Workforce composition and family status In an office, 1/3 of the workers are women. Of the women, 1/2 are married and 1/3 of the married women have children. Of the men, 3/4 are married and 2/3 of the married men have children. What fraction of all workers are without children?

Introduction / Context:This is a layered fraction problem about classifications (women/men, married, with children). The solution adds proportions stepwise and then complements to find the share without children.

Given Data / Assumptions:

• Total workforce = 1 (for convenience).
• Women = 1/3; Men = 2/3.
• Married women = (1/2) of women = 1/6; with children = (1/3) of married women = 1/18.
• Married men = (3/4) of men = 1/2; with children = (2/3) of married men = 1/3.

Concept / Approach:Compute the total fraction with children by summing the women-with-children and men-with-children shares. Subtract this from 1 to get the fraction without children.

Step-by-Step Solution:Women with children = 1/18.Men with children = 1/3.Total with children = 1/18 + 1/3 = 1/18 + 6/18 = 7/18.Therefore, without children = 1 − 7/18 = 11/18.

Verification / Alternative check:Convert to decimals as a quick check: 7/18 ≈ 0.3889, so without children ≈ 0.6111 which equals 11/18.

Why Other Options Are Wrong:5/11, 4/9, and 17/36 arise from partial or incorrect aggregation; 7/18 is actually the fraction with children, not without.

Common Pitfalls:Multiplying instead of taking fractions of group sizes; forgetting to complement at the end.

Final Answer:11/18