Multiplicative Patterned Selfie-Fractions Explorer
Fractions that recognise themselves through digit-splits and operations
Created by Inder J. Taneja Multiplicative Edition · v1.0
A selfie fraction N/D rewrites itself by splitting digits of N and D and applying an operation to each part, yielding the same reduced value. Numerator ops (2-part): A+B · A×B · A^B
Numerator ops (3-part): A+B+C · A×B×C · A×(B+C) · (A+B)×C · A×B+C · A+B×C · A^B+C · A+B^C · A^B×C · A×B^C Multiplicative denominator ops: A×B · A×B×C · A×(B+C) · (A+B)×C · A×B+C · A+B×C.
Example: 143/1386 = (1+4×3)/((13+8)×6) = 13/126.
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Multiplicative zero-extension family: keep the numerator fixed and append zeros to the denominator. Every displayed member is independently verified with multiplication-containing digit-splits. Obvious overlapping extensions and unchanged common-factor cancellations are excluded. Structured forms such as (1×1)/((23+8)×7) and (2×1)/((3+67)×5) remain included.
Discover multiplicative ×10 families
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Verify one supplied ×10 family
Enter a base fraction and press “Generate ×10 Family”.
Legacy insertion-family search
Insertion families start from a base selfie fraction and extend it by inserting a repeated block at a fixed position inside the denominator, producing a chain where every member is also a selfie fraction. 2-part denom:18/1782 → 18/17982 → 18/179982 → … (left part fixed, right part fixed) 3-part middle:130/1365 → 130/14365 → 130/144365 → … (left & right parts fixed, middle grows)
Ready.
Enter any fraction N/D to discover every selfie representation — all valid digit-splits and operations that reduce to the same value.
Run any search in tabs ①, ② or ③ first, then return here to download results as a .txt file. Each line is formatted as: k N/D = (num_op)/(denom_op);
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Search results — tab ①
saves as plain text file
Insertion families — tab ②
saves as plain text file
Verify result — tab ③
saves as plain text file
Combined
all results in one file
Run a search in tabs ①, ② or ③, then download the results as a modern .xlsx workbook. Separate columns are provided for the numerator, denominator, both digit-split expressions, and the complete pattern. A blank row separates consecutive pattern families.
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Excel workbook
each available result type is placed on its own worksheet
A selfie fraction N/D can be rewritten as f(digits of N)/g(digits of D) giving the same reduced value.
Named by analogy: the same subject, captured from a different angle.