Reciprocal and division of fractions space two various methods. When the numerator and also denominator that a portion are interchanged, then it is stated to it is in it’s reciprocal. Suppose a fraction is a/b, climate it’s reciprocal will certainly be b/a. A fraction is a numerical amount that is not a entirety number. Rather it to represent a component of the whole. Because that example, it speak how numerous slices of a pizza are continuing to be or eat of the entirety pizza, such together one-half (½), three-quarters (¾) etc. Division of fountain is an procedure performed top top fractions v multiple steps. Also, learn separating fractions here.

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Parts of FractionThe fraction has two parts:

NumeratorDenominator.

Types the Fraction: Fractions room basically of three types, proper, improper and also mixed. Discover the interpretations below.

Proper Fraction: If both the numerator and denominator room positive, and also the molecule is less than the denominator, then it is a suitable fraction.

Example: 2/5, 1/3, 3/6, 7/8. 9/11, etc.

Improper Fractions: Fractions having actually numerator greater than the denominator are dubbed Improper fractions.

Example: 8/3, 3/2, 6/3, 11/9, etc

Mixed Fraction: When a totality number and a proper fraction are combined, that is well-known as a mixed fraction.

All these details to be the basics that fractions. Now let us discover reciprocal that fractions together with its division.

## Reciprocal of Fractions

The portion obtained by swapping or interchanging Numerator and also Denominator v each various other is known as mutual of the offered fraction.

For example, a reciprocal of 5 is 1/5, a reciprocal of 8/3 is 3/8.

The mutual of a mixed portion can be acquired by convert it into an improper fraction and climate swap the numerator and also denominator.

For example, to find the mutual of (small 2frac13);

Convert the mixed portion into wrong fraction:(small 2frac13=frac73)Now invert the fraction: 7/3 and 3/7, whereby 3/7 is referred to as reciprocal the 7/3 or (small 2frac13).

Note: The product that a fraction and it’s mutual is always 1.

## Division the Fractions

Division entailing a portion follows specific rules. To carry out any division involving fraction just main point the very first number through the reciprocal of the second number. Actions are together follows:

Step 1: an initial change the department sign (÷) to multiplication sign (×)

Step 2: If we change the authorize of division to multiplication, in ~ the exact same time we have to write the mutual of the second term or fraction.

Step 3: Now, main point the numbers and also simplify the result.

These rule are typical for:

Division the the entirety number through a fraction.Division the a portion by a whole numberDivision that a fraction by one more fraction.

Note: that is to be provided that division of fountain is usually the multiplication of portion obtained by reciprocal of the denominator (i.e. Divisor).

### Examples of divisions of Fractions

Examples for each the the condition as mentioned previously are defined below.

Division the the entirety Number by a Fraction

Example 1: 16 ÷ 4/3

Solution: 16 ÷ 4/3 = 16/1 × 3/4

3/4 is the reciprocal of 4/3.

Hence, (16 × 3)/(1×4)

4 × 3 = 12

Therefore,

16 ÷ 4/3 = 12

Division of a portion by a totality Number

Example 2: Divide 8/3 by 3

Solution: We need to simplify, 8/3 ÷ 3

The reciprocal of 3 is 1/3.

Now creating the provided expression right into multiplication form,

8/3 × 1/3 = 8 /9

Therefore,

8/3 ÷ 3 = 8/9

Division of a fraction by another Fraction

Example 3: 8/3 ÷ 4/3

Solution: 8/3 ÷ 4/3

Reciprocal of second term 4/3 is 3/4.

Now main point the very first term with the reciprocal of the second term.

8/3 × 3/4 = 8/4 = 2

Hence,

8/3 ÷ 4/3 = 2

To perform department involving blended fraction, transform the mixed portion into one improper portion and follow the over steps.

Study more on the connected topics such together representing fractions on a number line at BYJU’S today!

The reciprocal of a portion will acquire by interchanging the numerator and denominator. For example, y/x is the mutual of the fraction x/y, i.e. Y/x = 1/(x/y).
When separating fractions by entirety numbers, we should transform the department into multiplication by composing the reciprocal of the divisor, i.e. A totality number. For example, separating 2/3 through 2 deserve to be performed by converting together (2/3) × (1/2). Hence, the simplification becomes basic now.
To simplify the department process when dividing fractions, reciprocals are provided so that division will be converted to multiplication. For example, (4/5) ÷ (8/7) can be composed as (4/5) × (7/8).

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The reciprocal rule of division method is “Multiply the dividend by the reciprocal of the divisor”. In simple words, invert the divisor and also multiply through the dividend.