Step-by-step explanation:
The denominators are 2, 3, and 4. The least common denominator is the least common multiple (LCM) of these numbers.
To find the LCM, first write the prime factorizations.
2 = 2¹
3 = 3¹
4 = 2²
The LCM is therefore 2² × 3 = 12.
Rewrite the fractions with a denominator of 12.
⁷/₄ + ¹/₂ + ⁵/₃ + ¹/₃ + ¹/₄ + ¹/₂
= ²¹/₁₂ + ⁶/₁₂ + ²⁰/₁₂ + ⁴/₁₂ + ³/₁₂ + ⁶/₁₂
Now that the denominators are the same, we can simply add the numerators.
= ⁽²¹⁺⁶⁺²⁰⁺⁴⁺³⁺⁶⁾/₁₂
= ⁶⁰/₁₂
= 5
