What is 2/9 plus 8/12? (Answer: 8/9)

Exact Answer

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Problem: What is 2/9 plus 8/12?
Formula / Expression: 2/9 + 8/12
Final Answer: 8/9
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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 2/9 by 4, and multiply the numerator and denominator of 8/12 by 3 so both fractions share the common base 36.
Working: 2 × 4/9 × 4 = 8/36 and 8 × 3/12 × 3 = 24/36

Step 3: Add the Numerators
Now add the numerators (8 + 24 = 32) and keep the common denominator 36 unchanged.
Working: 8 + 24/36 = 32/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 36, which is 4. Divide both the numerator and denominator by 4.
Working: 32 ÷ 4/36 ÷ 4 = 8/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 9 produces a repeating decimal (approximately 0.888889, or 88.8889%).
Working: 8 ÷ 9 = 0.888889 (88.8889%)

Key Values:
- Simplified Fraction: 8/9
- Mixed Number Form: 8/9
- Decimal Value: 0.888889
- Percentage: 88.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-8-12/
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2/9 + 8/12 = 8/9

Simplified Fraction

8/9

Mixed Number

Proper (8/9)

Decimal Value

0.888889

Percentage

88.8889%

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Step-by-Step Solution: 2/9 + 8/12

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 2/9 by 4, and multiply the numerator and denominator of 8/12 by 3 so both fractions share the common base 36.

2 × 4/9 × 4 = 8/36 and 8 × 3/12 × 3 = 24/36

Step 3

Add the Numerators

Now add the numerators (8 + 24 = 32) and keep the common denominator 36 unchanged.

8 + 24/36 = 32/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 36, which is 4. Divide both the numerator and denominator by 4.

32 ÷ 4/36 ÷ 4 = 8/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 9 produces a repeating decimal (approximately 0.888889, or 88.8889%).

8 ÷ 9 = 0.888889 (88.8889%)

Visual Representation

The diagram below illustrates 2/9 plus 8/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/9`
Mixed Number Form	`8/9`
Decimal Form	`0.888889`
Percentage	`88.8889%`

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Frequently Asked Questions

What is 2/9 plus 8/12 as a fraction?

2/9 + 8/12 in simplest fraction form is 8/9.

What is 2/9 plus 8/12 as a decimal?

2/9 + 8/12 converted to a decimal is 0.888889.

What is 2/9 plus 8/12 as a percentage?

2/9 + 8/12 expressed as a percentage is 88.8889%.

Does 2/9 plus 8/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.888889...) because the denominator contains prime factors other than 2 and 5.