Adding Fractions

Adding Fractions

How to add fractions (and mixed numbers) with same and different denominators

Adding Fractions with same denominator

• Simply add the top numbers together; for example, 1/8 + 2/8 = 3/8 (note: the bottom number stays the same)

• If the result is an Improper Fraction you can change to a mixed number if required; for example, 8/5 becomes 1 ⅜

• Remember, you may also be required to simplify; for example, 4/8 can be simplified to 1/2

Multiple Choice

5/8 + 5/8

• 10/16

• 5/16

• 8/10

• 10/8

Multiple Choice

• 4/5

• 4/10

• 2/5

• 5

Multiple Choice

• ³/₈

• ³/₁₆

• ¹/₈

• ²/₈

Adding Mixed Numbers with the same denominator

• Step 1 - Add the Whole numbers together

• Step 2 - Then just add the top numbers of the fractions together

• Step 3 - Add the results of the above to the Whole numbers you previously added together (if you end up with an Improper Fraction just convert to a Mixed Number first)

• For example, 1 2/5 + 2 4/5 (we start by adding the whole numbers to get 3 and then we add the top numbers to get 6/5; 6/5 becomes 1 1/5 which we add to 3 to get a final answer of 4 1/5)

Multiple Choice

4 1/3 + 2 1/3

• 6 1/3

• 6 2/3

• 6 2/6

• 7 2/3

Multiple Choice

3 4/5 + 4 3/5

• 7 2/5

• 8 2/5

• 6 3/5

• 8 9/5

Multiple Choice

9 1/2 + 7 1/2

• 17

• 16

• 14 1/2

• 16 1/2

Adding Fractions with different denominators

• Change the bottom numbers to a common denominator and then add the top numbers together; for example, ½ + ⅕ becomes 5/10 + 2/10 = 7/10

• If the result is an Improper Fraction you can change to a mixed number if required; for example, 8/5 becomes 1 ⅜

• Remember, you may also be required to simplify; for example, 4/8 can be simplified to 1/2

Multiple Choice

What is a good common denominator for this problem? 

$$\frac{3}{9}+\frac{1}{6}$$  

• 18

• 9

• 24

• 12

Multiple Choice

What is the sum of these fractions?

• 4/5

• 3/20

• 17/20

• 4/20

Adding Mixed Numbers with different denominators

• Step 1 - Add the Whole numbers together

• Step 2 - Change the bottom numbers of the fractions to a common denominator and then add the top numbers together; for example, ½ + ⅕ becomes 5/10 + 2/10 = 7/10

• Step 3 - Add the results of the above to the Whole numbers you previously added together (if you end up with an Improper Fraction just convert to a Mixed Number)

• For example, 1 ¾ + 2 ½ becomes 4 ¼ (1 + 2 = 3, then 3/4 + 2/4 = 5/4 which becomes 1 ¼ added to 3 = 4 ¼)

Multiple Choice

What is the sum?

Multiple Choice

$$4\frac{5}{12}+3\frac{1}{6}$$  

• $$7\frac{6}{18}$$  

• $$7\frac{8}{12}$$  

• $$7\frac{7}{12}$$  

• $$7\frac{5}{12}$$  

Multiple Choice

$$4\frac{2}{9}+8\frac{1}{2}$$  

• $$8\frac{3}{11}$$  

• $$12\frac{15}{18}$$  

• $$12\frac{13}{18}$$  

• $$12$$