How to add and multiply fractions

Every step

1. 1

   Find a common denominator (for addition)

   To add 1/3 + 1/4, find the least common multiple (LCM) of the denominators: LCM(3,4) = 12. Rewrite each fraction: 1/3 = 4/12 (multiply numerator & denominator by 4), 1/4 = 3/12 (multiply by 3).

   CHECKPOINT · Fractions have the same denominator (e.g., 4/12 + 3/12).
2. 2

   Add the numerators (for addition)

   Now that denominators match, add the numerators: 4/12 + 3/12 = 7/12. The denominator stays the same.

   CHECKPOINT · Numerators added, denominator unchanged (e.g., 7/12).
3. 3

   Multiply numerators and denominators (for multiplication)

   Multiplying 2/3 by 5/7: Numerators multiply (2*5=10), denominators multiply (3*7=21). So, 2/3 * 5/7 = 10/21.

   CHECKPOINT · Product fraction written (e.g., 10/21).
4. 4

   Simplify fractions

   Reduce fractions to lowest terms if possible. For 18/24, divide numerator and denominator by their GCD (6): 18/24 = 3/4. In previous examples, 7/12 and 10/21 are already in lowest terms.

   CHECKPOINT · Fraction expressed in simplest form.
5. 5

   Work with mixed numbers if needed

   To add 1 1/2 + 2 1/3, convert to improper: 1 1/2 = 3/2, 2 1/3=7/3. Find common denominator (6): 3/2 = 9/6, 7/3 = 14/6. 9/6 + 14/6 = 23/6 or 3 5/6.

   CHECKPOINT · Mixed numbers handled and result shown as proper or improper fraction.