Add, subtract, multiply and divide fractions.
Addition: (a/b) + (c/d) = (a·d + b·c) / (b·d) → simplify by GCF Subtraction: (a/b) − (c/d) = (a·d − b·c) / (b·d) → simplify by GCF Multiplication: (a/b) × (c/d) = (a·c) / (b·d) → simplify by GCF Division: (a/b) ÷ (c/d) = (a·d) / (b·c) → simplify by GCF Simplification: GCF(n, d) = largest integer dividing both n and d; simplified = (n/GCF) / (d/GCF)
Fractions are expressed as a/b and c/d, where the top number is the numerator and the bottom is the denominator. Each operation follows a distinct rule:
After any operation, divide both the result's numerator and denominator by their Greatest Common Factor (GCF) to express the answer in simplest form.
Step 1 — Apply the addition formula: (a·d + b·c) / (b·d) = (3·5 + 4·2) / (4·5) = (15 + 8) / 20 = 23/20 Step 2 — Find GCF(23, 20): factors of 23 are 1 and 23; factors of 20 are 1, 2, 4, 5, 10, 20 → GCF = 1 Step 3 — Simplify: 23/20 ÷ 1/1 = 23/20 (already in lowest terms; as a mixed number: 1 3/20)
Result: 23/20 (or 1 3/20 as a mixed number, ≈ 1.15)
The result 23/20 is an improper fraction, which can also be written as the mixed number 1 3/20. Since GCF(23, 20) = 1, the fraction is already fully simplified and cannot be reduced further. As a decimal, 23 ÷ 20 = 1.15.
A fraction represents a part of a whole. It is written as numerator/denominator, where the numerator counts how many parts you have and the denominator tells how many equal parts make up the whole.
A fraction is in lowest terms when GCF(numerator, denominator) = 1. Divide both parts by their GCF. For example, 12/18 → GCF(12,18) = 6 → 2/3.
You must have a common denominator before adding or subtracting. The safest common denominator is the Least Common Multiple (LCM) of the two denominators, though multiplying denominators always works and the formula above handles simplification at the end.
Multiply straight across: numerator × numerator and denominator × denominator. Simplifying before multiplying (cross-cancellation) keeps numbers smaller.
"Keep, Change, Flip" — keep the first fraction, change division to multiplication, flip (take the reciprocal of) the second fraction, then multiply.
Fractions are foundational in algebra, cooking, finance (interest rates are fractions of 100%), engineering ratios, and probability. Mastering them underpins nearly every area of quantitative reasoning.
The **GCF (Greatest Common Factor)** is used to *simplify* a fraction by dividing both numerator and denominator. The **LCM (Least Common Multiple)** is used to find the *least common denominator* when adding or subtracting fractions with unlike denominators. Both are tools for fraction arithmetic but serve opposite purposes.
Divide the numerator by the denominator. The quotient becomes the whole-number part and the remainder becomes the new numerator over the original denominator. Example: 23/20 → 23 ÷ 20 = 1 remainder 3 → **1 3/20**.
First convert each mixed number to an improper fraction (multiply the whole number by the denominator and add the numerator). Then multiply numerator × numerator and denominator × denominator, and simplify. Example: 1 1/2 × 2/3 → 3/2 × 2/3 = 6/6 = 1.
Equivalent fractions represent the same value but have different numerators and denominators. You create them by multiplying or dividing both parts by the same non-zero integer. For example, 1/2 = 2/4 = 3/6. The simplest equivalent fraction is the one in lowest terms.
Dividing by a number is the same as multiplying by its reciprocal. For fractions, the reciprocal of c/d is d/c. So (a/b) ÷ (c/d) becomes (a/b) × (d/c) = ad/bc. This is mathematically equivalent and avoids the complexity of dividing fractions directly.
Enter your numerator and denominator in the first fraction fields, select 'Simplify Only,' and click Calculate. The calculator finds the GCF of your two numbers and divides both by it, displaying the result in lowest terms.
Yes. Enter a negative sign before the numerator (e.g., −3 as the numerator with 4 as the denominator to represent −3/4). The calculator correctly processes sign rules for all four operations.
Division by zero is undefined in mathematics, so the calculator will flag it as an error. Every denominator must be a non-zero integer.
Yes. When the result is an improper fraction (numerator ≥ denominator), the calculator automatically displays both the improper fraction form and the equivalent mixed number (e.g., 23/20 and 1 3/20).
Absolutely. Use the 'Simplify Only' mode — just enter one fraction's numerator and denominator and the calculator returns it in lowest terms with the GCF shown.
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