Master adding and subtracting fractions with different denominators using common denominators. Learn pizza sharing and fraction conversion techniques.
Scenario: You and your friends are sharing pizzas! One pizza is cut into 4 slices, and another is cut into 6 slices. You eat 1/4 of the first pizza and 1/6 of the second pizza. How much pizza did you eat in total?
This is where different denominator fractions come in! We need to find a common denominator to add 1/4 + 1/6. Let's learn how to do this step by step.
A common denominator is a number that both denominators can divide into evenly. We use this to make fractions comparable.
For 1/4 and 1/6, common denominators are: 12, 24, 36...
We usually use the smallest one: 12
Once we find a common denominator, we convert both fractions to have that denominator.
1/4 = 3/12 and 1/6 = 2/12
Now we can add: 3/12 + 2/12 = 5/12
Look for the smallest number that both denominators can divide into evenly. This is called the Least Common Multiple (LCM).
Example: For 1/4 and 1/6, list multiples of 4 (4, 8, 12, 16...) and 6 (6, 12, 18, 24...). The first common number is 12.
Multiply both the numerator and denominator by the same number to get the common denominator.
Example: 1/4 = (1×3)/(4×3) = 3/12 and 1/6 = (1×2)/(6×2) = 2/12
Now that both fractions have the same denominator, add or subtract the numerators and keep the denominator.
Example: 3/12 + 2/12 = 5/12
Practice finding common denominators:
Solve pizza sharing problems:
1. 1/2 + 1/3 = ?
2. 1/4 + 1/6 = ?
3. 2/3 + 1/4 = ?
4. 3/5 + 1/2 = ?
5. 3/4 - 1/3 = ?
6. 5/6 - 1/2 = ?
7. 4/5 - 1/3 = ?
8. 7/8 - 1/4 = ?
9. 1/2 + 1/3 - 1/6 = ?
10. 2/3 - 1/4 + 1/6 = ?
11. 3/4 + 1/5 - 1/2 = ?
12. 5/6 - 1/3 + 1/4 = ?
Wrong: 1/2 + 1/3 = 2/5 (Can't add different denominators directly!)
Correct: 1/2 + 1/3 = 3/6 + 2/6 = 5/6 (Find common denominator first)
Wrong: For 1/4 and 1/6, using 8 as common denominator
Correct: Use 12 (the LCM of 4 and 6)
Always find a common denominator before adding or subtracting different denominator fractions
Use the Least Common Multiple (LCM) as the common denominator when possible
Convert both fractions to have the same denominator before operating
Use visual models to verify your answers and understand the concept