Fraction Simplifier
Reduce any fraction to lowest terms by dividing numerator and denominator by their GCF. Shows step-by-step working, decimal equivalent, percentage, and mixed number form.
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How It Works
Enter numerator and denominator. Press Simplify. The calculator finds GCF via the Euclidean algorithm and divides both. Shows: simplified fraction, GCF used, step-by-step (original → divide by GCF → simplified), decimal equivalent, percentage, and mixed number if improper. For 36/48: GCF=12, 36÷12=3, 48÷12=4, result=3/4.
Simplified = (n÷GCF)/(d÷GCF) | in lowest terms when GCF=136/48 → GCF=12 → 3/4 = 0.75 = 75%Improper fractions (numerator > denominator) automatically show as mixed numbers. 7/4: quotient=1, remainder=3, mixed number=1¾. 22/7: quotient=3, remainder=1, mixed number=3 1/7. To convert back: multiply whole part by denominator, add numerator. 1¾ = (1×4+3)/4 = 7/4.
Mixed number: n/d → q r/d where q=floor(n/d), r=n mod d7/4 = 1¾ | 22/7 = 3 1/7 | 11/3 = 3⅔Switch to Compare tab. Enter two fractions. The calculator finds LCD, converts both, compares numerators, and shows the relationship (>, <, or =). Also displays both as decimals for direct comparison. For 5/8 vs 7/12: LCD=24, 15/24 vs 14/24 → 5/8 > 7/12 (decimals: 0.625 vs 0.583).
Compare a/b vs c/d: convert to LCD, compare numerators5/8 vs 7/12: LCD=24 → 15/24 vs 14/24 → 5/8 > 7/12Switch to Operations. Enter two fractions, select +, −, ×, or ÷. Full step-by-step solution: for addition, finds LCD, converts both fractions, adds numerators, simplifies. For multiplication: multiply numerators, multiply denominators, simplify. Division: multiply by reciprocal of second fraction.
Add: LCD method | ×: (a×c)/(b×d) | ÷: ×reciprocal2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12If GCF(numerator, denominator)=1, the fraction is already in lowest terms and cannot be simplified. Examples: 7/11 (GCF=1), 5/13 (GCF=1), 8/15 (GCF=1). The calculator confirms "already in lowest terms" and shows the decimal and percentage without modifying the fraction.
GCF(n,d)=1 → fraction is already fully reducedGCF(7,11)=1 → 7/11 already in lowest termsQuick Reference
Verify these in the calculator above.
Simplify
12/18
2/3
Simplify
24/36
2/3
Simplify
48/72
2/3
Simplify
36/48
3/4
Mixed
7/4
1¾ (mixed)
Mixed
22/7
3 1/7
Whole
15/5
3
GCF
GCF(48,72)
24
Tips & Shortcuts
The Simplify tab shows the GCF used and the step-by-step process — useful for understanding why the fraction reduces to that specific form.
Mixed number form displays automatically for improper fractions — no separate conversion step needed.
For quick GCF check: if both numbers are even, divide by 2 first. If both end in 0 or 5, divide by 5. Repeat until no common factor is obvious.
The decimal equivalent in the result lets you verify the simplification: 3/4=0.75 should match your original fraction's decimal value.
Use the Compare tab to verify two fractions are equivalent: enter 12/16 and 3/4 — they should show as equal.
Common Mistakes
Stopping too early in simplification
Dividing 12/18 by 2 gives 6/9, which still simplifies by 3 to 2/3. Using GCF directly (GCF=6) gets to lowest terms in one step. The calculator always applies the GCF for complete simplification.
Confusing simplification with conversion
Simplifying 3/6 gives 1/2 — the VALUE is unchanged, only the representation. 3/6 = 1/2 = 0.5 are all the same number. Simplification makes the fraction easier to work with, not different.
Applying GCF to the whole number part of a mixed number
Mixed number 2 3/4: only simplify the fractional part (3/4 is already simplified). Do not try to simplify 2 and 3 together. To simplify a mixed number, convert to improper first: 2 3/4 = 11/4, then simplify (already done).
Dividing only the numerator or only the denominator by GCF
Both parts must be divided by the same number. Dividing only the numerator: 12/18 → 2/18 changes the VALUE. Must do both: 12÷6=2 AND 18÷6=3 → 2/3.
Expecting 0/n to simplify meaningfully
0/n = 0 for any non-zero n. The fraction is already "simplified" — 0 divided by anything is 0. The denominator does not matter. 0/7, 0/100, 0/1 are all equal to 0.
Frequently Asked Questions
Find GCF of numerator and denominator, then divide both by it. For 12/18: GCF(12,18)=6. 12÷6=2, 18÷6=3. Simplified: 2/3. The fraction is in lowest terms when GCF(numerator,denominator)=1.
12/18 simplified: GCF(12,18)=6. 12÷6=2, 18÷6=3. Answer: 2/3. Verify: GCF(2,3)=1, so 2/3 cannot be simplified further.
A fraction is in lowest terms (fully reduced) when the GCF of numerator and denominator equals 1 — they share no common factor other than 1. Examples: 1/2, 2/3, 3/4, 5/7 are all in lowest terms. 2/4, 6/9, 4/8 are not.
Same process — divide both by GCF. For 24/16: GCF=8, simplified=3/2. Then convert to mixed number: 3÷2=1 remainder 1, so 3/2=1½. The calculator shows both the improper form and the mixed number automatically.
Yes. If the denominator divides evenly into the numerator. 12/4=3, 18/6=3, 100/25=4. The calculator shows these as whole numbers, not fractions.
GCF (Greatest Common Factor) is the largest number that divides both numerator and denominator. Dividing both by GCF gives the fraction in lowest terms in one step, rather than dividing by smaller factors repeatedly. GCF(24,36)=12: 24/36 → 2/3 in one step vs dividing by 2 twice and then 3.
48/72: GCF(48,72)=24. 48÷24=2, 72÷24=3. Simplified: 2/3. Three-step verification: GCF(2,3)=1 ✓, 2/3=0.666... ✓, 48/72=0.666... ✓.
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