How to Add Fractions with Whole Numbers

Mathematics is a subject which brings out completely contrasting emotions in a student. Those who understand the simple tricks and procedures involved in solving a math problem are simply excited and look forward to any math exam, while on the other hand, solving a math problem can be taxing and confusing for students for whom numbers just keep rotating in their head, no matter how much they try to understand it all. But let me tell you, maths can actually be very simple and intriguing once you understand the simple basics! It's all in the mind; so just convince yourself that it is easy. I assure you, there's no subject simpler than mathematics. Now, let us understand the basic terms first like whole numbers and fractions, to further understand how to add fractions with whole numbers.

Whole numbers are all the natural numbers (1, 2, 3, 4,......, also called counting numbers) and 0. Simply speaking, whole numbers are 0, 1, 2, 3 and so on. Fractions are numbers indicating part of a whole. For instance, ¾ indicates 3 parts of 4. Here, 3 is called the numerator and 4 is called the denominator. In a fraction, we do the process of division. As in our example, 3 is divided by 4. Fractions can also be converted into decimal numbers, which means numbers with a decimal point (¾ = 0.75). However, without getting into the details of decimal numbers, let's concentrate on how to add fractions with whole numbers.

Adding Fractions with Whole Numbers

Before moving on to the actual process of addition, bear in mind that whole numbers are nothing but fractions with their denominators being 1. For instance, the whole number 7 is basically 7/1 with the denominator 1, as dividing by 1 makes no difference to the actual number. So, when we add a whole number with a fraction, it means, we are in fact adding two fractions with different denominators. All the examples given below will best explain this simple operation.

How to Add Fractions with Unlike Denominators
When we add two fractions with same denominator, we just add the two different numerators. For instance, 5/4 + 7/4 = 12/4. There's nothing special to do while adding fractions with different denominators except that we have to make the denominators same. In our case, we have to make the denominator of the whole number, which is 1, same as the denominator of the fraction to be added. It will be best explained through the following example.

Question: Do the following addition 4/5 + 3.

Step#1: Convert the whole number into a fraction by putting the denominator as 1. So, the question becomes 4/5 + 3/1.

Step#2: As we add fractions with unlike denominators, take the LCM (Least Common Multiple) of the denominators, which is actually the denominator of the fraction in the question. In our example, it is 5.

Step#3: Multiply and divide the whole number with the LCM so as to complete the process of making the denominators common.
4/5 + (3×5) ÷ (1×5) = 4/5 + 15/5.

Step#4: Now, just add the numerators and you get the required answer.
4/5 + 3 = 19/5.

Putting above steps in one line, you have to simply multiply and divide the whole number with the denominator of the fraction and add the number got in the numerator with the numerator of the fraction. And you have the answer with the denominator of the answer same as the fraction in question. That is easy, isn't it? Now, let's see how to add fractions with different denominators when variables come into picture.

How to Add Fractions with Variables
You must have come across some expression as 2x + 3 = 9. Here, 'x' is called a variable, which denotes some number. When we simplify this expression, we get x=3. Variables are symbols that represent a quantity or number and varies for different sets of expressions. Like, the value of x in 2x + 7 = 15 is different from the first expression. Now, what to do when we have to add fractions with variables. Don't worry, it's as simple as adding whole numbers with fractions.

What is a variable? It has some value in the given expression. So, it is some whole number. Hence, adding fractions with variable is very similar to adding fraction with a whole number. Consider the following example with the explanation given in the above mentioned steps.

Example 1: Add 3/5 + ×

Step#1: 3/5 + x/1
Step#2: LCM of denominators = 5
Step#3: 3/5 + (x×5) ÷ (1×5)
Step#4: Answer is (3+5x) ÷ 5 (remember, we cannot add a whole number and a variable)

What if the fractions themselves contain the variable and we have to add it with a whole number? Look out the following example and you will find out there's nothing different.

Example 2: Add 5x/2 + 7

Step#1: 5x/2 + 7/1
Step#2: LCM of denominators = 2
Step#3: 5x/2 + (7×2) ÷ (1×2)
Step#4: Answer is (5x+14) ÷ 2

Last variation in these kinds of examples can be where fraction and the number to be added both contain a variable. Check this example to understand it.

Example 3: Add 3x/4 + 7x

Step#1: 3x/4 + 7x/1
Step#2: LCM of denominators = 4
Step#3: 3x/4 + (7x×4)/(1×4)
Step#4: Answer is (31x) ÷ 5 (by simply adding the prefixed numbers of the common variable)

If the variable is in the denominator, the steps remain same with the variable becoming the LCM.

I hope I have simplified the process explaining how to add fractions with whole numbers with all the simple examples given above. You have to keep in mind that no maths problem is as difficult as it seems to be. Some clarity in basics, some practice, and a mind free of preconceived notions, can help you solve any problem with minimum fuss.