Fraction Calculator
Solve fraction problems with detailed steps. features mixed numbers, simplification, and visual explanations.
Solution Steps
Solved!
Explore More Tools
Fraction Masterclass: The Logic Behind the Math
Fractions can be tricky because they break the rules of "normal" counting numbers. You can't just add across the top and bottom! This guide explains the hidden logic behind the calculator, helping you understand Mixed Numbers, Improper Fractions, and Common Denominators.
The Two Faces of Fractions
Mixed Numbers
Best for Real Life. If you order pizza, you say "one and a half pizzas", not "three halves". It clearly separates the whole numbers from the fractional parts.
Improper Fractions
Best for Calculation. Math is easier when the number is all one piece. Calculating "3 halves" is simpler than calculating "1 and a half" because you don't have to juggle the whole number separately.
Cheat Sheet: The 4 Rules
- Adding (+)
Find a Common Denominator first. Change the tops (numerators) to match, then add them. Keep the bottom the same.
- Subtracting (-)
Same as adding. You cannot subtract slices of different sizes (e.g. halves vs quarters). Make them the same size first!
- Multiplying (×)
The easiest one! Just multiply straight across: Top × Top and Bottom × Bottom.
- Dividing (÷)
Keep, Change, Flip. Keep the first fraction, convert division to multiplication, and Flip the second fraction upside down.
Why learn fractions?
Cooking & Baking
"Add 1/2 cup of sugar, but double the recipe." You need to know that 1/2 × 2 = 1 whole cup.
Construction & DIY
Tape measures use fractions (1/16, 5/8). Adding "half an inch" to a specific cut requires fraction math.
Science & Chemistry
Mixing solutions often requires ratios and fractions to get the concentration correct.
Frequently Asked Questions
How do I add mixed numbers manually?
The easiest way is to convert them to improper fractions first. For example, to add 1 1/2 + 2 1/4: 1. Convert to 3/2 and 9/4. 2. Find a common denominator (4). 3/2 becomes 6/4. 3. Add: 6/4 + 9/4 = 15/4. 4. Convert back: 3 3/4.
What is an Improper Fraction?
An improper fraction is a fraction where the top number (numerator) is larger than or equal to the bottom number (denominator), like 5/4. It simply means the value is greater than 1. It is not 'wrong', it's just a different way to write a Mixed Number.
How do you divide fractions?
The golden rule is 'Keep, Change, Flip'. Keep the first fraction, Change division to multiplication, and Flip the second fraction (Reciprocal). Example: 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2.
Why do we need a common denominator?
You can only add or subtract 'like' things. Adding 1 slice of a small pizza (1/8) to 1 slice of a giant pizza (1/4) isn't just '2 slices'. You need to cut the big slice in half so everything is in 'eighths'. Then you have 1/8 + 2/8 = 3/8.
Can I convert a decimal to a fraction?
Yes. To convert 0.75, write it as 75/100. Then simplify by dividing top and bottom by their greatest common divisor (LCD). 75 ÷ 25 = 3, and 100 ÷ 25 = 4. So 0.75 = 3/4. Our calculator does this automatically.
What is the LCD (Least Common Denominator)?
The LCD is the smallest number that both denominators can divide into evenly. For 1/3 and 1/4, the LCD is 12 (3×4), because 12 is the first number in the multiplication tables of both 3 and 4.
How do I simplify a fraction?
Find a number that divides evenly into both the top and bottom. Keep dividing until you can't anymore. For 50/100, divide by 10 to get 5/10, then divide by 5 to get 1/2.
Does the order matter in subtraction?
Yes! Unlike addition (where 1+2 is same as 2+1), subtraction is not commutative. 1/2 - 1/4 = 1/4 (Positive), but 1/4 - 1/2 = -1/4 (Negative).
What are 'Reciprocals'?
A reciprocal is what you get when you flip a fraction upside down. The reciprocal of 3/4 is 4/3. Multiplying a number by its reciprocal always equals 1.