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Tarkib | Adadi

All numbers from 11 to 19 are mabnī (fixed) on the fatḥa (فتحة) at the end of each component, except for number 12 which is built on fatḥa in the accusative and genitive cases but on alif in the nominative case (due to its dual origin).

| Case | 11 (masc.) | 12 (masc.) | |------|------------|------------| | Nom. | Aḥada ʿashara | Ithnā ʿashara | | Acc. | Aḥada ʿashara | Ithnay ʿashara | | Gen. | Aḥada ʿashara | Ithnay ʿashara |

In algebra, the binomial (x + 3) is an expression composed of the parts x and 3. Solving equations often requires decomposing a term or composing like terms — a direct extension of tarkib adadi.

Traditional "times tables" are memory-based. Tarkib Adadi is understanding-based. When a student knows the composition of 10 (1+9, 2+8, 3+7, 4+6, 5+5), they are not just memorizing addition facts; they are understanding the structure of the decimal system. tarkib adadi

Ten is the base of our number system. Mastering these pairs is non-negotiable:

Build a tower of 8 bricks. Then snap it into two towers. Write the number bond (e.g., 5 and 3). Reassemble. Repeat until all bonds are found.

The first part (units 1–9) agrees in gender with the counted noun. The second part (ʿashara / ʿashrata) agrees oppositely. All numbers from 11 to 19 are mabnī

| Gender | 11 | 13 (example) | |--------|----|--------------| | Masculine noun | Aḥada ʿashara (أَحَدَ عَشَرَ) | Thalāthata ʿashara | | Feminine noun | Iḥdā ʿashrata (إِحْدَى عَشْرَةَ) | Thalātha ʿashrata |

Note: The feminine 11 takes Iḥdā (not Aḥada).

To check if a number is composite, follow these steps: Traditional "times tables" are memory-based

Step 1: Check divisibility by small primes. Try dividing the number by 2, 3, 5, or 7.

Step 2: Apply Divisibility Rules:

  • Divisible by 3? Add the digits. If the sum is divisible by 3, the number is composite.
  • Divisible by 5? If the number ends in 0 or 5, it is composite.

    • Step 3: Conclusion. If you find any factor other than 1 and the number itself, it is a Composite Number.

    Subtraction is often taught as "taking away," but through the lens of composition, subtraction becomes "finding the missing part." If a child knows 9 is composed of 6 and 3, then 9 – 6 = 3 becomes intuitive. This reduces reliance on finger-counting.