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# Math: Basic Tutorials : Adding Fractions

## Adding Fractions

Are you not sure where to start when it comes to adding fractions? This section will walk you through it, from finding the common denominator to simplifying your fractions and coming up with your solution.

## Examples

### Examples

### Method 1: Add 2 and 2 over 3 plus 1 and 1 over 4

### Method 2: Add 2 and 2 over 3 plus 1 and 1 over 4

## Summary and Worksheet

## Attribution

Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on the titles below to view each example.

Line 1: Add 1 over 2 plus 1 over 3

Line 2: Determine the lowest common denominator of 2 and 3 is 6.

Line 3: Change the fractions into equivalent fractions with a denominator of 6. Multiply the numerator and denominator of the first fraction by 3, so the numerator is 1 times 3 and the denominator is 2 times 3. Multiply the numerator and denominator of the second fraction by 2, so the numerator is 1 times 2 and the denominator is 3 times 2.

Line 4: Simplify the numerators and denominators of each fraction so the problem becomes 3 over 6 plus 2 over 6.

Line 5: Add the numerators together and keep the denominator the same, so the answer is 5 over 6.

Line 6: Remember to always check if the answer can be simplified. Since 5 and 6 have no common factors 5 over 6 can not be reduced.

Line 1: Method 1 for adding mixed numbers.

Line 2: Convert the mixed numbers to improper numbers. In the first fraction, the numerator becomes 2 times 3 plus 2 and the denominator stays as 3. In the second fraction, the numerator becomes 1 times 4 plus 1 and the denominator stays as 4.

Line 3: Simplify the numerators so the problem becomes 8 over 3 plus 5 over 4.

Line 4: Determine the lowest common denominator of 3 and 4 is 12. Change the fractions into equivalent fractions with a denominator of 12. Multiply the numerator and denominator of the first fraction by 4, so the numerator is 8 times 4 and the denominator is 3 times 4. Multiply the numerator and denominator of the second fraction by 3, so the numerator is 5 times 3 and the denominator is 4 times 3.

Line 4: Simplify the numerators and denominators of each fraction so the problem becomes 32 over 12 plus 15 over 12.

Line 5: Add the numerators together and keep the denominator the same, so the answer is 47 over 12.

Line 6: If necessary, convert 47 over 12 to the mixed number 3 and 11 over 12.

Line 7: Remember to always check the fraction is simplified. There are no common factors between 11 and 12, so the fraction 11 over 12 is simplified.

Line 1: Method 2 for adding mixed numbers.

Line 2: Add the whole numbers of the mixed numbers together. 2 plus 1 equals 3.

Line 3: Add the fractions part of the mixed numbers together. 2 over 3 plus 1 over 4.

Line 4: Determine the lowest common denominator of 3 and 4 is 12. Change the fractions into equivalent fractions with a denominator of 12. Multiply the numerator and denominator of the first fraction by 4, so the numerator is 2 times 4 and the denominator is 3 times 4. Multiply the numerator and denominator of the second fraction by 3, so the numerator is 1 times 3 and the denominator is 4 times 3.

Line 5: Simplify the numerators and denominators of each fraction so the problem becomes 8 over 12 plus 3 over 12.

Line 6: Add the numerators together and keep the denominator the same, so the fraction is 11 over 12.

Line 7: Place the whole number from Line 2 in front of the fraction so the answer is 3 and 11 over 12.

Line 8: Remember to always check the fraction is simplified. There are no common factors between 11 and 12, so the fraction 11 over 12 is simplified.

- Summary: Adding Fractions - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Adding Fractions - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.