How to Add Fractions with Whole Numbers: Student Tutorial

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Plus, learn how to add 2 mixed numbers

Co-authored by Luke Smith, MFA Reviewed by Grace Imson, MA

Last Updated: February 27, 2025 Fact Checked

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Adding Fractions & Whole Numbers

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Adding Mixed Numbers

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Before you can add a whole number and a fraction together, you need to make sure you’re dealing with just one type of number. To do this, we convert the whole number to a fraction and then find a common denominator. Then, the rest is simple addition! We talked to math tutor David Jia to show you how to do just that, as well as how to add two mixed numbers together. Read on to learn more!

Adding Whole Numbers & Fractions: Overview

Convert the whole number into a fraction by giving it a denominator of 1. Then, find a common denominator by multiplying the denominators of both fractions together. Multiply the numerators by the same factor as the denominators, then add the numerators together. Simplify your answer to a whole or mixed number.

Section 1 of 2:

Adding Fractions & Whole Numbers Together

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1
Convert the whole number into a fraction. To do this, simply add a denominator of $1$ to your whole number. Remember, the denominator tells you how many parts are needed to make a whole, and the numerator tells you how many parts you have . ^{[1]
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Research source} So, putting the whole number over 1 tells us we have that many whole parts.
- For example, $2+{\frac {3}{4}}$ . This will now become ${\frac {2}{1}}+{\frac {3}{4}}$ .
2
Multiply the denominators to find a common denominator. Before we can add the fractions, they need to match denominators, Jia says. There are two ways to do this. First, we could find the least common denominator . ^{[2]
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Research source} Or, we could simply multiply the two denominators together, which is often easier, so that’s how we’ll do it here.
- For example, we have ${\frac {2}{1}}+{\frac {3}{4}}$ . When we multiply the denominators together, we get $1*4$ , which is $4$ , so that’s our new common denominator.
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3
Convert both numerators to match the new denominator. Now, we need to make sure that our fractions still have the same value after we changed our denominator. To do this, we multiply the numerator of each fraction by the same number that we multiplied the denominator by. ^{[3]
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- For the first fraction, ${\frac {2}{1}}$ , we multiplied the denominator by $4$ , so we’ll do the same to the numerator: $2*4=8$ . Put this new numerator over the new denominator to get ${\frac {8}{4}}$ .
- Since $\frac{3}{4}$ already has a numerator of $4$ , we don’t have to multiply the numerator by anything—we can leave it as it is.
4
Add both fractions. Now that you've got two fractions of the same denominator, we can add both fractions' numerators together, leaving the denominator as it is. ^{[4]
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- For example, now we have ${\frac {8}{4}}+{\frac {3}{4}}$ . Adding these, we get ${\frac {11}{4}}$ .
5
Divide the numerator by the denominator to simplify your answer. We’re left with an improper fraction, but we can’t stop there. Now, we convert our improper fraction to a mixed fraction just by dividing the numerator into the denominator, Jia says. Doing this can get you either a mixed fraction or a whole number. Both would be correct depending on the numerator and denominator divisibility. For example, our final answer was ${\frac {11}{4}}$ :
- $11/4=2$ , with $3$ parts left over as the remainder.
- The whole number stands alone, and we put the remainder over our new denominator to find the fraction part of our mixed number. So the answer is now $2{\frac {3}{4}}$ .

Section 2 of 2:

Adding Mixed Numbers

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1
Convert both mixed numbers into improper fractions. Before we can add mixed numbers together, we need to make them improper fractions . Multiply each whole number by the denominator of the fraction that it’s next to. Then, add the product to that fraction’s numerator to get the new improper fraction. ^{[5]
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Research source} For example, say we want to add $3{\frac {1}{2}}+2{\frac {3}{4}}$ :
- Starting with the first fraction, we multiply $2*3=6$ . Then, add this to the fraction’s numerator: $6+1=7$ . Put this number over the denominator to get ${\frac {7}{2}}$ .
- Do the same operations with the second fraction, $2{\frac {3}{4}}$ . $4*2=8$ . Then, $8+3=11$ , so our second improper fraction is ${\frac {11}{4}}$ .
- Now, we have the equation ${\frac {7}{2}}+{\frac {11}{4}}$ .
2
Multiply the denominators to find a common denominator. Now we have two improper fractions, but before we can add them together, Jia reminds us that we need to make their denominators match. We can do this either by finding a least common multiple, or just by multiplying the denominators together, which, in this case, is easier. ^{[6]
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- We’re working with the fractions ${\frac {7}{2}}$ and ${\frac {11}{4}}$ , so multiply the denominators: $2*4=8$ . This means $8$ is our new common denominator.
3
Convert both numerators to match the new common denominator. We have a common denominator now, but we need to make sure our fractions still have the same value as before. Multiply the numerator of each fraction by the same number that we multiplied each denominator by when we found the common denominator. ^{[7]
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- For ${\frac {7}{2}}$ , we multiplied the denominator, $2$ by $4$ , so do the same to the numerator: $7*4=28$ . Place this new numerator over the new denominator to get ${\frac {28}{8}}$ .
- Our second fraction is ${\frac {11}{4}}$ and we multiplied the denominator, $4$ , by $2$ . Multiply the numerator by 2 as well: $11*2=22$ . Put this over the denominator to get ${\frac {22}{8}}$ .
- Now, we’re working with the equation ${\frac {28}{8}}+{\frac {22}{8}}$ .
4
Add the numerators together. Now, we have a simple equation, and both denominators match, so all we need to do is add the numerators together and put the sum over the common denominator to find our answer: ^{[8]
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- $28+22=50$ , our new improper fraction is ${\frac {50}{8}}$ .
5
Convert the improper fraction into a mixed number with division. We’re not done yet! We can’t leave our answer as an improper fraction—we need to simplify it. To do this, Jia reminds us that we just divide the numerator by the denominator. The number we get is the whole number in our improper fraction, and any remainder is the numerator of our leftover fraction.
- $50/8=6$ , with $2$ left over. That means we have 6 wholes, and 2 parts, so our improper fraction is $6{\frac {2}{8}}$ .
- Then, the fraction in our mixed number can be simplified : ${\frac {2}{8}}={\frac {1}{4}}$ . So, our final answer is $6{\frac {1}{4}}$ .

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Do you have to turn it into a mixed number?

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No, the answer is correct without turning it into a mixed number. It's just that mixed numbers are often more easily grasped than the equivalent improper fractions.

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25 1/2 + 18 1/5 as a mixed number

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First find common denominators. The least common denominator is 10. Multiply 1/2 by 5/5 to get 5/10. Then multiply 1/5 by 2/2 to get 2/10. 25 5/10 + 18 2/10 = 43 7/10. Your answer is 43 7/10.

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How do you multiply a whole number by a fraction?

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Multiply the whole number by the numerator and keep the denominator the same. Simplify and/or convert to a mixed number if desired. For example: 12 x 2/3 = 24/3 = 8.

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This article shows how to add fractions and whole numbers by converting the whole number to a fraction, to show you the process happening behind the scenes. Often, though, you can simply place the whole number next to the fraction to find your answer.

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If you have difficulty with multiplication, use a calculator if you have permission from your teacher.

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How to Add Fractions with Whole Numbers: Student Tutorial

Adding Whole Numbers & Fractions: Overview

Steps

Adding Fractions & Whole Numbers Together

Adding Mixed Numbers

Community Q&A

Video

Tips

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