What is 4/12 plus 8/9? (Answer: 11/9)

Exact Answer

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Problem: What is 4/12 plus 8/9?
Formula / Expression: 4/12 + 8/9
Final Answer: 1 2/9 (11/9)
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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 4/12 by 3, and multiply the numerator and denominator of 8/9 by 4 so both fractions share the common base 36.
Working: 4 × 3/12 × 3 = 12/36 and 8 × 4/9 × 4 = 32/36

Step 3: Add the Numerators
Now add the numerators (12 + 32 = 44) and keep the common denominator 36 unchanged.
Working: 12 + 32/36 = 44/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 44 and 36, which is 4. Divide both the numerator and denominator by 4.
Working: 44 ÷ 4/36 ÷ 4 = 11/9

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (11) is greater than the denominator (9), divide 11 by 9: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/9.
Working: 11/9 = 1 2/9

Step 6: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 9 produces a repeating decimal (approximately 1.222222, or 122.2222%).
Working: 11 ÷ 9 = 1.222222 (122.2222%)

Key Values:
- Simplified Fraction: 11/9
- Mixed Number Form: 1 2/9
- Decimal Value: 1.222222
- Percentage: 122.2222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-12-plus-8-9/
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4/12 + 8/9 = 11/9

Simplified Fraction

11/9

Mixed Number

1 2/9

Decimal Value

1.222222

Percentage

122.2222%

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Step-by-Step Solution: 4/12 + 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 4/12 by 3, and multiply the numerator and denominator of 8/9 by 4 so both fractions share the common base 36.

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

Step 3

Add the Numerators

Now add the numerators (12 + 32 = 44) and keep the common denominator 36 unchanged.

12 + 32/36 = 44/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 44 and 36, which is 4. Divide both the numerator and denominator by 4.

44 ÷ 4/36 ÷ 4 = 11/9

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (11) is greater than the denominator (9), divide 11 by 9: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/9.

11/9 = 12/9

Step 6

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 9 produces a repeating decimal (approximately 1.222222, or 122.2222%).

11 ÷ 9 = 1.222222 (122.2222%)

Visual Representation

The diagram below illustrates 4/12 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/9`
Mixed Number Form	`1 2/9`
Decimal Form	`1.222222`
Percentage	`122.2222%`

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Frequently Asked Questions

What is 4/12 plus 8/9 as a fraction?

4/12 + 8/9 in simplest fraction form is 11/9 (or 1 2/9 as a mixed number).

What is 4/12 plus 8/9 as a decimal?

4/12 + 8/9 converted to a decimal is 1.222222.

What is 4/12 plus 8/9 as a percentage?

4/12 + 8/9 expressed as a percentage is 122.2222%.

How do you write 4/12 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 11/9 can be written as the mixed number 1 2/9.

Does 4/12 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.222222...) because the denominator contains prime factors other than 2 and 5.