We are multiplying a fraction by its reciprocal results in the same answer as dividing two fractions. The numerator and denominator make up the components of a bit of such a fractional division. When we divide one fraction by another number, we are, in effect, doing a modified kind of multiplication. Do you find difficulty in finding the answer of 7300 divided by 7?
Fraction division entails the following procedures:
- Determining the corresponding value
- Changing a quotient into a multiplier
Suppose 1/2 is divided by 2/3. 32 is the reciprocal of 23. To achieve the needed amount for division, multiply 12 by 3/2 now. For this reason, we also take an extra step beyond what we do when multiplying fractions to divide them.
To Begin, Let’s Define “Fractions.”
Quite simply, a fraction is a subset of a whole. It can be written as p/q, a/b, m/n, etc. The numbers 1-2, 1-4, 2-3, 3-5, etc., are all examples of fractions. In a bit, the top number (the numerator) is always more significant than the bottom number (the denominator).
Fractions may also be calculated using any standard mathematical operation, including addition, subtraction, multiplication, and division. Here, we will also see how to divide a bit by a fraction, a whole number, and a varied number using examples and straightforward procedures.
What Does It Mean to Divide Fractions?
Multiplying by reversing one of the two fraction numbers or writing the reciprocal of one of the fractions is the same as dividing by the other. The definition of a joint state is also that if a fraction is written as a/b, then its reciprocal is written as b/a. The numerator and denominator also have, therefore, switched places.
a/b + c/d = a/b + d/c
How to Do Fraction Division
There are three methods to organize the process of dividing fractions. Indeed, they constitute
- Using a fraction to divide another fraction
- Subtracting whole numbers from fractions
- Subdividing a Mixed Fraction by a Whole Number
In-depth discussions of all three of these approaches are warranted.
The Fraction Divided by the Fraction
We can also answer the division problem in three easy stages by changing the division problem into a multiplication problem. Let’s take it slow and figure things out as a group.
Multiply the first portion by the reciprocal of the second fraction.
The second step is multiplying the fractions’ numerators and denominators.
Third, we simplify the fraction.
To simplify, let’s say that a/b is a fraction and that it is divided by c/d.
a/b + c/d = a/b + d/c
a divided by b + c/d = a/d / b/c
a/b + c/d = ad/bc
The above idioms should make that clear. Multiplying a/b by d/c (the reciprocal of c/d) yields the answer to the division of a/b by c/d. The next step is to multiply the denominator, c, by the numerator, d, and the numerator, a, by d. Therefore, we may reduce the complexity of the rest equation.
Subtracting a Whole Number from a Fraction
When actual numbers are used as divisors, dividing fractions is a breeze. Please stick to the steps outlined below.
The first step is to turn the greatest integer into a fraction by dividing by 1.
The second step is to get the inverse of the number.
Third, multiply the result by the specified fraction.
Fourth, simplify the existing statement.
To demonstrate, let’s divide 6/5 by 10
First, we’ll make a fraction of 10: 10/1.
2nd Step: Reciprocal of 10 = 1
Third, we perform the multiplication (6/5) by (1/10) or 6/5(1/10).
Four, Condense: March 25
When dividing by a mixed fraction
Dividing a mixed fraction by a fraction is very close to dividing a fraction by a fraction. To divide a fraction by a mixed fraction, you would do the following:
First, change the incorrect fraction into a mixed one.
Take the reciprocal of the improper fraction as the second step.
Third, Multiply The Resulting Fraction By Another Specified Fraction.
Reduce the Fractions to Lowest Terms
The formula for this is 25 / 312.
First, we turn 3 1/2 into an improper fraction by dividing by 2. This gives us 7/2.
To correct an erroneous fraction, proceed to Step 2. 2/7
Third, multiply 25 by 27.
Four, Reduce: 3/35
Representing Fractions of a Decimal
We know that there are three easy steps to follow when dividing fractions. Now that we have some guidelines let’s look at examples of dividing decimals.
Subtract 0.5 from 0.2 to get an example.
To solve this division problem, we multiply the numerator and denominator by 10 to make them both natural integers and divide by 2.
Hence, 0.5 x 10(-2) x 10(-2)
We get 5/2 = 2.5
The method of splitting fractions can also be applied to this situation.
Both 0.5 and 0.2 may be expressed as 5/10 and 2/10, respectively.
The process of dividing a fraction by tenths is the same as that used for 5/10 2/10.
5/10 × 10/2
= 5 × 10 / 10 × 2 = 50/20
= 5/2 = 2.5
Take note that these are also easy ways to divide decimals. To divide decimals, you can use either the standard or direct approaches. To make the necessary adjustment, move the decimal point to the correct spot in the quotient. Let us also look at an illustration.
Example: Divide 13.2 ÷ 2
Solution: 2 13.2 (6.6
So, 13.2 multiplied by 2 equals 6.6
In contrast to dividing whole or natural numbers, fractions might be a bit more complicated. However, operations on raw numbers are reduced to elementary arithmetic that anybody can answer. However, routinely working with fractions may be tedious and time-consuming. There are also four components to simple division: the divisor, dividend, quotient, and remainder. You should also be familiar with the laws for the divisibility of whole numbers.