بِسْمِ اللهِ الرَّحْمٰنِ الرَّحِيْم

In the Name of God, Most Gracious, Most Merciful

♥️🤲🕋♥️🕋🌹🌹🥀🤲🌹🕋♥️🤲

THE MATHEMATICS OF REVELATION

CHAPTER NINE — THE HOUSE OF FRACTIONS: A MASTERCLASS

OPENING THE DOOR TO THE HOUSE OF FRACTIONS

In CHAPTER 9 we showed how the companions calculated inheritance using their hands, their minds, and the mathematics available to them. They solved real problems of justice without calculators, paper ledgers, or modern numerals. But Allah did not leave inheritance to human opinion, and He did not leave it to be reinvented by every generation after the Prophet ﷺ.

Instead, Allah placed fractions directly into the Qur'an. Not general advice. Not vague instructions to "be fair." Precise mathematical shares. A system designed to survive long after the Prophet ﷺ, protecting widows, parents, daughters, sons, and families through the language of numbers.

Now, with the help of the House of Wisdom, we will make these fractions simple. We will show you what one-half, one-third, one-sixth, and one-eighth actually mean. We will visualize them, calculate them, and understand why Allah chose fractions as the architecture of justice. Welcome to the House of Fractions. Let us begin.

بِسْمِ اللهِ الرَّحْمٰنِ الرَّحِيْم

STEP 1 — BEGIN WITH THE HUMAN PROBLEM

Imagine your father passes away. He leaves behind 100 coins. He also leaves behind your mother, your two sisters, and your grandparents.

How do you divide the coins fairly?

If you give too much to one person, others will be hurt. If you give too little, someone will be left with nothing. If you guess, you might make a mistake that destroys your family.

This is not a hypothetical problem.

This is the most difficult question a family can face after losing someone they love.

What is fair? Who gets what? How do you measure justice when emotions are high and grief is overwhelming?

The answer lies in fractions.

STEP 2 — SHOW THE ORIGINAL REVELATION

بِسْمِ اللهِ الرَّحْمٰنِ الرَّحِيْم

In the Name of Allah, the Most Gracious, the Most Merciful

THE REVEALED FRACTIONS

Before we learn the mathematics, we must first look at the source.

The inheritance system is not derived from kings, judges, scholars, or philosophers.

It comes directly from Revelation.

In Surah An-Nisa, Allah reveals the foundations of inheritance across three verses:

Surah An-Nisa (4:11) — Children and Parents

Surah An-Nisa (4:12) — Husbands and Wives

Surah An-Nisa (4:176) — Siblings and Special Cases

Together, these verses establish the fractional architecture of inheritance.

Before we learn how to calculate the fractions, let us first see them directly from the Book of Allah.

SURAH AN-NISA (4:11)

يُوصِيكُمُ اللَّهُ فِي أَوْلَادِكُمْ ۖ لِلذَّكَرِ مِثْلُ حَظِّ الْأُنثَيَيْنِ ۚ فَإِن كُنَّ نِسَاءً فَوْقَ اثْنَتَيْنِ فَلَهُنَّ ثُلُثَا مَا تَرَكَ ۖ وَإِن كَانَتْ وَاحِدَةً فَلَهَا النِّصْفُ ۚ وَلِأَبَوَيْهِ لِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ مِمَّا تَرَكَ إِن كَانَ لَهُ وَلَدٌ

"Allah instructs you concerning your children: for the male, what is equal to the share of two females. But if there are only daughters, two or more, for them is two-thirds of one's estate. If there is only one, for her is half. And for one's parents, to each one of them is a sixth of his estate if he left children..."

SURAH AN-NISA (4:12)

وَلَكُمْ نِصْفُ مَا تَرَكَ أَزْوَاجُكُمْ إِن لَّمْ يَكُن لَّهُنَّ وَلَدٌ ۚ فَإِن كَانَ لَهُنَّ وَلَدٌ فَلَكُمُ الرُّبُعُ مِمَّا تَرَكْنَ ۚ مِن بَعْدِ وَصِيَّةٍ يُوصِينَ بِهَا أَوْ دَيْنٍ ۚ وَلَهُنَّ الرُّبُعُ مِمَّا تَرَكْتُمْ إِن لَّمْ يَكُن لَّكُمْ وَلَدٌ ۚ فَإِن كَانَ لَكُمْ وَلَدٌ فَلَهُنَّ الثُّمُنُ مِمَّا تَرَكْتُم

"And for you is half of what your wives leave if they have no child. But if they have a child, then for you is one-fourth of what they leave. And for the wives is one-fourth if you leave no child. But if you leave a child, then for them is one-eighth..."

