What Does Equivalent Mean In Math

Common Mathematical Symbols And Terminology: Maths Glossary

Mathematical symbols and terminology can be confusing and can be a barrier to learning and understanding basic numeracy.

This page complements our numeracy skills pages and provides a quick glossary of common mathematical symbols and terminology with concise definitions.

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Making The Denominators The Same

The denominators of the fractions, 2/6 and 3/9 are 6 and 9. The Least Common Multiple of the denominators 6 and 9 is 18. Let us make the denominators of both fractions 18, by multiplying them with suitable numbers.

We can observe that both the fractions are equivalent to the same fraction 6/18. Thus, the given fractions are equivalent.

Note: If the fractions are NOT equivalent, we can check the greater or smaller fraction by looking at the numerator of both the resultant fractions. Hence, this method can also be used for comparing fractions.

Fractions Equivalency In Ks1 And Ks2

Children first learn about halving and quartering a shape in Key Stage 1.

In Year 3 they are introduced to the concept of equivalence, where they are shown different shapes like the ones above and asked to write them as fractions.

Children continue to practise equivalent fractions in Year 4 and it is expected that they will still need diagrams to make this clear to them at this stage.

Children in Year 4 also start learning about decimals and need to know that 0.25 is equivalent to 1/4, 0.5 is equivalent to 1/2 and 0.75 is equivalent to 3/4. This can be demonstrated with the use of some blank hundred squares:

In Year 5, children are expected to find equivalent fractions without the use of diagrams. At this stage, they would learn that whatever the numerator is multiplied by the denominator must also be multiplied by the same number, for example:

Children in Year 5 also need to relate fractions to their decimal representations .

In Year 5, children would also need to order a set of fractions that had different denominators. For example:

1/3 2/4 5/6 2/3 1/12

One way of doing this would be to change all the denominators so that they were the same. This would mean multiplying the numerator and the denominator by the same number.

In Year 6, children need to use their knowledge of equivalent fractions to simplify fractions.

Simplifying a fraction means finding an equivalent fraction where the numbers are reduced as much as possible.

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What Does Equal Mean

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Divide The Numerator And Denominator By The Same Number

To find the equivalent fractions for any given fraction, divide the numerator and the denominator by the same number. For example, to find an equivalent fraction of 72/108, we will first find their common factors. We know that 2 is a common factor of both 72 and 108. Hence, an equivalent fraction of 72/108 can be found by dividing its numerator and denominator by 2. Thus, 36/54 is an equivalent fraction of 72/108. Let us see how the fraction is further simplified:

• 2 is a common factor of 36 and 54. Thus, 36/54= \= 18/27
• Again, 3 is a common factor of 18 and 27. Thus, 18/27= \= 6/9
• Again, 3 is a common factor of 6 and 9. Thus, 6/9=\= 2/3

Therefore, a few equivalent fractions of 72/108 are 36/54, 18/27, 6/9, and 2/3. Here, 2/3 is the simplified form of 72/108 as there is no common factor of 2 and 3.

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How To Find That Two Ratios Are Equivalent Or Not

Two or more than two ratios can be compared with each other. In order to find whether they are equivalent or not, first, we convert them into like fractions. After converting, denominators of all the fractions become equal and if the numerators of all the fractions also become equal, the fractions are said to be equivalent fractions.

Also, if the two fractions a/b and c/d become equivalent, then the four quantities a, b, c, and d are said to be in proportion. It can be written as a:b::c:d.

Give 2 Equivalent Fractions For 6/8

In order to write the equivalent fraction for 6/8, let us multiply the numerator and denominator by 2 and we will get / = 12/16. Therefore, 6/8 and 12/16 are equivalent fractions. Now, let us get another equivalent fraction for 6/8, by dividing it by a common number, say, 2. After dividing the numerator and denominator by 2 and we will get / = 3/4. Therefore, 6/8 and 3/4 are equivalent fractions.

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S To Determine Equivalent Fractions

How can we determine if two fractions are equivalent or not? It is possible by these methods:

• Method 1: Make the Denominators the same
• Method 2: Cross Multiply
• Method 3: Convert to decimals

Method 1:

For example, find if 2/3 and 6/9 are equivalent.

LCM of 3 and 9 = 9

Multiply 2/3 by 3/3 to make the denominator equal to 9.

2/3 × 3/3 = 6/9

Hence, by making the denominators the same, we can see, 2/3 and 6/9 are equivalent fractions.

Method 2:

Given, two fractions 1/2 and 3/6

Cross multiply both the fractions to get:

1 x 6 = 6

Since, both the values are equal, therefore, 1/2 and 3/6 are equivalent fractions.

