How To Find An Equivalent Fraction By Multiplying

Equivalent Fractions

Equivalent fractions can be divers as fractions that may have different numerators and denominators but they represent the same value. For case, 9/12 and vi/8 are equivalent fractions because both are equal to 3/4 when simplified.

All equivalent fractions go reduced to the same fraction in their simplest form as seen in the above example. Explore the given lesson to go a amend idea of how to find equivalent fractions and how to bank check if the given fractions are equivalent.

i.	What are Equivalent Fractions?
2.	How to Discover Equivalent Fractions?
3.	How to Decide if Ii Fractions are Equivalent?
4.	Equivalent Fractions Nautical chart
5.	FAQs on Equivalent Fractions

What are Equivalent Fractions?

Two or more fractions are said to exist equivalent if they are equal to the same fraction when simplified. For example, the equivalent fractions of i/5 are 5/25, half dozen/30, and iv/20, which on simplification, event in the same fraction, that is, 1/five.

Equivalent Fractions Definition

Equivalent fractions are defined as those fractions which are equal to the aforementioned value irrespective of their numerators and denominators. For instance, both vi/12 and four/eight are equal to 1/two, when simplified, which means they are equivalent in nature.

Equivalent Fractions Examples

Here are some examples of equivalent fractions.

Example: 1/two, 2/4, three/6, and 4/8 are equivalent fractions. Let us see how their values are equal. We volition represent each of these fractions as circles with shaded parts. Information technology tin be seen that the shaded parts in all the figures represent the same portion if seen every bit a whole.

Hither, nosotros tin run into that the amount of shaded portion is the same in all the circles. Hence, ane/two, 2/iv, three/6, and four/8 are equivalent fractions.

How to Find Equivalent Fractions?

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified. Permit usa sympathise the two ways in which we can brand equivalent fractions:

• Multiply the numerator and the denominator by the same number.
• Split up the numerator and the denominator by the same number.

Multiply the Numerator and Denominator past the Same Number

To find the equivalent fractions for whatever given fraction, multiply the numerator and the denominator by the same number. For case, to find an equivalent fraction of three/iv, multiply the numerator iii and the denominator iv by the same number, say, 2. Thus, vi/viii is an equivalent fraction of three/4. Nosotros can notice some other equivalent fractions by multiplying the numerator and the denominator of the given fraction past the same number.

• 3/iv= \(\dfrac{3 \times 3}{4 \times 3}\) =9/12
• iii/4=\(\dfrac{iii \times 4}{4 \times 4}\) =12/16
• 3/4=\(\dfrac{3 \times v}{4 \times 5}\) =15/xx

Thus, the equivalent fractions of three/4 are 6/viii, 9/12, 12/16, and 15/xx.

Separate the Numerator and Denominator by the Same Number

To find the equivalent fractions for any given fraction, split the numerator and the denominator by the aforementioned number. For example, to notice an equivalent fraction of 72/108, nosotros will kickoff discover their common factors. We know that two 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. Permit us see how the fraction is further simplified:

• 2 is a common cistron of 36 and 54. Thus, 36/54= \(\dfrac{36 \div 2}{54 \div 2}\)= 18/27
• Once more, 3 is a common factor of 18 and 27. Thus, 18/27= \(\dfrac{18 \div 3}{27 \div three}\)= 6/9
• Again, three is a common factor of vi and 9. Thus, half dozen/9=\(\dfrac{6 \div three}{9 \div 3}\)= ii/3

Therefore, a few equivalent fractions of 72/108 are 36/54, 18/27, half dozen/9, and 2/3. Here, 2/3 is the simplified form of 72/108 as in that location is no common cistron (other than i) of 2 and 3.

How to Make up one's mind if Two Fractions are Equivalent?

We need to simplify the given fractions to observe whether they are equivalent or not. Simplification to get equivalent numbers tin be washed to a point where both the numerator and denominator should still be whole numbers. There are various methods to identify if the given fractions are equivalent. Some of them are:

• Making the denominators the same.
• Finding the decimal course of both the fractions.
• Cross multiplication method.
• Visual method.

Let u.s.a. identify whether 2/half-dozen and 3/nine are equivalent fractions by each of these methods.

Making the Denominators the Same

The denominators of the fractions, 2/half-dozen and 3/9 are 6 and ix. The Least Common Multiple (LCM) of the denominators 6 and 9 is 18. Permit united states of america make the denominators of both fractions 18, by multiplying them with suitable numbers.

• 2/6=\(\dfrac{2 \times 3}{6 \times 3}\)= 6/18
• 3/9=\(\dfrac{3 \times 2}{9 \times two}\)= 6/18

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

Note: If the fractions are Non equivalent, we can check the greater or smaller fraction by looking at the numerator of both the resultant fractions. Hence, this method tin as well be used for comparing fractions.

Finding the Decimal form of Both the Fractions

Permit united states of america discover the decimal course of both the fractions ii/6 and 3/9 to run into if they requite the same value.

• two/6= 0.3333333...
• 3/9= 0.3333333...

The decimal values of both the fractions are the same and hence, they are equivalent.

Cross Multiplication Method

To identify whether 2/6 and 3/9 are equivalent, we cross multiply them. If both the products are the same, the fractions are equivalent.

Since both the products here are 18, the given fractions are equivalent.

Visual Method

Allow us represent each of the fractions ii/6 and 3/9 pictorially on identical shapes and check if the shaded portions of both are equal.

Nosotros tin see that the shaded portions of both the circles depict the same value. In other words, information technology can be seen that the shaded parts in both the figures represent the same portion if seen as a whole. Hence, the given fractions are equivalent.

