Like Fractions And Unlike Fractions

A fraction represents a part of a whole, consisting of two main components. The numerator, which is the number above the line, indicates how many parts are taken. The number below the fraction line is called the denominator, which shows into how many equal parts the whole is divided. For example, if a pizza is divided into six equal slices, then each slice is “one sixth” or  “1 by 6” or \(1\over6\) of the whole.

 Like fractions have similar denominators. In like fractions, the whole is divided into the same number of equal parts. For example, \({4\over10} ,{5\over10}\), and \(6\over 10\); here, the denominators are the same. So they are like fractions.

Unlike fractions, which have different denominators. In other words, unlike fractions divide the whole into different numbers of equal parts. For example, \({3 \over 8}, {{2 \over 4}}, {\text { and }}, {{2 \over 3}}\) . Here, the denominators are different. So, they are unlike fractions.

In this section, we will compare the like and unlike fractions. It will help students to identify which fraction is greater or smaller. 
 

There are four basic arithmetic operations for like and unlike fractions. The four operations are:

• Addition
• Subtraction
• Multiplication
• Division

Let us look at how to conduct each of these operations on like and unlike fractions.

Adding Like and Unlike Fractions 

Adding like and unlike fractions involves adding fractions with the same or different denominators: like fractions are added by combining the numerators, while unlike fractions must first be converted to like fractions using a common denominator before adding.

Addition of Like Fractions:

Like fractions have the same denominator, so to add like fractions, we add the numerators together and keep the same denominator. 

Example: \({2\over5} + {6\over5} = {(2 + 6)\over5} = {8\over5 }\)
 

Addition of Unlike Fractions:
Unlike fractions with different denominators, we must convert them to like fractions before adding.

• First, find the least common multiple and convert each fraction into an equivalent fraction
• Then add the numerators and keep the denominator the same. 
   

Example: \({3 \over 5} + {1 \over 2}\)

LCM of 5 and 2 is 10

Converting the fractions to equivalent fractions: 

\({3\over 5} = {6\over10}\)

\({1\over 2} = {5\over 10} \)

Adding: 

\({6\over10} + {5\over10 }= {11\over10} \\ \ \\ {11\over10 }= {1{1\over10}}\)

Subtraction of Like and Unlike Fractions

Subtraction of like and unlike fractions involves subtracting fractions with the same or different denominators like fractions are subtracted by subtracting the numerators, while unlike fractions must first be converted to like fractions using a common denominator before subtraction.

Subtraction of Like Fractions
Like fractions have the same denominator, so we only subtract the numerators and keep the denominator unchanged.

Example: \({9\over 11} - {4\over 11}\)

\( {9\over 11} - {4\over 11} = {9 - 4\over 11}\)
 

\( = {5\over 11}\)

Subtraction of Unlike Fractions
Unlike fractions that have different denominators, we first make the denominators the same before subtracting.

Step 1: Find the LCM (The Least Common Multiple) of the denominators.

Step 2: Convert each fraction into an equivalent fraction with the LCD.

Step 3: Subtract the numerators, keeping the denominator fixed.

Example: \({7 \over 8}- {1 \over 3} \)

LCM of 8 and 3 is 24

Convert fractions into equivalent fractions:

\( {7 \over 8} = {21 \over 24}\)

\( {1 \over 3} = {8 \over 24} \)

Subtract: \( {21 \over 24} - {8 \over 24} \)

\( {21 \over 24} - {8 \over 24} = {21 - 8 \over 24} \\ \ \\ = {13 \over 24} \)

Multiplication of Like and Unlike Fractions
Fractions are multiplied the same way, whether their denominators are the same or not. To multiply fractions, we multiply the numerators and the denominators.
 

Multiplying like fractions example: \(\frac{5}{2} \times \frac{6}{2} = \frac{5 \times 6}{2 \times 2} = \frac{30}{4} \)

Multiplying unlike fraction example: \(\frac{2}{5} \times \frac{6}{4} = \frac{2 \times 6}{5 \times 4} = \frac{12}{20} \)



Division of Like and Unlike Fractions
Division of like and unlike fractions is done by multiplying the first fraction by the reciprocal of the second fraction. This method works for all fractions, whether like or unlike.

• First, write the reciprocal of the second fraction 
   
• Then, multiply the first fraction by the reciprocal

Example: Dividing like fractions

\({6\over 11} ÷ {3\over11}\)

The reciprocal of \(3\over11\) is \(11\over3\)

Multiply: \(\frac{6}{11} \times \frac{11}{3} = \frac{6 \times 11}{11 \times 3} \)

\(=\frac{66}{33} \\ \ \\ = \frac{6}{3} \\ \ \\ = 2 \)

Example: Dividing unlike fractions

\(\frac{5}{8} \div \frac{2}{3}\)

The reciprocal of 2/3 is \(\frac{2}{3} {\text { is }}\frac{3}{2}\)

Multiply \(= \frac{5}{8} \times \frac{3}{2} = \frac{5 \times 3}{8 \times 2}\)
 

\(= \frac{15}{16}\)

Understanding like and unlike fractions helps students work with fractions more effectively in everyday situations. Here are some real-life examples of like and unlike fractions.

 

• Cooking and baking: Fractional quantities are commonly required for ingredients, such as ¼ cup of sugar and 2/4 cup of flour. If two elements have different denominators, they must be transformed to like fractions before adding.
   

• Construction and Measurement: Carpenters often measure materials using fractions of inches, for example, ¾ inch and ½ inch. Before combining lengths, they convert them into like fractions to ensure accuracy.
   

• Budgeting and Finance: When calculating expenses, fractions are often used to represent parts of the total budget. For example, ½ of the budget for groceries and ¼ for entertainment. To know the total portion spent, convert these unlike fractions to like fractions before adding.
   

• Art and Design: Artists mix paints in fractional parts, for example, ⅔ of blue and ⅓ of yellow to make green. If the proportions have different denominators, they are converted into like fractions to maintain color balance.
   

• Computer Graphics: In computer graphics, like fractions simplify texture mapping, and unlike fractions adjust scaling or Bézier curve weights, ensuring precision in rendering and modeling.

Learning like and unlike fractions helps students understand how fractions relate to each other, strengthens their calculation skills, and builds a solid foundation for solving real-life math problems with confidence.

• To add or subtract like fractions, simply add or subtract the numerators and keep the denominator the same.
   
• When dividing fractions, use the rule Keep → Change → Flip: keep the first fraction, change the division sign (÷) to multiplication (×), and flip the second fraction to its reciprocal.
   
• Parents can help students use fraction apps or games, such as fraction puzzles, matching activities, and drag-and-drop tools, to make learning fun and interactive. 
   
• Teachers can use visual tools such as fraction circles, bars, and number lines to show that denominators remain the same in like fractions.
   
• Teachers can teach students to simplify before multiplying. For example, \({3\over8} × {4\over9} \), here we can cancel 3 and 9, and 4 and 8. Then \( {3\over8} × {4\over9} \implies {{1\over2} × {1\over3}} = {1\over6} \).
   
• Always simplify the final answer when the numerator and denominator share a common factor.