Equivalent Fractions For 3 6

What are Equivalent Fractions?

Fractions represent equal parts of a whole or a collection. A fraction has two parts. The number on the top of the line is chosen the numerator which tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator and it shows the total number of equal parts the whole is divided into or the total number of equal parts which are there in a collection.

Definition of Equivalent Fractions

The fractions that represent the same value only look different(i.e different numerators or denominators) are chosen equivalent fractions. In other words, ii or more than fractions are said to be equivalent fractions if they are equal to the same fraction afterwards nosotros simplify them.

In the above epitome,

$\frac{1}{3}$, $\frac{2}{6}$, $\frac{three}{9}$ and $\frac{iv}{12}$ seem to exist unlike but they are equivalent fractions as on simplification, we get the fraction $\frac{i}{three}$.

Let us consider this through an instance:

Ann and Eden bought a cake. They decided to share the cake. Ann had $\frac{4}{8}$ of the cake whereas Eden had $\frac{1}{2}$ of the cake. Did they divide the cake equally?

Yeah; they did. Two fractions might look dissimilar but, upon simplification, have the same mathematical value and hence $\frac{4}{8}$ and $\frac{1}{2}$ are called equivalent fractions.

Consider, for case, $\frac{5}{x}$ and $\frac{2}{4}$ . They also seem dissimilar, but when we simplify them; they present the same value i.e, $\frac{1}{2}$.

How to Check Whether the Fractions are Equivalent or Not?

In that location are different ways to check whether the fractions are equivalent or not:

• Brand the denominators the aforementioned

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

For instance: In gild to check whether $\frac{2}{eight}$ and $\frac{3}{12}$ are equivalent or not, we will observe the LCM of viii and 12.

Step one: Find LCM of denominators

              LCM(8, 12) = 24

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

             $\frac{two \times iii}{8 \times three}$ = $\frac{half-dozen}{24}$ and $\frac{3 \times 2}{12 \times ii}$ = $\frac{6}{24}$

Since both the fractions came out to be $\frac{6}{24}$, then they are equivalent fractions.

• Finding the decimal form for both the fractions.

Decimal form of $\frac{2}{8}$ is 0.25.

Decimal grade of $\frac{iii}{12}$ is 0.25.

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

• Cantankerous multiplication method

Nosotros volition multiply the fractions. If the product comes out to be the aforementioned, the fractions are equivalent.

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

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

• Visual Method

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

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

Finding an Equivalent Fraction

To find equivalent fractions, we multiply or divide both the numerator and the denominator by the same number. There are two ways in which we tin can make equivalent fractions:

• Multiply the numerator and denominator by the same number

We tin can multiply the numerator and the denominator by the aforementioned number in society to notice the equivalent fractions.

For example: Nosotros have to discover two equivalent fractions for $\frac{iii}{8}$.

Multiplying the numerator and denominator past 2.

$\frac{iii \times 2}{eight \times 2}$ = $\frac{half-dozen}{16}$

Multiplying the numerator and denominator by 3.

$\frac{3 \times iii}{8 \times 3}$ = $\frac{ix}{24}$

The 2 equivalent fractions for $\frac{three}{8}$ are $\frac{six}{16}$ and $\frac{9}{24}$.

• Separate the numerator and denominator by the same number.

We tin can dissever the numerator and the denominator by the same number in social club to find equivalent fractions.

For case: To detect equivalent fractions for $\frac{lxx}{100}$.

First discover the common factors of lxx and 100.

The common factors of seventy and 100 are ii, 5 and 10.

Multiplying the numerator and denominator by 2.

$\frac{70 \div 2}{100 \div 2}$ = $\frac{35}{50}$

Multiplying the numerator and denominator past 5.

$\frac{70 \div 5}{100 \div v}$ = $\frac{fourteen}{twenty}$

Multiplying the numerator and denominator by 10.

$\frac{70 \div 10}{100 \div ten}$ = $\frac{seven}{ten}$

The equivalent fractions for $\frac{70}{100}$ are $\frac{35}{50}$ , $\frac{fourteen}{xx}$, and $\frac{7}{10}$.

Solved Examples

ane. Bank check if $\frac{3}{9}$, $\frac{4}{12}$ and $\frac{v}{15}$ are equivalent fractions.

Upon simplifying $\frac{3}{nine}$, nosotros go $\frac{1}{3}$. Similarly, upon simplifying $\frac{iv}{12}$, nosotros get $\frac{1}{3}$. And, upon simplifying $\frac{five}{15}$ nosotros again go the same value, $\frac{one}{3}$. As we get the same values later on the simplification, these are equivalent fractions.

2. What will be the value of 10 if $\frac{ii}{3}$ = $\frac{x}{12}$.

Since $\frac{2}{iii}$ = $\frac{10}{12}$, it means we have multiplied the denominator by iv. So, we volition multiply the numerator also by 4.

x = 2 $\times$ 4 = 8

three. Observe three equivalent fractions for $\frac{two}{3}$.

Multiplying both numerator and denominator by 2, we get $\frac{2 \times 2}{iii \times 2}$ = $\frac{four}{6}$.

Multiplying both numerator and denominator by 3, we get $\frac{2 \times 3}{3 \times three}$ = $\frac{6}{nine}$.

Multiplying both numerator and denominator by 4, we get $\frac{2 \times 4}{3 \times four}$ = $\frac{eight}{12}$.

The three equivalent fractions for $\frac{two}{three}$ are $\frac{4}{half-dozen}$, $\frac{6}{nine}$ and $\frac{8}{12}$.

Practice Problems

Equivalent Fractions

Attend this Quiz & Test your knowledge.

$\frac{3}{iv}$

$\frac{4}{3}$

$\frac{iii}{5}$

$\frac{five}{3}$

Correct answer is: $\frac{3}{4}$
On dividing both numerator and denominator of $\frac{12}{16}$ by 4, nosotros get $\frac{3}{4}$.

2

three

4

5

Correct answer is: 4
two $\times$ 4 = 8 and v $\times$ 4 = 20, and then both numerator and denominator should be multiplied past 4.

$\frac{40}{70}$

$\frac{threescore}{90}$

$\frac{20}{lxx}$

$\frac{25}{xxx}$

Correct respond is: $\frac{60}{90}$
On dividing both numerator and denominator of $\frac{60}{90}$ by 20, we go the fraction $\frac{2}{3}$.

Decision

Equivalent fractions have dissimilar face values, simply upon simplifying them, they give the same numerical values. Yous can find these fractions past multiplying the denominator and numerator with the aforementioned number/value. Head to SplashLearn to learn virtually the equivalent fractions in a fun and easy fashion.

Frequently Asked Questions

How to figure out whether fractions are equivalent or not?

To make up one's mind whether fractions are equivalent or non, simplify the fractions to their lowest terms. If after simplification the fractions are the same, and then they are equivalent if not so they are not equivalent.

How to find equivalent fractions to a given fraction?

We tin can either multiply or divide both the numerator and the denominator of the given fraction by the aforementioned number to generate equivalent fractions to the given fraction.

Why are equivalent fractions important?

Equivalent fractions aid u.s. in adding, subtracting, multiplying, dividing fractions, and as well in comparison and ordering fractions which helps us solve many real-fourth dimension issues.

Equivalent Fractions For 3 6,

Source: https://www.splashlearn.com/math-vocabulary/fractions/equivalent-fractions

Posted by: jewellcracenduch.blogspot.com

Share this post