Fraction Formulas Explained

01 — Adding Fractions

a/b + c/d = (ad + bc)/bd

Accessible text: a over b plus c over d equals a times d plus b times c, all over b times d. Written solutions use the least common denominator. Worked example: 1/2 + 1/3 = 5/6. Edge case: adding a zero numerator leaves the other fraction. Adding fractions calculator

02 — Subtracting Fractions

a/b − c/d = (ad − bc)/bd

Keep the sign. Worked example: 3/4 − 1/6 = 7/12. Edge case: 1/3 − 2/3 = −1/3. Subtracting fractions calculator

03 — Multiplying Fractions

a/b × c/d = ac/bd

Worked example: 2/3 × 3/5 = 2/5. Edge case: a zero numerator makes the product zero. Multiplying fractions calculator

04 — Dividing Fractions

a/b ÷ c/d = a/b × d/c

Worked example: 3/4 ÷ 2/5 = 15/8. Edge case: a zero divisor is undefined. Dividing fractions calculator

05 — Simplifying Fractions

n/d = (n÷g)/(d÷g), g = gcd(n,d)

Worked example: 24/36 = 2/3. Edge case: 7/13 is already simplest. Simplify fractions

06 — Mixed Number Conversion

w n/d = (wd + n)/d

Worked example: 2 1/3 = 7/3. Edge case: −2 1/3 = −7/3. Mixed number calculator

07 — Decimal Conversion

0.375 = 375/1000 = 3/8

Worked example: 0.125 = 1/8. Edge case: repeating 1/3 is not a finite decimal. Decimal converter

08 — Comparing Fractions

a/b ? c/d by comparing ad and bc

Worked example: 3/4 > 2/3 because 9 > 8. Edge case: 1/2 equals 2/4. Compare fractions