What is 3/9 plus 4/12? (Answer: 2/3)

Exact Answer

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

Step 3: Add the Numerators
Now add the numerators (12 + 12 = 24) and keep the common denominator 36 unchanged.
Working: 12 + 12/36 = 24/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 36, which is 12. Divide both the numerator and denominator by 12.
Working: 24 ÷ 12/36 ÷ 12 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-4-12/
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3/9 + 4/12 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 3/9 + 4/12

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

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

Step 3

Add the Numerators

Now add the numerators (12 + 12 = 24) and keep the common denominator 36 unchanged.

12 + 12/36 = 24/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 36, which is 12. Divide both the numerator and denominator by 12.

24 ÷ 12/36 ÷ 12 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 3/9 plus 4/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 3/9 plus 4/12 as a fraction?

3/9 + 4/12 in simplest fraction form is 2/3.

What is 3/9 plus 4/12 as a decimal?

3/9 + 4/12 converted to a decimal is 0.666667.

What is 3/9 plus 4/12 as a percentage?

3/9 + 4/12 expressed as a percentage is 66.6667%.

Does 3/9 plus 4/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.