Method 3:

If two fractions are given, we can simply find their decimals to check if they are equivalent fractions.

Let us check if 1/4 and 3/12 are equivalent fractions by converting them in decimal form.

1/4 = 0.25

Since, both the fractions result in the same decimal, thus they are equivalent.

Structures According To Bourbaki

“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.”

“Evident as the notion of mathematical structure may seem these days, it was at least not made explicit until the middle of the 20th century. Then it was the influence of the Bourbaki-project and then later the development of category theory which made the notion explicit” .

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 P × X × P)) × X. is the powerset of A.) In particular, a pair consisting of an element 0 N and a unary function S : N N belongs to N × P #Definition” rel=”nofollow”> 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 × P × P. Similarly, every algebraic structure on a set belongs to the corresponding set in the scale of sets on X.

Non-algebraic structures on a set X often involve sets of subsets of X , in other words, elements of P)). For example, the structure of a topological space, called a topology on X, treated as the set of “open” sets or the structure of a measurable space, treated as the -algebra of “measurable” sets both are elements of P). These are second-order structures.

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How To Find Equivalent Fractions:

Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change that fraction into an equivalent fraction, but it will not change its value. Equivalent fractions may look different, but they have the same value. Let’s look at some more examples of equivalent fractions.

For Example : to find equivalent fraction of `2/3` we multiply both numerator and denominator by 2 then we get equivalent fraction `4/6` .

How To Check Whether The Fractions Are Equivalent Or Not

There are different ways to check whether the fractions are equivalent or not:

• Make the denominators the same

We can check whether the fractions are equivalent or not by making the denominators the same i.e., by finding the LCM of the denominators and then multiplying them with suitable numbers.

For example: In order to check whether $\frac$ and $\frac$ are equivalent or not, we will find the LCM of 8 and 12.

Step 1: Find LCM of denominators

LCM = 24

Step 2: Multiply by suitable numbers to make denominator the same = 24

$\frac$ = $\frac$ and $\frac$ = $\frac$

Since both the fractions came out to be $\frac$, so they are equivalent fractions.

• Finding the decimal form for both the fractions.

Since, the decimal form of both the fractions is 0.25, so they are equivalent fractions.

• Cross multiplication method

We will multiply the fractions. If the product comes out to be the same, the fractions are equivalent.

2 $\times$ 12 = 24 8 $\times$ 3 = 24

Since both the products are same, the fractions are equivalent.

We can determine the equivalent fractions on identical shapes and check whether the shaded portions are equal or not.

In the above image, we see the shaded portions of both the circles depicts the same value. So, they are equivalent fractions.

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What Does Equivalent And Equal Mean In Math

The equal set definition is that when two sets have the same elements. However, it does not matter which order the elements are arranged. The only thing that matters in an equal set is that the same elements are present in each set. … Equivalent sets do not have to hold the same number but the same number of elements.

How To Define Equivalent In Mathematics

In mathematics, Equivalent meanings are used in two different ways. First, within the framework of a particular mathematical theory , a notion may have more than one meaning. In the context of a given mathematical form, these concepts are identical . Second, there could be a mathematical framework. In the prior example, the equivalence of two definitions implies that a mathematical entity follows one definition if and only if it meets the other definition. In the above case, the sense of equivalence is more complex since the structure is more abstract than the entity. Several different artifacts can follow the same structure.

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I Get The Difference But Isnt It A Little Harsh

It depends. If the teacher has already taught the commutative property of multiplication, then this is a fine substitution to make. And it is awesome that the student realized this! Kudos! What a mathlete!

If the teacher has not covered the commutative property, then it might be unwise to let a student continue with this line of thought if they dont understand the reasons why fully.

Its common for beginners to get confused as to when it is okay to switch the order of values in binary operations. We know that the following are not equal.

But this is easily confused with the child who sees that sometimes its okay to switch the order and other times its not and hasnt learned when or why.

By focusing on the meaning of these operations as they relate to repeated addition, arrays and area, teachers are creating a deeper understanding and trying to prevent students from making these kinds of mistakes.

Examples Of Equivalent In A Sentence

equivalentequivalentequivalentequivalent WSJequivalent CNNequivalent Chicago Tribuneequivalent ProPublicaequivalent Forbesequivalent clevelandequivalent Better Homes & Gardensequivalent BostonGlobe.com

These example sentences are selected automatically from various online news sources to reflect current usage of the word ‘equivalent.’ Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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How To Check Two Fractions Are Equivalent Fraction:

Simplify all fractions. If they reduce to be the same fraction, then the fractions are equivalent

For example : we will check the fractions fractions `6/15` and `10/50` are equivalent.

we will simplify both the fractions-

`6/15`= `/`=`2/5`

`10/50`= `/`=`1/5`

the fractions `2/5` and `1/5` are not same, hence fractions are not equivalent

What Is The Meaning Of Its Equivalent

This is a question our experts keep getting from time to time. Now, we have got the complete detailed explanation and answer for everyone, who is interested!

