How to Add Fractions With Whole Numbers

Mathematics 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 who find it difficult to understand the subject.

But 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. We will make you understand the basic terms to the complex ones, to further understand how to add fractions with whole numbers.

Whole numbers are natural numbers including 0. They are 0, 1, 2, 3, and so on. Fractions indicate a part of a whole. For instance, ¾ indicates 3 parts of 4. Here, 3 is the numerator and 4 is the denominator. In fractions, we do the process of division. As in our example, 3 is divided by 4. They can also be converted into decimal numbers.(¾ = 0.75).

Whole numbers are fractions with their denominators being 1. For instance, 7 is basically 7/1 with the denominator 1, as dividing by 1 makes no difference. So, when we add a whole number with a fraction, it means, we are in fact adding two fractions with different denominators. It will be clear after observing some examples.

While adding two fractions with same denominator, we just add the two different numerators. For instance, 5/4 + 7/4 = 12/4.
For fractions with different denominators, we need to make the denominators same in both the fractions. In our case, we have to make the denominator, the same as the denominator of the fraction to be added.

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

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

Step#2: 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 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.

Simplifying the steps, 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. Denominator of the result is the same as that of the fraction.
That is easy, isn't it? Now, let's see how to do the same with different denominators 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 and varies for different sets of expressions. Like, the value of x in 2x + 7 = 15 is different from the first expression.

A variable has some value in the given expression. Hence, adding fractions with variables is very similar to the previous process. An example will provide more insight to the steps involved.

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? An illustration on how to tackle these kind of problem should be helpful.

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

The last variation in these kinds of examples can be where both the expressions contain a variable. Let us see some examples of those tricks too.

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.

The process of adding fractions to whole numbers might have helped clear the concept with all the examples. 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.