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 the whole number it is divided into. For example, if a pizza is divided into six equal slices, then each slice is “one sixth” or  “1 by 6” or “ 16”  of the whole.

What is Like Fractions? 

Like fractions have similar denominators. 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. 
 

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: 68 + 48 = 6 + 48 = 108

Unlike Fractions

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

Step 2: For converting each fraction with the common denominator, then calculate the common multiples of all the denominators of the fractions. 

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

Example: To add 23 and 34:

First, we must change the unlike denominators to a common denominator; for that, we need to find the least common denominator of 3 and 4.
Multiples of 3: 3, 6, 9, 12, 15….
Multiples of 4: 4, 8, 12, 16….

Here, the least common multiple that appears in both lists is 12. Therefore, 12 is the LCD of 3 and 4.

Next, we convert the fractions to get the denominator 12.

Convert: 23 = 2 × 43 × 4 = 812
34 = 3 × 34 × 3 = 912

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 17/12 into a mixed number, divide 17/12; then we will get 1 as the quotient, 5 as the remainder, and the denominator stays the same as 12. So, 17/12 as a mixed number is 1512.

Subtraction of Like Fractions and Unlike Fractions

Like Fractions

Step: Subtract the numerators directly.

Example: 710 - 310 = 7 - 310 = 410

Unlike Fractions

Step 1: Find a common denominator (LCD).
Step 2: Convert each fraction.
Step 3: Subtract the numerators.

Example: Subtract 56 from 34:
The LCD of 6 and 4 is 12.
Now convert: 34 = 3 × 34 × 3 = 912, 56 = 5 × 26 × 2 = 1012
After converting into like fractions with the same denominators. We subtract: 912 - 1012 = 9 - 1012 = -112.

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: 25 × 37 = 2 × 35 × 7 = 635. 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: 49 ÷ 23 = 49 × 32 = 4 × 39 × 2 = 1218
Simplify: 1218 = 23
 

Understanding like and unlike fractions helps students to 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.

• Purchase and discounts: When providing discounts or splitting bills while purchasing, we frequently work with fractions.

• Dividing food and resources: Fractions are commonly used when sharing food like cake, biscuits, or pizza; fractions are used to divide them evenly. If a cake is cut into 6 equal slices and one person eats 3/6 while another eats 2/6, the total consumed is easy to find.