Asked by: Mozelle Langosh

1 : equal in force, amount, or value also : equal in area or volume but not superposable a square equivalent to a triangle. 2a : like in signification or import. b : having logical equivalence equivalent statements. 3 : corresponding or virtually identical especially in effect or function.

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< Less Than And > Greater Than

This symbol < means less than, for example 2 < 4 means that 2 is less than 4.

This symbol > means greater than, for example 4 > 2.

These symbols mean less than or equal to and greater than or equal to and are commonly used in algebra. In computer applications < = and > = are used.

These symbols are less common and mean much less than, or much greater than.

What Is Equal Sign Definition Facts & Example Splashlearn

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Choose The Right Synonym For Equivalent

same, selfsame, very, identical, equivalent, equal mean not different or not differing from one another. same may imply and selfsame always implies that the things under consideration are one thing and not two or more things. took the same route derived from theselfsame source very, like selfsame, may imply identity, or, like same may imply likeness in kind. the very point I was trying to make identical may imply selfsameness or suggest absolute agreement in all details. identical resultsequivalent implies amounting to the same thing in worth or significance. two houses equivalent in market value equal implies being identical in value, magnitude, or some specified quality. equal shares in the business

Multiplying Numerator And Denominator By The Same Number

For example, consider the fraction 1/5

• Multiplying numerator and denominator with 2, we get 1/5 × 2/2 = 2/10
• Multiplying numerator and denominator with 3, we get 1/5 × 3/3 = 3/15
• Multiplying numerator and denominator with 4, we get 1/5 × 4/4 = 4/20

Therefore, we can conclude that,

1/5 = 2/10 = 3/15 = 4/20

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Representation Of Equivalent Symbol

If A B and B A , then A and B are said to be equal, a relationship that is symbolically written as A = B in this job.

• Equivalent Expressions: An algebraic expression is an expression composed of variables, coefficients, constants, and mathematical functions, such as addition, subtraction, multiplication, and division. Generally, if two objects are the same, they’re considered identical. Similarly, in mathematics, equivalent expressions are expressions that are the same, even though the expression looks different. Look at 3 × 3 + 1 and 5 × 2 expressions. They’re both equivalents to 10. That is, they are equivalent expressions.

How to find that two mathematical expressions are equivalent expressions or not?

Ans. In general, to prove that two mathematical expressions are equivalent we keep them as equal. Later, we evaluate the left-hand side expression and right-hand side expression, and if both sides are equal then the given expressions are equivalent expressions.

For Example: Check whether 3 × 9 + 5 × 2 is equivalent to 7 × 3 + 4 × 4 or not.

Solution: To check the equivalency of both the equations, we put both of them equal to each other.

3 × 9 + 5 × 2 = 7 × 3 + 4 × 4

27 + 10 = 21 + 16

So, the given expressions are equivalent to each other.

Remember: We also need to give attention to the units obtained on both sides.

A = B

A B and B A A = B

The first image represents an equal set and the second image represents an equivalent set.

What Is The Meaning Of Equivalent In Math

There are two ways in which one can define an equivalent in math. This is because the term equivalent in mathematical theory is a notion that has multiple meanings. Equivalent means that different terms and expressions with a similar value are considered equal in mathematical form.

Equal Vs Equivalent

In math, equivalent is different from equal. Equal means same in all aspects, whereas equivalent means similar but not identical.

For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

In simple words we can say that two things or quantities are equal when they are exactly the same like ½ is equal to ½ but ½ is equivalent to 2/4 as they represent the same value.

Equivalent Expressions

Two mathematical expressions are said to be equivalent if they yield the same result upon solving them.

For example, lets solve the following numerical expressions:

25 × 5 = 125

Also, 10$^$ + 5$^$ = 100 + 25 = 125

Thus, the above two expressions are equivalent and can be written as:

25 × 5 = 10$^$ + 5$^$Similarly, the two math expressions 2 × and 4$^$ ÷ 4 are also equivalent as both can be simplified to 4.

Equivalent Fractions

Two fractions are equivalent if the value, proportion, or quantity they represent is the same. Equivalent fractions can have different numerators and denominators.

For example: $\frac$ = $\frac$ = $\frac$ = $\frac$

Equivalent Ratios

Equivalent ratios are those which can express a similar or the same relationship between numbers or values.

Application

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