Question

what is the definition of subtracting
fractions

Answer 1

Subtracting fractions means finding the difference between two fractional quantities. To subtract fractions you must express them with the same denominator (a common denominator), then subtract the numerators and keep the common denominator. Finally, simplify the result if possible.

Steps
- If denominators are the same: subtract numerators, keep the denominator.
Example: 5/8 − 3/8 = (5−3)/8 = 2/8 = 1/4.
- If denominators are different: find a common denominator (usually the least common multiple), convert each fraction to an equivalent fraction with that denominator, subtract the numerators, then simplify.
Example: 3/4 − 1/6. LCM(4,6)=12 → 3/4 = 9/12, 1/6 = 2/12, so 9/12 − 2/12 = 7/12.
- You can also use the product denominator formula: a/b − c/d = (ad − bc)/(bd). (This uses bd as a common denominator; you may need to simplify the result.)
Example: 3/4 − 1/6 = (3·6 − 1·4)/(4·6) = (18−4)/24 = 14/24 = 7/12.
- For mixed numbers: either convert to improper fractions first or subtract whole parts and fractional parts, borrowing if necessary.
Example: 2 1/3 − 1 3/4 = 7/3 − 7/4 = (28−21)/12 = 7/12.
- If the numerator becomes negative, the result is a negative fraction (e.g., 1/5 − 4/5 = −3/5).

Always simplify the final fraction to lowest terms.