How do you add and subtract fractions?

To add or subtract fractions, they must have the same denominator (called a common denominator). Find the Least Common Denominator (LCD) of the two fractions, convert each fraction to have that denominator, then add or subtract the numerators. Finally simplify the result by dividing numerator and denominator by their Greatest Common Divisor (GCD). Example: 1/2 + 1/3 • LCD of 2 and 3 = 6 • Convert: 1/2 = 3/6, 1/3 = 2/6 • Add numerators: 3/6 + 2/6 = 5/6 • 5/6 is already fully simplified (GCD of 5 and 6 = 1) • Answer: 5/6 Example: 3/4 − 1/6 • LCD of 4 and 6 = 12 • Convert: 3/4 = 9/12, 1/6 = 2/12 • Subtract: 9/12 − 2/12 = 7/12 • Answer: 7/12

How do you multiply and divide fractions?

To multiply fractions: multiply the numerators together and the denominators together, then simplify. You can often simplify before multiplying by cancelling common factors between any numerator and any denominator — this is called cross-cancellation and keeps numbers smaller. To divide fractions: flip the second fraction (find its reciprocal) and then multiply. 'Keep, change, flip' — keep the first fraction, change division to multiplication, flip the second fraction. Multiplication example: 2/3 × 3/4 • Numerators: 2 × 3 = 6 • Denominators: 3 × 4 = 12 • Result: 6/12 = 1/2 (simplified) • Or cross-cancel: 2/3 × 3/4 → (2×1)/(1×4) = 2/4 = 1/2 Division example: 3/4 ÷ 2/5 • Flip: 2/5 → 5/2 • Multiply: 3/4 × 5/2 = 15/8 • Mixed number: 1 7/8

How do you simplify a fraction to lowest terms?

To simplify a fraction: find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. The GCD is the largest number that divides both numbers evenly. A fraction is in lowest terms (fully simplified) when the GCD of the numerator and denominator is 1. Example: simplify 12/18 • Factors of 12: 1, 2, 3, 4, 6, 12 • Factors of 18: 1, 2, 3, 6, 9, 18 • GCD = 6 (largest common factor) • 12/18 = (12÷6)/(18÷6) = 2/3 • Check: GCD(2,3) = 1 ✓ — fully simplified Quick GCD methods: • List factors and find the largest common one (good for small numbers) • Euclidean algorithm: GCD(18,12) = GCD(12,6) = GCD(6,0) = 6 (fast for large numbers) • This calculator uses the Euclidean algorithm automatically

How do you convert between mixed numbers and improper fractions?

A mixed number has a whole part and a fraction part (e.g. 1 3/4). An improper fraction has a numerator larger than the denominator (e.g. 7/4). They are equivalent — 1 3/4 = 7/4. Mixed → Improper: multiply the whole number by the denominator, add the numerator. Keep the same denominator. • Formula: a b/c = (a×c + b)/c • Example: 1 3/4 = (1×4 + 3)/4 = 7/4 • Example: 2 1/2 = (2×2 + 1)/2 = 5/2 Improper → Mixed: divide numerator by denominator. The quotient is the whole number, the remainder is the new numerator. • Example: 7/4 → 7 ÷ 4 = 1 remainder 3 → 1 3/4 • Example: 15/8 → 15 ÷ 8 = 1 remainder 7 → 1 7/8 This calculator handles mixed numbers directly — enable the 'Mixed Numbers' toggle to enter whole and fraction parts separately.

What is the Least Common Denominator (LCD) and how is it found?

The Least Common Denominator (LCD) is the smallest number that is a multiple of both denominators. It is the same as the Least Common Multiple (LCM) of the two denominators. Finding the LCD is the key step in adding or subtracting fractions with different denominators. Methods to find the LCD: • List multiples: multiples of 4: 4,8,12,16... multiples of 6: 6,12,18... → LCD = 12 • Use LCM formula: LCM(a,b) = |a×b| / GCD(a,b) • Example: LCD(4,6) = (4×6)/GCD(4,6) = 24/2 = 12 Common LCD examples: • LCD(2,3) = 6 · LCD(3,4) = 12 · LCD(4,6) = 12 • LCD(5,7) = 35 (coprime — no common factors) • LCD(6,9) = 18 · LCD(8,12) = 24 • When one denominator is a multiple of the other (e.g. 3 and 6), the LCD is just the larger one

Fraction Calculator — Add, Subtract, Multiply & Divide

The Fraction Calculator performs all four arithmetic operations on fractions — addition, subtraction, multiplication, and division — plus simplification to lowest terms. Toggle Mixed Numbers mode to work with mixed numbers like 1 3/4 instead of improper fractions. The result is shown as a simplified...

FRACTION CALCULATOR

e.g. 1 ¾ instead of 7/4

1/2 + 1/3

FRACTION 1

FRACTION 2

RESULT

≈ 0.83333333

STEP-BY-STEP

Find LCD of 2 and 3: LCD = 6

Convert: 1/2 = 3/6, 1/3 = 2/6

Add numerators: 3 + 2 = 5

Result: 5/6

QUICK EXAMPLES

LIVE DIAGRAM

NUMBER LINE

RESULT (fraction)

5/6

RESULT (mixed)

5/6

DECIMAL

0.83333333

SIMPLIFIED

5/6

Red = first fraction · Blue = second · Black = result

EQUIVALENT FRACTIONS

5/6

10/12

15/18

20/24

All equivalent to 5/6

Created with❤️byeaglecalculator.com

HOW TO USE

1
Select the operation using the +, −, ×, ÷ buttons, or = to simplify a single fraction.
2
Enter the numerator and denominator for each fraction. Enable Mixed Numbers to add a whole number component for mixed numbers like 1 3/4.
3
The result appears instantly as a simplified fraction, a mixed number, and a decimal. All three forms are shown simultaneously.
4
Read the step-by-step solution — it shows the LCD method for addition/subtraction, or the multiplication steps for multiply/divide.
5
Check the number line — both fractions and the result are plotted to scale, making it easy to see their relative sizes.

WORKED EXAMPLE

Example 1 (add): 1/2 + 1/3. LCD = 6. 3/6 + 2/6 = 5/6. Example 2 (subtract): 3/4 − 1/6. LCD = 12. 9/12 − 2/12 = 7/12. Example 3 (multiply): 2/3 × 3/4. 6/12 = 1/2. Example 4 (divide): 3/4 ÷ 2/5. Flip: 3/4 × 5/2 = 15/8 = 1 7/8. Example 5 (mixed): 1 3/4 + 2 1/2 = 7/4 + 5/2 = 7/4 + 10/4 = 17/4 = 4 1/4. Example 6 (simplify): 12/18 → GCD=6 → 2/3.

REFERENCE FORMULAS

FRACTION RULES REFERENCE

OPERATION	FORMULA	NOTES
Addition	a/b + c/d = (a×d + c×b) / (b×d)	Find LCD then add numerators
Subtraction	a/b − c/d = (a×d − c×b) / (b×d)	Find LCD then subtract numerators
Multiplication	a/b × c/d = (a×c) / (b×d)	Multiply numerators and denominators
Division	a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)	Multiply by the reciprocal of the divisor
Simplification	a/b = (a÷GCD) / (b÷GCD)	Divide both by Greatest Common Divisor
Mixed → Improper	a b/c = (a×c + b) / c	Convert mixed number to improper fraction
LCD formula	LCD(a,b) = \|a×b\| / GCD(a,b)	Least Common Denominator for adding fractions

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Last updated: April 28, 2026 · Formula verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.