thus, the equivalent weight is obtained by the ratio of the molar mass of the substance and the number of equivalents. It can be mathematically represented as. Equivalent weight = Molar Mass number of equivalents .


What is the equivalent of 2 12?

1/6Equivalent fractions of 1/6 : 2/12 , 3/18 , 4/24 , 5/ Equivalent fractions of 5/6 : 10/12 , 15/18 , 20/24 , 25/


What is the equivalent of 8 12?

2/32/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.


Equivalent Definition

Equivalent: When two or more quantities have the same value. An equal sign is used to show that the quantities are the same value.


What is equivalent?

The quantities can be represented by a number, fraction, decimal, or percentage. Equivalent does not always mean that the values look identical.


Equivalent Numbers

Numbers can be used to represent values in different ways. The different representations are equivalent to each other. They look different but represent the same value. They can take on different forms and can be changed from one form to another. When the value changes, it is referred to it as converting.


Equivalent Fractions

Fractions are equivalent to one another when they represent the same ratio or value. A fraction has a numerator and a denominator. The denominator describes the number of parts 1 whole has been split into. The numerator describes how many of those parts are being used.


Equivalent Decimals

A decimal has a whole number part, which is written before the decimal point, and a ratio part, after the decimal point. It describes a portion of a full value. Each number after the decimal point shows a different portion of a whole number.


Using Equivalent Math

Numbers can be converted from one form to another. Fractions can be changed to decimals, just as decimals can be changed to fractions. When numbers are converted from one form to another, they represent the same value and are equivalent. Numbers describe a value or a quantity. Equivalent forms are used to describe different things better.


Directions and Rules

Hand out bingo cards and bingo chips to each player. This can be played alone or with a group. However many bingo cards you have is the number of people that can play.


What does “equivalent” mean in English?

Middle English, from Middle French or Late Latin; Middle French, from Late Latin aequivalent-, aequivalens, present participle of aequivalēre to have equal power, from Latin aequi- + valēre to be strong — more at wield. Keep scrolling for more. Keep scrolling for more.


How many questions are there in the vocabulary quiz?

Test your vocabulary with our 10-question quiz!


What is equivalent in math?

First, within a particular mathematical theory (for example, Euclidean geometry ), a notion (for example, ellipse or minimal surface) may have more than one definition. These definitions are equivalent in the context of a given mathematical structure ( Euclidean space, in this case). Second, a mathematical structure may have more than one definition (for example, topological space has at least seven definitions; ordered field has at least two definitions ).


How many definitions does a mathematical structure have?

Second, a mathematical structure may have more than one definition (for example, topological space has at least seven definitions; ordered field has at least two definitions ). In the former case, equivalence of two definitions means that a mathematical object (for example, geometric body) satisfies one definition if and only if it satisfies …


How to find scale of sets?

According to Bourbaki, the scale of sets on a given set X consists of all sets arising from X by taking Cartesian products and power sets, in any combination, a finite number of times. Examples: X; X × X; P ( X ); P ( P ( X × X) × X × P ( P ( X ))) × X. (Here A × B is the product of A and B, and P ( A) is the powerset of A .) In particular, a pair (0, S) consisting of an element 0 ∈ N and a unary function S : N → N belongs to N × P ( N × N) (since a function is a subset of the Cartesian product ). A triple (+, ·, ≤) consisting of two binary functions N × N → N and one binary relation on N belongs to P ( N × N × N) × P ( N × N × N) × P ( N × N ). Similarly, every algebraic structure on a set belongs to the corresponding set in the scale of sets on X .


Is equivalence more abstract than object?

In the latter case, the meaning of equivalence (between two definitions of a structure) is more complicated, since a structure is more abstract than an object. Many different objects may implement the same structure.


Can math be explained by a single concept?

“Mathematics […] cannot be explained completely by a single concept such as the mathematical structure. Nevertheless, Bourbaki’s structuralist approach is the best that we have.” ( Pudlák 2013, page 3)


Is a natural number isomorphic?

The two isomorphic implementations of natural numbers, mentioned in the previous section, are isomorphic as triples ( N ,0, S ), that is, structures of the same signature (0, S) consisting of a constant symbol 0 and a unary function S. An ordered semiring structure ( N, +, ·, ≤) has another signature (+, ·, ≤) consisting of two binary functions and one binary relation. The notion of isomorphism does not apply to structures of different signatures. In particular, a Peano structure cannot be isomorphic to an ordered semiring. However, an ordered semiring deduced from a Peano structure may be isomorphic to another ordered semiring. Such relation between structures of different signatures is sometimes called a cryptomorphism .


