Division of Fractions

Division is the process of splitting quantities into equal parts. In division, we divide a number by the divisor to get the quotient. Here, we will learn the step-by-step process for dividing two fractions. For instance, \({5\over8} \div {1\over6}\). Now, let’s learn the division of fractions step by step.  

There are certain steps that need to be followed while dividing fractions. Let us learn about these steps here: 

Step 1: Taking the inverse of the second fraction.

Step 2: Simplify the fraction 

Step 3: Multiply the first fraction with the inverse of the second fraction. 

For example,\({5\over15} \div {6\over12} \)

Step 1: Taking the inverse of the second fraction
The inverse of the second fraction \(6\over12\) is \(12\over6\)

Step 2: Simplifying the fractions
\({5\over15} = {1\over3}\)
\({12\over6} = 2\)
 

Step 3: Multiplying the fraction with the inverse of the second fraction. 
\({{1\over3} \times 2} = {2\over3}\)

Let’s learn about the different types of division of fractions like division of fraction with whole number, the division of fraction by fraction, the division of fraction with decimals, the division of fractions with mixed numbers.
 

To divide a fraction with whole numbers, we multiply the whole number by the denominator of the fraction.

Step 1: Taking the inverse of the whole number, that is, 1 by the whole number.
 

Step 2: Multiply the fraction with the new divisor.

For example, \({3\over5} ÷ 4\)
 

Step 1: Replace the whole number (4) with its reciprocal
The reciprocal of 4 is \(1\over4\). 

Step 2: Multiply the fraction with the new divisor
\({3\over5} × {1\over4} = {3\over20}\)
 

To divide a fraction by a decimal, we should first convert the decimal into fraction. Given below are the steps to divide a fraction by a decimal:
 

Step 1: Converting the decimal to fraction.
 

Step 2: Taking the inverse of the divisor.
 

Step 3: Simplify the fraction and multiply the fractions. 

For example, \({3\over4} \div {0.5}\)
 

Step 1: Converting the 0.5 to fraction
0.5 in fraction is \({5\over10} = {1\over2}\) 

Step 2: Taking the inverse of the divisor
Dividing \({3\over4} \div {1\over2 }\)
The inverse of \(1\over 2 \)is \(2\over1\) 
 

Step 3: Simplify the fraction and multiply the fractions. 
\({3\over4} \times {2\over1} = {6\over4}\) 
\(= {3\over2} \)
 

To divide a fraction by a mixed fraction, we should first convert the mixed fraction into an improper fraction. Then, continue with the division process as usual.  

For example: \({​2\over3} \div {1{1\over2}} \)

\({1{1\over2}}\) can be converted into an improper fraction as; 
\({1{1\over2}} ={1 \times 2 + {1\over 2}}\)
\(= {3\over 2}\)

So, \({2\over3} \div {3\over2} = {2\over 3} × {2\over3}  \)
\(= {4\over 9}\)

• Remember the mnemonic “keep, change, flip,” which means to divide fractions: keep the first fraction, change division to multiplication, and flip the second fraction. 
   
• When dividing the mixed number, first convert the mixed number to an improper fraction and then divide the fractions. 
   
• After dividing the fraction, check if the answer shares common factors and simplify the large number to a smaller number. 
   
• To understand division of fractions, students can use visual models like fraction bars or a number line to visualize it.  
   
• When solving word problems related to the division of fractions, read the questions carefully and highlight the dividend and divisor. 
   
• Practicing daily helps students understand the concept and improves their mathematics skills. 

The division of fractions happens every day, and thus it has varied applications. We use it for cooking, time management, construction, and so on. Here are a few real-life applications of dividing fractions. 

 

• In cooking, to find the amount of ingredients required for the recipe, we use the division of fractions. That is, if we require \(3\over 4\) cups of sugar for 1 cup of flour, then for \(1\over 2\) cup of flour the required amount of sugar is half of \(3\over 4\), which is \({3\over4} \times {1\over2} = {3\over8}\)

• To share any object among a group, we use division of fraction.
   

• In construction, to cut the wooden plank of \(3\over4\) meter long into pieces of \(1\over8\) meters, we need to divide. That is, \({3\over4} \div {1\over8} = {3\over4} \times {8\over1} = {6}\).
   

• To split the time into smaller intervals, we use the division of fractions. For example, if a task takes \(3\over4 \)hours and if we want to divide it into sessions of \(1\over8\) hours, we divide it, \({3\over4} \div {1\over8} = {3\over4} × {8\over1} = 6 \) sessions. 
   

• In classrooms, teachers use division of fractions to divide the materials or questions among students.