Complete Fraction-Percentage Families

Once you know the base value 1/n, every fraction k/n is simply k × (1/n)%. Memorize these families to convert instantly during exams.

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Family of 3 (1/3 = 33.33%)

Fraction	Percentage
1/3	33.33%
2/3	66.66%

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Family of 4 (1/4 = 25%)

Fraction	Percentage		Fraction	Percentage
1/4	25%		5/4	125%
2/4 = 1/2	50%		7/4	175%
3/4	75%		9/4	225%

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Family of 6 (1/6 = 16.66%)

Fraction	Simplified	Percentage
1/6	—	16.66%
2/6	1/3	33.33%
3/6	1/2	50%
4/6	2/3	66.66%
5/6	—	83.33%

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Family of 9 (1/9 = 11.11%)

Fraction	Percentage		Fraction	Percentage
1/9	11.11%		5/9	55.55%
2/9	22.22%		6/9 = 2/3	66.66%
3/9 = 1/3	33.33%		7/9	77.77%
4/9	44.44%		8/9	88.88%

Pattern: Ninths produce repeating digits — 1/9 = 11.11%, 2/9 = 22.22%, etc.

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Family of 11 (1/11 = 9.09%)

Fraction	Percentage		Fraction	Percentage
1/11	9.09%		5/11	45.45%
2/11	18.18%		6/11	54.54%
3/11	27.27%		7/11	63.63%
4/11	36.36%

Pattern: Elevenths produce repeating two-digit blocks — 09, 18, 27, 36, 45, 54, 63...

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Family of 16 (1/16 = 6.25%)

Fraction	Simplified	Percentage
1/16	—	6.25%
2/16	1/8	12.5%
3/16	—	18.75%
5/16	—	31.25%
7/16	—	43.75%
9/16	—	56.25%
15/16	—	93.75%

Pattern: Sixteenths increase by 6.25 each step.

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Family of 20 (1/20 = 5%)

Fraction	Percentage		Fraction	Percentage		Fraction	Percentage
1/20	5%		7/20	35%		13/20	65%
3/20	15%		9/20	45%		15/20 = 3/4	75%
5/20 = 1/4	25%		11/20	55%		17/20	85%
						19/20	95%

Also: 21/20 = 105% (more than 100%)

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Family of 25 (1/25 = 4%)

Fraction	Percentage		Fraction	Percentage		Fraction	Percentage
1/25	4%		5/25 = 1/5	20%		9/25	36%
2/25	8%		6/25	24%		10/25 = 2/5	40%
3/25	12%		7/25	28%		11/25	44%
4/25	16%		8/25	32%		12/25	48%

Also: 13/25 = 52%

Pattern: Twenty-fifths increase by 4% each step. Very clean for mental math.

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Family of 40 (1/40 = 2.5%)

Fraction	Percentage		Fraction	Percentage
3/40	7.5%		11/40	27.5%
7/40	17.5%		13/40	32.5%
9/40	22.5%		19/40	47.5%

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Family of 50 (1/50 = 2%)

Fraction	Percentage		Fraction	Percentage
2/50	4%		12/50	24%
3/50	6%		13/50	26%

Pattern: Fiftieths increase by 2% each step.

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How to Use in Exams

Recognizing percentages → fractions:

• See 45.45% in a problem? → That's 5/11. Now use 5/11 instead of the decimal.
• See 43.75%? → That's 7/16.
• See 83.33%? → That's 5/6.

Recognizing fractions → percentages:

• Need 7/20 of 4000? → 35% of 4000 = 1400. Much faster than dividing.

The golden rule: Always convert percentages to fractions (or vice versa) BEFORE computing. Fractions make multiplication/division trivial.

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Practice: Identify the Fraction

#	Percentage	Fraction
1	22.22%	2/9
2	36.36%	4/11
3	18.75%	3/16
4	83.33%	5/6
5	55.55%	5/9
6	43.75%	7/16
7	27.27%	3/11
8	77.77%	7/9
9	45%	9/20
10	32%	8/25