Fraction Fabricator
Combine parts to make a whole!
Common Denominator Visualizer
Enter fractions to see the bars align.
Visualizing how different slices become equal sizes.
The Pizza Slice Dilemma
Imagine you have half a pizza left ($1/2$) and your friend has one-third of a pizza ($1/3$). You want to combine them into one box. You cannot just add $1+1$ and $2+3$ to get $2/5$. That would mean you somehow have less than half a pizza! Mastering the art of adding and subtracting fractions is essential to solving this problem correctly.
The Golden Rule
The golden rule of adding and subtracting fractions is that you must have a Common Denominator. You cannot add “halves” to “thirds” directly because the slice sizes are different. You must cut them into smaller, equal-sized pieces first.
- Find the LCD: Find the Least Common Multiple of the bottom numbers. For 2 and 3, it is 6.
- Resize: Convert $1/2$ to $3/6$ (multiply top and bottom by 3). Convert $1/3$ to $2/6$ (multiply top and bottom by 2).
- Combine: Now that both are “sixths,” you can add the tops: $3 + 2 = 5$. The result is $5/6$.
Visualizing the Math
Visual models help understand adding and subtracting fractions better. In the tool above, you will see bars representing your fractions. Notice how the tool automatically splits the bars into smaller segments so they match perfectly. This visual proof shows why we need that common denominator.
Simplifying the Answer
When adding and subtracting fractions, simplifying the result is the final step. If you end up with $4/8$, you should reduce it to $1/2$. This keeps numbers clean and easy to understand. Whether you are a carpenter measuring wood or a chef adjusting a recipe, this skill connects math to the real world.
Ultimately, adding and subtracting fractions is just about finding a common language for numbers so they can work together.
Frequently Asked Questions
Can I just add the denominators?
Never! The denominator tells you the size of the slice. Adding them changes the size, which breaks the math. You only add the numerators (the count).
What if the top is bigger than the bottom?
That is an “improper fraction” (like $5/4$). It is perfectly valid, but you can convert it to a mixed number ($1\ 1/4$) to see how many wholes you have.
Do I always need the Least Common Denominator?
No, any common denominator works! However, using the smallest one keeps the numbers smaller and makes simplifying at the end easier.
How do I subtract a larger fraction from a smaller one?
The process is the same, but your numerator will be negative (e.g., $1/4 – 3/4 = -2/4 = -1/2$).