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How to Add and Subtract Fractions
To add or subtract fractions, find a common denominator. The LCD (least common denominator) is the LCM of the denominators. Convert each fraction to the common denominator, then add or subtract the numerators. Example: 3/4 + 1/2 = 3/4 + 2/4 = 5/4.
How to Multiply and Divide Fractions
To multiply fractions, multiply the numerators together and the denominators together: (a/b) × (c/d) = ac/bd. To divide, multiply by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc. Always simplify the result.
Simplifying Fractions
To simplify (reduce) a fraction, divide both numerator and denominator by their greatest common factor (GCF). For example, 12/18: GCF of 12 and 18 is 6, so 12/18 = 2/3. A fraction is fully simplified when the GCF of its numerator and denominator is 1.
Converting Between Fractions and Decimals
To convert a fraction to a decimal, divide the numerator by the denominator: 3/4 = 0.75. To convert a decimal to a fraction, write the decimal over the appropriate power of 10 and simplify: 0.75 = 75/100 = 3/4. Repeating decimals like 0.333... = 1/3.
Frequently Asked Questions
An improper fraction has a numerator larger than the denominator (e.g., 5/4). It can be converted to a mixed number: 5/4 = 1¼. Both representations are mathematically equivalent.
Division by zero is undefined in mathematics. A fraction with a zero denominator has no value. The calculator will show an error if you enter 0 as any denominator.
The LCD is the least common multiple (LCM) of the denominators. For 3/4 and 1/6, the LCM of 4 and 6 is 12. So convert to 9/12 and 2/12 before adding or subtracting.
Yes. A negative sign can be placed on the numerator, denominator, or in front of the fraction — all are equivalent. By convention, the negative sign is usually placed on the numerator or in front: -3/4.