What are Equivalent Fractions?

In math, equivalent fractions can be defined as fractions with different numerators and denominators that represent the same value or proportion of the whole.


How many equivalent fractions can a child show?

Instead of handing out regular fraction worksheets to your children, ask your child to divide the pizza or pancakes such that he can show three equivalent fractions.


What are equivalent expressions?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value (s) for the variable (s).


When two expressions are equivalent, what is the meaning of the expression?

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. Arrange the terms in the same order, usually -term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.


How to make an equation true for all values of a variable?

For the equation to be true for all values of the variable, the two expressions on each side of the equation must be equivalent. For example, if for all values of , then: must equal . must equal . Distribute any coefficients on each side of the equation.


What happens if all the terms in two expressions are identical?

If all of the terms in the two expressions are identical, then the two expressions are equivalent.


How to distribute coefficients?

Distribute any coefficients: Combine any like terms on each side of the equation: -terms with -terms and constants with constants. Arrange the terms in the same order, usually -term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.


Let’s learn!

In algebra, equivalent decimals are two decimal numbers that are equivalent, that is, they represent the same value or amount.


Let’s do it!

Instead of teaching equivalent decimals and then handing out practice worksheets to your children, ask them to find the equivalent decimals of the numbers you say or convert the fractions you say into equivalent decimals.


What is an equivalent set?

Equivalent Set Definition. Two sets are said to be equivalent if their cardinality number is the same. This means that there must be one to one correspondence between elements of both sets. Here, one to one correspondence means that for each element in set A, there exists an element in set B until sets get exhausted.


How to tell if two sets are equivalent?

Ans: Two sets A and B are said to be equivalent if they have the same cardinality i.e. n (A) = n (B). In a general way, two sets are equivalent to each other if the number of elements in both sets is equal.


What does equal set mean?

Equal Set Definition – Two sets A and B are said to be equal only if each element of set A is also present in an element of the set B. In another way, we can say if two sets are the subsets of each other, they are said to be equal. It is represented by:


Why are all the four sets of a triangle equal?

In the above diagram, all the four sets are equivalent sets because the number of elements is the same in all the four sets of triangle, smiley, star and heart. Here n (Triangle) = n (Smiley) = n (Stars) = n (Heart) = 6.


What is the symbol for unequal sets?

Unequal sets are represented by the symbol of “≠” i.e. not equal to.


Why are two sets of shapes equal?

These are equal sets because the number of elements is the same and their elements are also the same.


What happens if two sets A and B have the same cardinality?

If two sets A and B have the same cardinality then there exists an objective function from set A to B.

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Overview

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The meaning of ‘equivalent’ generally refers to two numbers, expressions, or quantities with the same value. There are many ways to express an equivalent quantity – it can be denoted either by a bar or an equivalent symbol. Children find this topic very interesting for several reasons as they can relate to it in their daily l…

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External links


Isomorphic implementations


Deduced structures and cryptomorphisms


Ambient frameworks

• nLab:structured set “Almost everything in contemporary mathematics is an example of a structured set.” (quoted from Section “Examples”)
• nLab: structure in model theory
• nLab: stuff, structure, property


Structures according to Bourbaki

Natural numbers may be implemented as 0 = { }, 1 = {0} = {{ }}, 2 = {0, 1} = {{ }, {{ }}}, 3 = {0, 1, 2} = {{ }, {{ }}, {{ }, {{ }}}} and so on; or alternatively as 0 = { }, 1 = {0} ={{ }}, 2 = {1} = {{{ }}} and so on. These are two different but isomorphic implementations of natural numbers in set theory. They are isomorphic as models of Peano axioms, that is, triples (N,0,S) where N is a set, 0 an element of N, and S (called the successor function) a map of N to itself (satisfying appropriate conditions). In t…


Mathematical practice

The successor function S on natural numbers leads to arithmetic operations, addition and multiplication, and the total order, thus endowing N with an ordered semiring structure. This is an example of a deduced structure. The ordered semiring structure (N, +, ·, ≤) is deduced from the Peano structure (N, 0, S) by the following procedure: n + 0 = n, m + S (n) = S (m + n), m · 0 = 0, m · S (n) = m + (m · n), and m ≤ n if and only if there exists k ∈ N such that m + k = n. And conversely…


Canonical, not just natural

A structure may be implemented within a set theory ZFC, or another set theory such as NBG, NFU, ETCS. Alternatively, a structure may be treated in the framework of first-order logic, second-order logic, higher-order logic, a type theory, homotopy type theory etc.


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