Adding Fractions With Unlike Denominators

When two fractions have different denominators, they are often referred to as unlike fractions. Fractions like 2/7 and 8/9 are examples. To find their sum, we first need to determine their Least Common Multiple (LCM). The next step is to multiply the numerator and denominator of both fractions by the correct factors to make them like denominators.

To add fractions with unlike denominators, follow the steps given below:

Step 1: We first determine the Least Common Multiple (LCM) of the denominators of the given fractions.

Step 2: Then, make the denominators the same by multiplying the numerator and denominator by the appropriate factors.

Step 3: Find the sum of these fractions by adding their numerators.

Step 4: Express the sum in its simplest form.

As we have learned the different steps involved in adding unlike fractions, let’s understand them with the help of an example:

Adding 2 Fractions with Different Denominators

To add 2 fractions with different denominators, we use the same steps as discussed:
Add 3/4 + 5/8
Solution:
 

1. We first find the LCM of 4 and 8:

•  LCM = 8

2. Now, we make the denominators equal by converting them to 8:

• Since 5/8 already has 8 as the denominator, we will only convert the denominator of 3/4.

3. Determine what, when multiplied by 4, gives 8:

4. Multiply by 2 with both the numerator and denominator resulting 6/8.

5. Now add the numerators, since the denominators are the same. 
3/4 + 5/8 = 6/8 + 5/8 = (6 + 5)/8 = 11/8.

• We can express it as a mixed fraction of 1 3/8.

Adding 3 Fractions with Different Denominators

Similarly, we add three fractions with different denominators:
Add 2/3 + 4/7 + 5/7
Solution: 

1.The LCM of 3 and 7 is 21

2. Now, we will multiply the fractions by appropriate factors that give 42 as the denominator:

• 2/3 → (2 × 7)/ (3 × 7) = 14/21
   
• 4/7 → (4 × 3) / (7 × 3) = 12/21
   
• 5/7 → (5 × 3)/ (7 × 3) = 15/21

3. Add the numerators:

• (14 + 12 + 15)/21 = 41/21

4. Convert to a mixed fraction:

• 41/21 = 1 20/21

Adding Mixed Fractions with Unlike Denominators

Before adding mixed fractions, we must convert them into improper fractions and follow similar steps. Let’s look at the steps involved using an example:
Add 3 2/5 and 2 3/4 

Convert into improper fractions:

3 2/5 = (3 × 5 + 2) /5 = 17/5
2 3/4 = (2 × 4 + 3)/4 = 11/4

LCM of 4 and 5 is 20

Now, convert the fractions to have the same denominator, 20

17/5 = (17 × 4) / (5 × 4) = 68/20
11/4 = (11 × 5)/ (4 × 5) = 55/20

Add the numerators:
(68 + 55)/ 20 = 123/20

Convert to a mixed fraction:
123/20 = 6 3/20

Solving unlike fractions helps students develop problem-solving skills. Let’s look at a few real-life applications with unlike denominators:

• When cooking a recipe, the quantity of ingredients usually comes in different fractions. For example: 1/3 cup of flour and 1/2 cup of sugar.

• It helps us divide food items into different fractional portions. For example, 3/8 and 4/7 of a cake.

• Understanding the addition of unlike fractions enables us to determine the total distance covered. For example: running 1/5 of a mile in the afternoon and 3/5 in the evening.

• Adding unlike fractions is useful in determining the total amount to be filled in a jar.