Adding Fractions with Different Denominators
Learn to add fractions when the bottom numbers are not the same by finding a common denominator.
Definition
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Worked Examples
Calculate
Find the LCD of 2 and 3
Multiples of 2: 2, 4, 6, 8... Multiples of 3: 3, 6, 9... The smallest common multiple is 6 → LCD = 6
Convert to sixths
→
Convert to sixths
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Add the numerators
→
Check if simplification is needed
5 and 6 share no common factors other than 1 → Already simplified
Answer:
Common Mistakes
Adding both numerators AND denominators:
Why it's wrong: This is the most common error! Denominators tell you the SIZE of each piece. You cannot add pieces of different sizes directly.
Correct: Find a common denominator first, then add only the numerators:
Using any common multiple instead of simplifying at the end
Why it's wrong: While using 24 instead of 12 works, your answer will need simplifying:
Correct: Either use the LCD from the start, or remember to simplify your final answer:
Forgetting to multiply both numerator and denominator
Why it's wrong: If you only change the denominator, you change the value of the fraction!
Correct: Always multiply top AND bottom by the same number to create an equivalent fraction
Interactive Visual
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Practice Problems
18 problemsWhat is the LCD (Least Common Denominator) of and ?
Why It Matters
- Cooking: Combining cup of flour with cup more
- Time: Adding hour of homework and hour of reading
- Construction: Measuring inch plus inch for a project
- Sports: A runner completes of a track, then more
Real World Applications
Cooking and Recipes
Recipes often require combining different fractional amounts of ingredients.
Example:
A recipe needs cup of oil and you want to add cup more for extra moisture. Total oil = cup.
You have cup of sugar and need to add cup more.
How much sugar do you have in total?
Step 1: Write the mathematical expression
Add the fractions:
Time Management
Adding time spent on different activities often involves unlike fractions.
Example:
You spend hour on math and hour on reading. Total: hour (50 minutes).
You practice piano for hour and guitar for hour.
How long did you practice music in total?
Step 1: Write the mathematical expression
Add the time fractions:
DIY and Construction
Measuring materials often requires adding fractions with different denominators.
Example:
You need a piece of wood that is inch plus inch thick. Total: inch.
You combine two pieces of fabric: one is meter and another is meter.
What is the total length of fabric?
Step 1: Write the mathematical expression
Add the lengths:
Key Takeaways
- 1To add fractions with different denominators, first find a common denominator
- 2The Least Common Denominator (LCD) is the smallest number both denominators divide into
- 3Convert each fraction to an equivalent fraction with the LCD
- 4Add the numerators and keep the denominator the same
- 5Simplify the result if possible, and convert to a mixed number if greater than 1
Frequently Asked Questions
Glossary
- Unlike denominators
- Fractions that have different bottom numbers, like and
- Common denominator
- A number that all denominators in a problem divide into evenly
- Least Common Denominator (LCD)
- The smallest common denominator — makes calculations easier
- Equivalent fraction
- A fraction that represents the same value, like