Divide Fractions by Whole Numbers

We are well-acquainted with the rules of dividing whole numbers with one another. The trouble lies in dividing fractions with fractions or fractions with whole numbers. Various dividing fractions calculators are available on the internet. But why do we need dividing fractions calculators when we can learn to divide fractions?

What are Fractions? 

First, let’s recall what a fraction is. A fraction is the representation of a whole quantity into parts. It means if whole chalk is divided into two halves, then a fraction is used to denote those two divided parts. A fraction consists of two parts – the top part is known as the numerator, and the bottom part is the denominator. Can you recall how to write a fractional value?

In the above example of chalk, the whole chalk was one unit, which later was cut into two parts. Therefore, the fractional representation of those two parts will be 1/2and 1/2. In this, 1 is the numerator, and 2 is the denominator.

Multiplying ½ and ½ is simple. What do we get? ¼? Multiplication of fractions is direct and simple. The operation between same-facing fractions occurs. For example, ½ x ½ means 1 x 1 and 2 x 2. Therefore, the result will be ¼. Now, what about dividing fractions? Shall we do the lengthier method of using divisor, dividend, and quotient?

How to Divide Fractions? 

People generally confuse dividing fractions because they cannot remember the simple rule of thumb. Make sure to remember the rule described in the upcoming steps.

Rule number 1: Keep

How do we keep the fractions? Same as they are represented in the questions? No! To keep a fraction means keeping the first fractional value as it is before proceeding to the next step.
For example, a question asking about dividing fractions consists of three values:3/5 ÷ 6/7. In this, ⅗ will be kept as it is before performing division. So, to operate the question, it now becomes 3/5 ÷ 6/7.

Rule number 2: Change

After learning to keep the fraction, the next step is to change. Take a guess what it could be? Change the question? Or the numerical value? Neither of these! We need to change the division sign into multiplication. Yes, you got it right! Dividing fractions means changing the sign to multiplication but does not operate. But why divide, and not add or subtract? Because multiplication is the opposite of division, and addition is the opposite of subtraction. There is a third rule remaining. So, after the second rule, i.e., changing, the question now becomes 3/5 x 6/7.

Rule number 3: Flip

After performing rules numbers 1 and 2, the third rule is the most important and simplest one. It says flip! Many are confused when they learn flipping and tend to flip the entire fractional value, which is wrong. Only the value after the multiplication sign needs to be flipped. In this case, the number 6/7 must be flipped. After rule number 3, the final question becomes 3/5 x 7/6.

And that’s it! The basic rules on how to divide fractions are complete. Then, apply the multiplication operation between the numbers, which is direct and face to face, and get the final answer. Therefore, after dividing 3/5 ÷ 6/7, i.e., 3/5 x 7/6, the final answer is 21/30. How? 7 x 3 and 5 x 6. Multiplication is direct and face to face and easier than division. It means numerator gets multiplied by numerator directly and denominator by denominator.

Another rule to always keep in mind, divide the numerator and multiply the denominator when dividing fractions. The opposite holds when multiplying fractions. The key rule is to operate the operator in the numerator that is asked in the question.

Let us take another example, as explained in the picture below. Remember the rule: Keep, Change and Flip to divide any fractions without using a dividing fractions calculator.

Dividing fractions was effortless. Now, how to divide fractions with whole numbers? Are they complicated or uncomplicated?

Dividing Fractions by a Whole Number 

Why do we need to learn how to divide fractions with whole numbers? Understanding dividing fractions by whole numbers assist in representing bigger quantities into small units. For instance, if we got a slice of bread. We need to cut the whole bread into 3 halves. 3 halves? What is that number? Yes, 3 halves! Confusing, right? So, instead of saying 3 halves, we say cut the slice of bread into ⅙ parts. That’s understandable, isn’t it? This is where dividing fractions by whole numbers come into existence.

The rule for dividing fractions is applicable while dividing fractions by whole numbers. Keep, Change and Flip. But the whole numbers do not have a denominator! What to do in that case? Well, every whole number has a denominator, 1. Therefore, anything multiplied or divided by 1 will give the same number. But infractions, dividing the number by 1 will result in the same value. Therefore, keeping 1 as the denominator is allowable.

Now, coming back to the rule. Consider a question 8/9 ÷ 6. The first rule says to keep the first part of the question. Consequently, 8/9 is retained as it is. Therefore, the question after rule number 1 becomes 8/9 ÷ 6.
The next rule says to flip the division sign into a multiplication sign. Hence, after operating rule number 2, the question becomes 8/9 x 6.

The third rule says to flip the last part of the question. For example, the above question can be written as 8/9 ÷ 6/1. So, after flipping the last part of the question, it becomes 8/9 x 1/6.

The final step is to operate the multiplication operator and obtain the results. The result will be 8/54, because 8 x 1 = 8 and 9 x 6 = 54. The fractional value can be simplified further as it is divisible by 2. So, the final answer will be 4/27.

What can we conclude from this? Where to operate the whole number when dividing fractions by whole numbers? The general rule is to multiply the whole number in the fraction’s denominator. Yes, every time we need to do that! For instance, let us divide ¾ with a whole number 5. One can directly multiply 5 with the fraction’s denominator, which is 4 here. The final answer after division will be 3/20, which is the final answer we will get after applying the Keep, Change, and Flip rule.

Now, we know why mentioning ⅙ is better than saying 3 halves. So, after learning how to divide fractions with whole numbers, can we divide a fraction with a decimal? And can we divide a fraction with a mixed fraction? Obviously! Use the universal rule: Keep, Change and Flip and practice the examples below.

Dividing fractions with Examples

Example 1: What is the answer to the fraction 4/6÷4/46?
Solution: Using the universal rule, keeping 4/6 as it is, changing the division sign into multiplication, and flipping 4/46, the final answer will be:
4/6×46/4= 23/3. 23/3 is the simplified answer as 46 and 6 are divisible by 2.

Example 2: What is the answer to 6/7÷ 8 ÷ 2/9?
Solution: If a question contains more than two fractions, the universal rule will be the same. The only difference is to flip two fractions after keeping the first one.
In this case, the question becomes 6/7×1/8 x 9/2.
Multiplying the fractions, we get 54/112. How? 6 x 1 x 9 and 7 x 8 x 2.
Simplifying the fraction, we get 27/56.

Example 3: Simplify 42/45÷ 0.6
Solution:
This example can be solved in two ways.

Way 1
While dealing with the whole number, we know we can directly multiply the whole number with the denominator. So, if we consider 0.6 as a whole number, we can multiply it directly with the denominator.
The final answer will be: 42/45x 1/0.6 42/(45x 0.6)= 42/27.

Way 2
Converting the decimal value 0.6 into fractions and applying the Keep, Change, and Flip rule.
0.6 can be written as 6/10.
Therefore, the question becomes 42/45÷6/10.
To solve this, applying the keep, change, and flip rule, we get,
42/45×10/6= 420/270. This fractional value can be simplified as 42/27.
So, one can choose either of the two methods to solve dividing fractions with decimals.