What is 4/12 plus 5/9? (Answer: 8/9)

Exact Answer

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Problem: What is 4/12 plus 5/9?
Formula / Expression: 4/12 + 5/9
Final Answer: 8/9
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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 5/9 by 4 so both fractions share the common base 36.
Working: 4 × 3/12 × 3 = 12/36 and 5 × 4/9 × 4 = 20/36

Step 3: Add the Numerators
Now add the numerators (12 + 20 = 32) and keep the common denominator 36 unchanged.
Working: 12 + 20/36 = 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-4-12-plus-5-9/
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4/12 + 5/9 = 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: 4/12 + 5/9

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 5/9 by 4 so both fractions share the common base 36.

4 × 3/12 × 3 = 12/36 and 5 × 4/9 × 4 = 20/36

Step 3

Add the Numerators

Now add the numerators (12 + 20 = 32) and keep the common denominator 36 unchanged.

12 + 20/36 = 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 4/12 plus 5/9 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 4/12 plus 5/9 as a fraction?

4/12 + 5/9 in simplest fraction form is 8/9.

What is 4/12 plus 5/9 as a decimal?

4/12 + 5/9 converted to a decimal is 0.888889.

What is 4/12 plus 5/9 as a percentage?

4/12 + 5/9 expressed as a percentage is 88.8889%.

Does 4/12 plus 5/9 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.