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 1/6 of the whole.

 

 

What is Like Fractions? 

 

Like fractions have similar denominators. In like fractions, the whole is divided into the same number of equal parts. For example, 4/10, 6/10, and 8/10; here, the denominators are the same. So they are like fractions.

 

 

What is Unlike Fractions?

 

Unlike fractions have different denominators. In other words, unlike fractions divide the whole into different numbers of equal parts. For example, ⅜ and 4/6. 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. 
 

 

Features	Like Fractions	Unlike Fractions
Definition	Fractions that have the same denominator.	Fractions that have different denominators.
Examples	3/6, 5/6, 2/6	3/4, 4/6, 6/8
How to Compare	Compare the numerators directly. The fraction with the larger numerator is greater.	Convert to a common denominator (LCD), then compare the numerators.
Comparison Examples	5/6 > 2/6 because 5 is greater than 2.	Convert 2/5 = 14/35, 3/7 = 15/35. Since 15 is greater than 14, 3/7 > 2/5.

 

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.

 

 

Addition of Like Fractions and Unlike Fractions

 

Like Fractions

Step: In like fractions, we need to simply add the numerators since the denominators are the same.

Example: 6/8 + 4/8 = 10/8

 

 

Unlike Fractions

Step 1: Find a common denominator (the least common denominator)

 

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

 

Step 3: Add the numerators while keeping the denominator fixed.

 

Example: To add 2/3 + 3/4: 

Find the LCD of 3 and 4 → 12

Convert into fractions:

 

2/3 = 8/12, 3/4 = 9/12

Add the numerators:

then 8/12 + 9/12 = 17/12
 

Now we add: 812 + 912 = 8 + 912 = 1712

The result can also be expressed as a mixed number, as the fraction is improper. To convert \(\frac{17}{12}\) into a mixed number, divide \(\frac{17}{12}\); then we will get 1 as the quotient, 5 as the remainder, and the denominator stays the same as 12. So, \(\frac{17}{12} = 1 \frac{5}{12}\).

 

 

Subtraction of Like Fractions and Unlike Fractions

 

Like Fractions

Step: Subtract the numerators directly.

Example: 7/10 - 3/10 = (7-3)/10 = 4/10

 

 

Unlike Fractions

Step 1: Find the LCD of the denominators.

Step 2: Convert fraction to have the LCD.

Step 3: Subtract the numerators.

 

Example: Subtract 5/6 from 3/4:
The LCD of 6 and 4 is 12.
Now convert:  3/4 = 9/12, 5/6 = 10/12Convert to LCD 12 → 9/12 - 10/12
After converting into like fractions with the same denominators. We subtract: 9/12 - 10/12 = -1/12.

 

 

Multiplication of Like and Unlike Fractions

 

Fractions are multiplied in the same way, whether they are like or unlike. 

 

Step: Multiply the numerators and denominators together.

Example: 2/5 × 3/7 = (2×3)/(5×7) = 6/35. Students can simplify before multiplying by cancelling common factors between any numerator and any denominator.

 

 

Division of Like Fractions and Unlike Fractions

 

 

Fractions are divided by multiplying by the divisor’s reciprocal.

 

 

Step 1: Write the second fraction’s reciprocal (reverse the numerator and denominator).

 

Step 2: Multiply the first fraction by this reciprocal.

 

 

Example: To divide 49 by 23:

 

Find the reciprocal of 23, which is 32.
Multiply: 4/9 ÷ 2/3 = 4/9 × 3/2
Simplify: 2/3

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.