What is 9/12 plus 8/9? (Answer: 59/36)

Exact Answer

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Problem: What is 9/12 plus 8/9?
Formula / Expression: 9/12 + 8/9
Final Answer: 1 23/36 (59/36)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 9/12 by 3, and multiply the numerator and denominator of 8/9 by 4 so both fractions share the common base 36.
Working: 9 × 3/12 × 3 = 27/36 and 8 × 4/9 × 4 = 32/36

Step 3: Add the Numerators
Now add the numerators (27 + 32 = 59) and keep the common denominator 36 unchanged.
Working: 27 + 32/36 = 59/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 36 is 1, confirming that 59/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/36

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (36), divide 59 by 36: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/36.
Working: 59/36 = 1 23/36

Step 6: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 36 produces a repeating decimal (approximately 1.638889, or 163.8889%).
Working: 59 ÷ 36 = 1.638889 (163.8889%)

Key Values:
- Simplified Fraction: 59/36
- Mixed Number Form: 1 23/36
- Decimal Value: 1.638889
- Percentage: 163.8889%

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Solved with FractionsCalc:
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9/12 + 8/9 = 59/36

Simplified Fraction

59/36

Mixed Number

1 23/36

Decimal Value

1.638889

Percentage

163.8889%

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Step-by-Step Solution: 9/12 + 8/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(12, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 9/12 by 3, and multiply the numerator and denominator of 8/9 by 4 so both fractions share the common base 36.

9 × 3/12 × 3 = 27/36 and 8 × 4/9 × 4 = 32/36

Step 3

Add the Numerators

Now add the numerators (27 + 32 = 59) and keep the common denominator 36 unchanged.

27 + 32/36 = 59/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 36 is 1, confirming that 59/36 cannot be reduced further—it is already in its simplest irreducible form.

59/36

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (59) is greater than the denominator (36), divide 59 by 36: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/36.

59/36 = 123/36

Step 6

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 36 produces a repeating decimal (approximately 1.638889, or 163.8889%).

59 ÷ 36 = 1.638889 (163.8889%)

Visual Representation

The diagram below illustrates 9/12 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/36`
Mixed Number Form	`1 23/36`
Decimal Form	`1.638889`
Percentage	`163.8889%`

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Frequently Asked Questions

What is 9/12 plus 8/9 as a fraction?

9/12 + 8/9 in simplest fraction form is 59/36 (or 1 23/36 as a mixed number).

What is 9/12 plus 8/9 as a decimal?

9/12 + 8/9 converted to a decimal is 1.638889.

What is 9/12 plus 8/9 as a percentage?

9/12 + 8/9 expressed as a percentage is 163.8889%.

How do you write 9/12 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 59/36 can be written as the mixed number 1 23/36.

Does 9/12 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.638889...) because the denominator contains prime factors other than 2 and 5.