Two further calculation chapters of the matn: rounding out shares that don’t divide evenly among heads (tashih), and combining calculations when deaths occur in succession before the estate is divided (munasakhat) — ar-Rahbiyyah closes its calculation section with this chapter.
Tashih
When a group’s shares do not divide evenly by its number of heads, multiply the entire problem by the smallest multiplier (juz’us-sahm):
- Count the heads of the group that doesn’t divide evenly (male counts as 2, female as 1 in ‘ashabah bil-ghair).
- Tabayun (GCD of shares-heads = 1) → multiplier = the full number of heads. Tawafuq (GCD > 1) → multiplier = heads ÷ GCD (wafq).
- More than one group that doesn’t divide evenly → combine the multipliers (multiply those that are coprime; take the LCM where they share factors).
Tawafuq example: 2 shares for 6 sisters → GCD 2 → multiplier 3, not 6. The correct tashih is always the most reduced one — the same spirit as the poem itself.
Munasakhat
Munasakhat = an heir dies before the first deceased’s estate is divided, so that heir’s share flows on to their own heirs. The matn’s recipe has three steps:
flowchart LR
classDef mayit fill:#7f1d1d,stroke:#ef4444,color:#fee2e2
classDef proses fill:#713f12,stroke:#ca8a04,color:#fef9c3
classDef hasil fill:#3b0764,stroke:#a855f7,color:#f3e8ff
A["Problem 1: the first deceased<br/>(calculate normally, note the share<br/>of the second deceased)"]:::mayit --> B["Problem 2: the second deceased<br/>(calculate normally, its own base)"]:::mayit
B --> C["Jami'ah:<br/>share of deceased-2 vs base of problem-2 —<br/>tawafuq? use wafq ·<br/>tabayun? multiply in full"]:::proses
C --> D["Combined base =<br/>base-1 × multiplier →<br/>all final shares"]:::hasil
- Work problem 1 in full; mark the share of the second deceased (call it s).
- Work problem 2 (the heirs of the second deceased) with its own base (call it a).
- Combine: compare s and a — if tawafuq, multiply problem 1 by the wafq of a; if tabayun, by the full a. Recipients of problem 2 get their shares × (s ÷ GCD).
A full worked example with numbers is in the case studies in the Ibn Uthaymin bundle — the technique is identical across madhhabs, so it is not repeated here; what changes between madhhabs is only the content of each problem (e.g. if problem 2 involves a grandfather-and-siblings, the matn calculates it with the Zayd system, chapter 08).
Two munasakhat pitfalls
- Dual roles — the same person can inherit in both problems under a different status (wife in problem 1 = mother in problem 2). Write down their role per problem; don’t merge them before the jami’ah.
- The order of death must be certain — if it is not known who died first (a simultaneous calamity), there is in fact no mutual inheritance at all (chapter 09), and munasakhat does not occur.
Sources: Matn ar-Rahbiyyah, chapter on at-tashih & al-munasakhat (Shamela 11372); Sharh al-Hazimi (Shamela 36125). Full list in 15-references.