What is 1/9 plus 9/12? (Answer: 31/36)

Exact Answer

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Problem: What is 1/9 plus 9/12?
Formula / Expression: 1/9 + 9/12
Final Answer: 31/36
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).
Working: LCD(9, 12) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 1/9 by 4, and multiply the numerator and denominator of 9/12 by 3 so both fractions share the common base 36.
Working: 1 × 4/9 × 4 = 4/36 and 9 × 3/12 × 3 = 27/36

Step 3: Add the Numerators
Now add the numerators (4 + 27 = 31) and keep the common denominator 36 unchanged.
Working: 4 + 27/36 = 31/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 36 is 1, confirming that 31/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 36 produces a repeating decimal (approximately 0.861111, or 86.1111%).
Working: 31 ÷ 36 = 0.861111 (86.1111%)

Key Values:
- Simplified Fraction: 31/36
- Mixed Number Form: 31/36
- Decimal Value: 0.861111
- Percentage: 86.1111%

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Solved with FractionsCalc:
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1/9 + 9/12 = 31/36

Simplified Fraction

31/36

Mixed Number

Proper (31/36)

Decimal Value

0.861111

Percentage

86.1111%

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Step-by-Step Solution: 1/9 + 9/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).

LCD(9, 12) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 1/9 by 4, and multiply the numerator and denominator of 9/12 by 3 so both fractions share the common base 36.

1 × 4/9 × 4 = 4/36 and 9 × 3/12 × 3 = 27/36

Step 3

Add the Numerators

Now add the numerators (4 + 27 = 31) and keep the common denominator 36 unchanged.

4 + 27/36 = 31/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 36 is 1, confirming that 31/36 cannot be reduced further—it is already in its simplest irreducible form.

31/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 36 produces a repeating decimal (approximately 0.861111, or 86.1111%).

31 ÷ 36 = 0.861111 (86.1111%)

Visual Representation

The diagram below illustrates 1/9 plus 9/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/36`
Mixed Number Form	`31/36`
Decimal Form	`0.861111`
Percentage	`86.1111%`

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Frequently Asked Questions

What is 1/9 plus 9/12 as a fraction?

1/9 + 9/12 in simplest fraction form is 31/36.

What is 1/9 plus 9/12 as a decimal?

1/9 + 9/12 converted to a decimal is 0.861111.

What is 1/9 plus 9/12 as a percentage?

1/9 + 9/12 expressed as a percentage is 86.1111%.

Does 1/9 plus 9/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.861111...) because the denominator contains prime factors other than 2 and 5.