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Addition and Subtraction of Fractions with Like, Unlike Denominators and Whole Numbers

Add and Subtract Fractions

The basic mathematical procedures of addition and subtraction are also relevant to fractions. Because we take distinct steps in each situation, it is vital to grasp whether the fractions have like or unlike denominators to add and subtract fractions easily. When solving problems involving addition and subtraction fractions, the linkage of these concepts is a key criterion for getting the proper solution.

Fractions are a component of a larger whole. Fractions can be solved using fundamental arithmetic methods. As a result, fractions can be added, subtracted, multiplied, and divided. Let’s review fractions before going on to the addition of fractions.

Like Fractions: Two or more fractions in which the same denominator are known as ‘like fractions’. For example, 3/7, 4/7, 8/7, etc., are like fractions. Note that 7/7 is not a similar fraction because it can be simplified to Unlike Fractions: When the denominator between 2 or more fractions is not the same, the fractions are termed, unlike fractions. For example, 1/7, 5/6, ⅔, etc., are unlike fractions.

In this article, we shall learn to add and subtract both Like and Unlike Fractions. 

How to Add and Subtract Fractions with Like Denominators

Addition of Like Fractions

The addition of fractions with like fractions is quite easy and exactly like the addition of whole numbers. Read the steps below to learn the method to add fractions:

Step 1: Write the like fractions properly with the ‘+’ symbol.

Step 2: Since the denominator is the same in the added fractions, the resultant fraction will also contain the same denominator. 

Step 3: Add the numerators. 

Step 4: Write the answer in the form a/b. Where a is the sum of the numerator and b is the denominator of the addends. 

Example: Add 11/3 with 4/3 

Solution: Reading the steps carefully and applying them to this question, we get:               

Step 1: 11/3 + 4/3

Step 2: The denominator of the answer will be 3. Since they are like functions.

Step 3: 11 + 4 = 15 (adding numerator)

Step 4: Writing the resultant fraction: 15/3 

We can see that in 15/3, 15 can be divided 5 times by 3. Thus the result equals 5. If possible, always simplify your answers. 

Subtracting of Like Fractions

Subtracting two or more fractions with the same denominators follows a similar approach to adding fractions discussed above. The steps involved in subtracting fractions with equal denominators are as follows:

Step 1: Write the like fractions in order with ‘-‘ symbols between them.

Step 2: The denominator of the result will be the same as the denominator of the fractions being subtracted. 

Step 3: Subtract the numbers in the numerators accordingly.

Step 4: Write the answer in the form a/b. Where a is the difference of the numerator and b is the denominator. 

Example: Subtract 3/7 by 9/7.

Solution: Apply the steps mentioned above carefully→           

Step 1: 9/7 – 3/7

Step 2: Since they are like functions, the answer’s denominator will be 7.

Step 3: 9 – 3 = 6 (subtracting the numerator)

Step 4: Writing the resultant fraction: 6/7. 

If the difference of the numerators is a negative number, then the fraction is written in the form -a/b.

This concludes the concept of how to add and subtract fractions when the denominator is alike. Next, we shall learn how to add and subtract fractions with different denominators.

How to Add and Subtract Fractions with Unlike Denominators

Adding Fractions with Unlike Denominators

The addition of fractions with unlike denominators is quite a tricky task. It is not as simple as adding ‘like fractions’ because the denominators here are of different magnitude. The resultant denominator, in this case, is the LCM (Least Common Multiple) of the denominators. See the steps below to understand the trick to solve unlike fractions:

Step 1: Write the like fractions properly with the ‘+’ sign.

Step 2: Find the resultant denominator by finding the LCM of the denominators. 

Step 3: Multiply the numerators according to the LCM. Add the respective numbers to get the value of the resultant numerator.

Step 4: Write the outcome in the form a/b. Where a is the total of the numerator and b is the denominator (LCM). 

Example: Add the fractions given as 5/4 and 2/9.

Solution: We will solve this using the stepwise approach mentioned above:

Step 1: 5/4 + 2/9

Step 2: Since they are unlike fractions, we have to find the LCM of 4 and 9. 36 is the LCM of 4 and 9.

Step 3: Now, we multiply the numerators accordingly. For 5/4, 4 divides 36 nines times; hence we will multiply 5 by 9 = 45. Similarly, for 2/9, 9 divides 36 four times; hence 2 is multiplied by 4 = 8. Now we add 45 and 8 = 45 + 8 = 53.

Step 4: Therefore, the resulting fraction is 53/36. It cannot be simplified; hence the fraction remains 53/36.

The LCM is taken to make the, unlike fractions into like fractions. The rest of the procedure remains the same. 