SURAH AN-NISA (4:176)

يَسْتَفْتُونَكَ ۖ قُلِ اللَّهُ يُفْتِيكُمْ فِي الْكَلَالَةِ ۚ إِنِ امْرُؤٌ هَلَكَ لَيْسَ لَهُ وَلَدٌ وَلَهُ أُخْتٌ فَلَهَا نِصْفُ مَا تَرَكَ ۚ وَهُوَ يَرِثُهَا إِن لَّمْ يَكُن لَّهَا وَلَدٌ ۚ فَإِن كَانَتَا اثْنَتَيْنِ فَلَهُمَا الثُّلُثَانِ مِمَّا تَرَكَ

"They ask you for a legal ruling. Say: Allah gives you a ruling concerning one who leaves neither descendants nor ascendants. If a man dies leaving a sister, she shall have half of what he left. If there are two sisters, they shall have two-thirds of what he left..."

THE FRACTIONS OF THE QUR'AN

النِّصْفُ — One-Half (½)

الرُّبُعُ — One-Quarter (¼)

الثُّمُنُ — One-Eighth (⅛)

الثُّلُثُ — One-Third (⅓)

الثُّلُثَانِ — Two-Thirds (⅔)

السُّدُسُ — One-Sixth (⅙)

Heir Fraction A single daughter ½ Two or more daughters ⅔ Parents (if children exist) ⅙ each Wife (if children exist) ⅛ Wife (if no children) ¼

Why does Allah give fractions instead of just saying "be fair"?

Because fairness without measurement is impossible.

Generosity without calculation leads to injustice.

Justice requires precision.

And precision requires mathematics.

Fractions are how Allah teaches us to measure justice.

STEP 3 — EXPLAIN THE CONCEPT IN PLAIN LANGUAGE

What is a fraction?

A fraction is a part of something whole.

Think of a pie.

• If you cut the pie into two equal pieces, each piece is one-half (½).

• If you cut it into three equal pieces, each piece is one-third (⅓).

• If you cut it into four equal pieces, each piece is one-quarter (¼).

• If you cut it into six equal pieces, each piece is one-sixth (⅙).

• If you cut it into eight equal pieces, each piece is one-eighth (⅛).

Now think of your father's 100 coins as the pie.

• ½ of 100 is 50 coins.

• ⅓ of 100 is 33 coins.

• ¼ of 100 is 25 coins.

• ⅙ of 100 is 16 coins.

• ⅛ of 100 is 12 coins.

Fractions are how we divide things fairly.

STEP 4 — VISUALIZE THE MATH

Let us visualize the fractions.

[A circle divided into 2 equal pieces — ½ shown]
One-Half (½)

[A circle divided into 3 equal pieces — ⅓ shown]
One-Third (⅓)

[A circle divided into 4 equal pieces — ¼ shown]
One-Quarter (¼)

[A circle divided into 6 equal pieces — ⅙ shown]
One-Sixth (⅙)

[A circle divided into 8 equal pieces — ⅛ shown]
One-Eighth (⅛)

These are the fractions Allah uses in the Qur'an.

They are not abstract numbers.

They are real shares.

Real portions.

Real rights.

STEP 5 — SHOW THE PROBLEM

Now let us try to divide the inheritance using these fractions.

A man dies leaving:

• A wife

• Two daughters

• Both parents

The Fractions

• Two daughters: ⅔

• Parents: ⅙ + ⅙ = ⅓

• Wife: ⅛

The Problem

We need to add these fractions together to see if they fit into 1 whole estate.

But fractions have different denominators (3, 6, 8).

We cannot add them directly.

We need to find a common denominator.

STEP 6 — HOW THE EARLY MUSLIMS SOLVED IT

The companions did not have calculators.

They did not have numerals.

They did not have paper ledgers.

What did they have?

They had their hands.

The system they used was called Ḥisāb al-ʿUqūd — "Number Reckoning by Finger Folding."

It could represent numbers up to 9,999 on two hands.

Calculations were performed mentally, and intermediate results were stored by positioning the fingers in particular ways.

The Prophet ﷺ explicitly commanded them:

"واعقدن بالأنامل فإنَّهنَّ مسئولاتٌ مستنطقاتٌ"

"Count using the finger joints (al-anāmil), for they will be questioned and made to speak."

This was a specific, technical instruction for a method of calculation.

The companions solved this problem with their minds and their hands.

But it was hard.

It required training.

It required memory.

It required practice.

Not everyone could do it.

STEP 7 — THE HOUSE OF WISDOM

Two centuries later, the House of Wisdom in Baghdad gave the world something extraordinary:

Al-Khwarizmi and the Hindu-Arabic numerals.

