Equivalent Fractions: Examples, Meaning, Methods

Fraction is a number that represents a portion of a whole number. A single object or a collection can make up the whole. The 7/8 number is a fraction. The numerator, in this case, is 7, and the denominator is 8. For any fraction, it is easy to find the numerator and denominator. Equivalent fractions are fractions with distinctive numerators and denominators that add up to the same number. 4/8 and 6/12, for example, are equivalent fractions because they both equal 1/2. Equivalent fractions are fractions that comprise the same proportion of the total.

Read Also: Difference Between Fraction and Rational Numbers

Key Terms: Equivalent fraction, Numerator, Denominator, Number, Proportion, multiplying, Methods, fraction.

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Equivalent Fractions

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Equivalent fractions are two or more fractions that are equivalent if both outcomes after simplifying are the same fraction. Assume a/b and c/d are two fractions that yield equivalent fractions, such as x/y, after simplification. They are now equal.

Example:

For example, 1/2, 2/4, and 4/8 are equivalent fractions. Let's see how their values compare. Each of them is depicted as a shaded quadrilateral pattern. The shaded portions in all the figures represent the same fraction when seen as a whole.

We can see that all the shapes have the same amount of shaded area. As a result, the fractions 1/2, 2/4, and 4/8 are equivalent.

Check Important Notes for Real Numbers

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Finding the Equivalent Fractions

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Equivalent fractions are those in which the numerator and denominator are multiplied or divided by the same number. And that's why these fractions are reduced to the same number when simplified. Let's look at how we can make equivalent fractions in two different ways:

1. Multiplying the same number to the numerator and denominator.

Multiply the numerator and denominator by the same number to find equivalent fractions for any given fraction. Let us take the fraction 1/7 as an example.

• We get 1/7 x 2/2 = 2/14 by multiplying the numerator and denominator with 2.
• We get 1/7 x 3/3 = 3/21 by multiplying the numerator and denominator with 3.
• We get 1/7 x 4/4 = 4/28 by multiplying the numerator and denominator with 4.

As a result, we can draw the conclusion that 

1/7 = 2/14 = 3/21 =4/28

2. The numerator and denominator are both divided by the same number.

Divide the numerator and denominator by the same number to find equivalent fractions for any given fraction. We have to obtain the equivalent fraction of 16/40, for example.

To find the highest common factor between the numbers 16 and 40.

HCF = (16, 40) =8

To get the equivalent fraction of 16/40, divide the numerator and denominator by 8.

(16÷8)/ (40÷8) = 2/5

As a result, 2/5 equals 16/40.

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To check if two fractions are equivalent:

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To determine whether the given fractions are equivalent, we must simplify them. To check whether they are equivalent or not, simplify until both the numerator and denominator are whole numbers. There are several methods for determining whether two fractions are equivalent. Here are a few examples:

1. Making the denominators the same.
2. Converting both the fractions to decimal form.
3. Method of cross multiplication.
4. Visual method.

Let's look at these methods one by one to see if 3/9 and 5/15 are equivalent fractions.

Method 1)

The fractions 3/9 and 5/15 have denominators of 9 and 15. The denominators 9 and 15 have a Least Common Multiple (LCM) of 45. By multiplying the denominators of both fractions with appropriate numbers, we can make the denominators of both fractions 45.

• 3/9 = 3×59×5= 15/45
• 5/15= 5×315×3= 15/45

Both fractions are equivalent to the same fraction of 15/45, as can be seen. As a result, the given fractions are equal.

Method 2)

We can find the decimals of two fractions to see if they are equivalent fractions.

By converting 3/9 and 5/15 to decimal forms, we can see if they are equivalent fractions.

3/9 = 0.333

5/15 = 0.333

Because both fractions produce the same decimal, they are equivalent.

Check Also: Methods of Integration

Method 3)

Two fractions, 3/9 and 5/15, are given.

To get the following result, multiply both fractions together:

Numerator of 1st Fraction X Denominator of 2nd Fraction 

And

Numerator of second Fraction X Numerator of 1st Fraction

3 x 15 = 45 and 9 x 5 = 45

Given the fact that both values are equal, 3/9 and 5/15 are equivalent fractions.

Method 4)

Let's see if each of the fractions 2/6 and 3/9 have the same shape and see if the shaded portions of both are the same.

The shaded parts of both circles represent the same value, as can be seen. In other words, when viewed as a whole, the coloured segments in both figures depict the same part. As a result, the given fractions are equal.

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Things to Remember

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1. All equivalent fractions can be reduced to their simplest form by dividing the numerator and denominator by the HCF. To get an equivalent fraction, you can only multiply or divide, not add or subtract, because the fraction we get from addition and subtraction isn't equal to the value we have.
2. Equivalent fractions are fractions that have the same value despite their appearance. Equivalent ratios are two ratios that measures have the same value. Multiply or divide both numbers by the same number to find an equivalent ratio.
3. The fraction with the higher numerator is the bigger fraction having denominators the same. The fraction with the smallest numerator is the smallest. And, the fractions are equivalent if the numerators are equal considering that the denominator is equal.
4. Equivalent fractions concepts assist us in determining and calculating larger parts as well as reducing them to equivalent smaller parts. If the numerator and denominator of a fraction have no common factor except 1, which is said to be in the simplest or lowest form.

Read More: Addition and Subtraction of Integers

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