Subtracting Fractions with Unlike Denominators

Subtracting, unlike fractions, is yet another tricky but important arithmetic concept of fractions. It follows the same procedure as adding, unlike fractions. The only change is that we find the difference here instead of summing. The stepwise approach to subtracting two unlike fractions is:

Step 1: Write the like fractions properly with the subtraction ‘-‘ sign.

Step 2: The resultant denominator is calculated by finding the LCM of the denominators. 

Step 3: Accordingly, multiply the numerators with the LCM. Add the outcomes to find the value of the resulting numerators. 

Step 4: The outcome should be written in the a/b form. Where a is the difference of the numerator and b is the LCM of the denominator. 

Example: Subtract the fractions given as 3/4 and 1/8

Solution: We will solve this using the stepwise approach mentioned above:

Step 1: 3/4 – 1/8

Step 2: Since they are unlike fractions, we must find the LCM of 4 and 8. 8 is the LCM because 4 x 2 = 8 and 8 x 1 = 8.

Step 3: Now, we multiply the numerators accordingly. For 3/4, 4 divides 8 two times; hence we will multiply 3 by 2 = 6. Similarly, for 1/8, 8 divides itself 1 time; hence 1 is multiplied by 1 = 1. Now we subtract 6 and 1 = 6 – 1 = 5.

Step 4: Therefore, the resulting fraction is 5/8.

Sometimes you may find the LCM to be one of the denominators. This is possible when the denominators are multiples of each other. The highest multiple becomes the denominator.

Adding and Subtracting Fractions with Whole Numbers

We have learned how to add or subtract a fraction with another fraction. Now let us learn how to add and subtract fractions with whole numbers. Try always to make the fractions in improper form for arithmetic operation. The trick behind the addition or subtraction of a fraction and whole number is to convert the whole number into a fraction. This can be done by placing 1 as the denominator of the whole number. 

The whole number and fraction can be added or subtracted using the procedure discussed for unlike fractions.

Example: Add 6/5 and 11 

Solution: Step 1: Convert 11 into fractional form as 11/1.

               Step 2: The LCM of 6/5 and 11/1 is 5. Because 5 is a multiple of 1.

               Step 3: Multiplying 6 by 1 in 6/5 and 11 by 5 in 11/1. Add the numerators  

                            6 + 55 = 61.

               Step 4: The resultant fraction is 61/5. 

Note that the LCM in the case of addition and subtraction of two fractions is always the bigger number. This is because every number is a multiple of 1. 

Important Reminders:

  • To sum unlike fractions, use these steps:

a) Using the LCM of the denominator, convert the given fractions to like fractions.

b) Determine the corresponding fractions of the following fractions with the LCM as the denominator.

c) Add the numerators while keeping the denominator the same.

  • Never individually subtract or sum the numerators and denominators of unlike fractions. This will yield a faulty result. Follow the rules mentioned in every topic of this article.
  • It is not essential to find the LCM of the denominators while adding or subtracting, unlike fractions. Any standard multiple will suffice. So we can get a common multiple by multiplying the two denominators. Although this produces larger-looking numbers, it may be reduced to its simplest form.

Frequently Asked Questions

1. How to Add and Subtract Fractions?

Ans. To add a fraction, you just add the numerators. To subtract a fraction, you just subtract the denominators. For example: to add one-third and two-thirds, multiply 1 by 2 and then multiply 3 by 3. Add those two numbers together to get 7/9.If you want to subtract one-third from two-thirds, multiply 1 by 2 and then multiply 3 by 3 again. Then subtract the two numbers that you just multiplied together—in this case, 6/9.

2. How to Add and Subtract Fractions with Different Denominators?

Ans. Addition and subtraction of fractions with different denominators is a simple process that requires you to add or subtract the numerators, multiply the denominators by the same number, and then add or subtract the resulting numerators again.

3. How to Add and Subtract Fractions with Whole Numbers?

Ans. To add and subtract fractions with whole numbers, you first need to convert each fraction into a fraction that has the same denominator. For example, if you had to add 1/2 + 1/4, you’d convert both of those into 3/4 by dividing both by 2. Then, you would add them together as if they were whole numbers. To subtract one fraction from another, it’s similar—just make sure that the denominators are the same for both to start off with!

4. How to Add and Subtract Fractions with Mixed Numbers?

Ans. To add or subtract fractions with mixed numbers, you’ll first have to convert them into improper fractions. To do this, you simply take the larger fraction, divide it by the smaller one, and then multiply that result by 100%. Then you can add or subtract as normal.

5. What are the Rules for Adding and Subtracting Fractions?

Ans. The rule of adding and subtracting fractions is pretty simple:

1) If the denominators are the same, add the numerators together and write that over the denominator of the first fraction.

2) If the denominators are not equal, you’ll need to multiply them by some common number (that is, a number that both denominators divide evenly into). Then add or subtract as usual.

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