Al-Khwarizmi wrote On the Calculation with Hindu Numerals, introducing the Indian system to the Islamic world and, later, to Europe.

He wrote Kitab al-Jabr wa-l-Muqabala — "The Compendious Book on Calculation by Completion and Balancing" — which gave the world the word algebra and the method of solving equations.

He made it easy.

Now we can solve the problem with symbols, numerals, and paper.

Let us do it.

STEP 8 — SOLVING THE PROBLEM (MODERN WAY)

A man dies leaving:

• A wife

• Two daughters

• Both parents

The Fractions

• Two daughters: ⅔

• Parents: ⅙ + ⅙ = ⅓

• Wife: ⅛

Step 1: Find a Common Denominator

The denominators are 3, 6, and 8.

The common denominator is 24.

Step 2: Convert the Fractions

• Two daughters: ⅔ = 16/24

• Parents: ⅓ = 8/24

• Wife: ⅛ = 3/24

Step 3: Sum the Shares

16/24 + 8/24 + 3/24 = 27/24

Step 4: Recognize the Problem

27/24 is greater than 1.

The claims exceed the estate.

Step 5: Apply 'Awl — Expand the Base

Instead of 24, use 27 as the base.

Step 6: The New Shares

Heir Original Share New Share Two Daughters 16/24 16/27 Parents 8/24 8/27 Wife 3/24 3/27 = 1/9

The wife's eighth has become a ninth.

STEP 9 — WHY THIS MATTERS

Fractions are not just math.

They are mercy.

When a family loses someone they love, the last thing they need is confusion.

The last thing they need is conflict.

The last thing they need is fighting over money.

Allah gave fractions to prevent that.

He gave clear shares.

Fixed shares.

Measurable shares.

He gave the widow a share.

He gave the orphan a share.

He gave the parents a share.

He gave the daughters a share.

No one is forgotten.

No one is left out.

No one is cheated.

Fractions are how Allah protects the vulnerable.

STEP 10 — THE CIVILIZATIONAL INSIGHT

What did the House of Wisdom give us?

It gave us simplicity.

It gave us symbols.

It gave us numerals.

It gave us paper.

It gave us speed.

It gave us accessibility.

But the companions did not need it to be easy.

They needed it to be just.

And it was.

Fractions became the language of justice.

The hand became the instrument.

And Baghdad made it easy.

THE MATHEMATICS OF REVELATION

CHAPTER NINE — THE HOUSE OF FRACTIONS: A MASTERCLASS

بِسْمِ اللهِ الرَّحْمٰنِ الرَّحِيْم

TURNING THE PAGE

We have spent this chapter learning fractions the way the companions learned them — with their hands, their minds, and the mathematics of Revelation.

We have seen how they calculated inheritance, found common denominators, and applied 'awl — all without numerals, without paper, without calculators.

It was hard.

But they did it because they had to.

Because justice required it.

Because Revelation commanded it.

Now we turn the page.

WHAT CAME BEFORE

Before the House of Wisdom, the world calculated with systems like Roman numerals.

Try adding these:

XXIII + XLV

It is possible.

But it is slow.

It is confusing.

And imagine doing this for taxes, trade, and inheritance across an entire empire.

Now try multiplying:

XII × VIII

Again, it works for small numbers.

But imagine larger numbers.

Imagine thousands.

Imagine millions.

It was a nightmare.

The Roman system had no zero.

No place value.

No easy way to calculate.

WHAT BAGHDAD GAVE US

Then came Baghdad.

The House of Wisdom.

Al-Khwarizmi.

Hindu-Arabic numerals.

The difference:

Roman Baghdad XXVII 27 CCXLVIII 248 MMMDXXVIII 3,528

Now look at that.

With Roman numerals, you have to add and subtract just to read the number.

With Hindu-Arabic numerals, you just read it.

Place value made everything easier.

Zero made everything possible.

WHAT AL-KHWARIZMI GAVE US

Al-Khwarizmi wrote Kitab al-Jabr wa-l-Muqabala — "The Compendious Book on Calculation by Completion and Balancing."

The word al-jabr gave us "algebra."

The Latin version of his name gave us "algorithm."

He made it easy.

In his own words, the purpose of the book was practical:

"What is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade..."

This was not mathematics for philosophers.

This was mathematics for real people.

For merchants.

For judges.

For families.

For inheritance.

For civilization itself.

THE ROAD AHEAD

We have seen how the companions calculated with their hands.

We have seen how Baghdad transformed calculation.

Now we move into the House of Wisdom itself.

CHAPTER TEN — THE HOUSE OF WISDOM

How Algebra Changed Civilization

Class dismissed.

For now. Inshallah see you on the. Next chapter inshallah