Equivalent Fractions Chart

Charts and tables are often used to represent concepts in a amend manner since they serve as a handy reference for calculations and are easier to understand. Ballast charts and tables, like the one given beneath, brand it easier for the students to sympathise equivalent fractions. Let us use the post-obit chart to find the equivalent fractions of 1/4.

From this nautical chart, we tin observe that the equivalent fractions of i/4 are: two/8, 3/12, four/16,...

Tips on Equivalent Fractions

• Two fractions are said to be equivalent if their values (decimal/graphical) are the same.
• We normally multiply the numerator and denominator of a fraction by the same number to go its equivalent fraction.
• The 'Cross multiplication method' is used to determine whether any two fractions are equivalent or non.
• 'Making the denominators the aforementioned' is another method used to decide if ii or more fractions are equivalent.

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Equivalent Fractions Examples

1. Example 1: Are 12/twenty and 22/30 equivalent fractions?

   Solution:

   Method 1:

   To cheque if the given fractions are equivalent, we will make the denominators the same by multiplication. The denominators of the fractions 12/20 and 22/30 are 20 and thirty. The LCM of the denominators is lx. Let us make the denominators of both the fractions equal to 60, by multiplying them with the suitable numbers: 12/20=\(\dfrac{12 \times 3}{20 \times 3}\)= 36/lx, 22/thirty=\(\dfrac{22 \times 2}{xxx \times ii}\)= 44/sixty. Here, it can be seen that 36 is not equal to 44, that is 36 < 44. Therefore, 12/20 and 22/xxx are non equivalent fractions.

   Method 2:

   This tin can exist checked past the cantankerous multiplication method. If we cross multiply the given fractions, we volition go 20 × 22 = 440, and 12 × xxx = 360. We can see that 440 is not equal to 360. Therefore, 12/twenty and 22/30 are not equivalent fractions.

2. Example 2: If the numerator of a fraction equivalent to nine/18 is 27, what is its denominator?

   Solution:

   We know that, 9/eighteen=27/? Here, the numerators of the ii fractions are nine and 27 respectively. Now, we have to observe a number, which, when multiplied by 9 gives 27. Nosotros know that nine × 3 = 27. Hence, we multiply the numerator and the denominator of the given fraction by 3 =\(\dfrac{nine \times 3}{eighteen \times 3}\)= 27/54. Therefore, the denominator of the equivalent fraction of 9/18 is 54.

3. Example iii: Check whether the given fractions are equivalent or non: 7/13 and 5/eleven

   Solution: Permit united states of america check the equivalence of the given fractions past the cross multiplication method. If we cross multiply the given fractions, we will go 13 × 5 = 65, and 7 × eleven = 77. We can see that 65 is non equal to 77. Therefore, 7/xiii and five/11 are not equivalent fractions.

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Practice Questions on Equivalent Fractions

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FAQs on Equivalent Fractions

What are Equivalent Fractions in Math?

Two or more fractions are said to exist equivalent fractions if they are equal to the same value irrespective of their numerators and denominators. For instance, 2/4 and eight/16 are equivalent fractions because they get reduced to 1/2 when simplified.

What are the Examples of Equivalent Fractions?

There tin be many examples of equivalent fractions, similar, viii/12 and six/9 are equivalent fractions because they get reduced to the same fraction (2/3) when simplified. Similarly, 4/7 and 28/49 are as well equivalent fractions.

How to Discover Equivalent Fractions?

If the given fractions are simplified and they become reduced to a mutual fraction, then they can exist termed as equivalent fractions. Apart from this, at that place are diverse other methods to identify whether the given fractions are equivalent or not. Some of them are:

1. Making the denominators the same.
2. Past finding the decimal form of both the fractions.
3. Cross multiplication method.
4. Visual method.

What does information technology Mean when Two Fractions are Equivalent?

When two fractions are equivalent, information technology ways they are equal to the same value irrespective of their different numerators and denominators. In other words, when they are simplified they get reduced to the same fraction.

Why are Equivalent Fractions Important?

Equivalent fractions help united states of america to add, subtract, multiply, divide fractions, and compare fractions which helps us solve many existent-time bug.

What is an Equivalent Improper Fraction?

An equivalent improper fraction means an equivalent fraction in an improper form. A fraction is said to exist improper when its numerator is greater than its denominator. For example, iii/two is an improper fraction that is equivalent to 9/six.

How to Figure out Equivalent Fractions?

Any ii fractions can be considered to be equivalent if they are equal to the aforementioned value. There are various methods to detect out if the fractions are equivalent. The basic method is by reducing them. If they get reduced to the same fraction they are considered to be equivalent.

How to Write Equivalent Fractions?

Equivalent fractions can exist written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified. For example, let the states write an equivalent fraction for 2/3. Nosotros will multiply the numerator and denominator by 4 and we will get (2 × four)/(3 × iv) = 8/12. Therefore, 8/12 and 2/iii are equivalent fractions.

Requite two Equivalent Fractions for six/8.

In order to write the equivalent fraction for 6/8, let us multiply the numerator and denominator past 2 and we will get (6 × two)/(viii × 2) = 12/xvi. Therefore, 6/eight and 12/16 are equivalent fractions. At present, permit us get another equivalent fraction for half-dozen/eight, by dividing it past a common number, say, 2. Afterward dividing the numerator and denominator by two and we will get (vi ÷ 2)/(8 ÷ 2) = 3/4. Therefore, vi/8 and 3/4 are equivalent fractions.

Source: https://www.cuemath.com/numbers/equivalent-fractions/#:~:text=To%20find%20the%20equivalent%20fractions,equivalent%20fraction%20of%203%2F4.

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