What is 3/39 plus 2/4? (Answer: 15/26)

Exact Answer

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Problem: What is 3/39 plus 2/4?
Formula / Expression: 3/39 + 2/4
Final Answer: 15/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 39 × 4 = 156.
Working: LCD(39, 4) = 156

Step 2: Convert to Equivalent Fractions with Common Denominator 156
Multiply the numerator and denominator of 3/39 by 4, and multiply the numerator and denominator of 2/4 by 39 so both fractions share the common base 156.
Working: 3 × 4/39 × 4 = 12/156 and 2 × 39/4 × 39 = 78/156

Step 3: Add the Numerators
Now add the numerators (12 + 78 = 90) and keep the common denominator 156 unchanged.
Working: 12 + 78/156 = 90/156

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 156, which is 6. Divide both the numerator and denominator by 6.
Working: 90 ÷ 6/156 ÷ 6 = 15/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 26 produces a repeating decimal (approximately 0.576923, or 57.6923%).
Working: 15 ÷ 26 = 0.576923 (57.6923%)

Key Values:
- Simplified Fraction: 15/26
- Mixed Number Form: 15/26
- Decimal Value: 0.576923
- Percentage: 57.6923%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-39-plus-2-4/
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3/39 + 2/4 = 15/26

Simplified Fraction

15/26

Mixed Number

Proper (15/26)

Decimal Value

0.576923

Percentage

57.6923%

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Step-by-Step Solution: 3/39 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 39 × 4 = 156.

LCD(39, 4) = 156

Step 2

Convert to Equivalent Fractions with Common Denominator 156

Multiply the numerator and denominator of 3/39 by 4, and multiply the numerator and denominator of 2/4 by 39 so both fractions share the common base 156.

3 × 4/39 × 4 = 12/156 and 2 × 39/4 × 39 = 78/156

Step 3

Add the Numerators

Now add the numerators (12 + 78 = 90) and keep the common denominator 156 unchanged.

12 + 78/156 = 90/156

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 156, which is 6. Divide both the numerator and denominator by 6.

90 ÷ 6/156 ÷ 6 = 15/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 26 produces a repeating decimal (approximately 0.576923, or 57.6923%).

15 ÷ 26 = 0.576923 (57.6923%)

Visual Representation

The diagram below illustrates 3/39 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/26`
Mixed Number Form	`15/26`
Decimal Form	`0.576923`
Percentage	`57.6923%`

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Frequently Asked Questions

What is 3/39 plus 2/4 as a fraction?

3/39 + 2/4 in simplest fraction form is 15/26.

What is 3/39 plus 2/4 as a decimal?

3/39 + 2/4 converted to a decimal is 0.576923.

What is 3/39 plus 2/4 as a percentage?

3/39 + 2/4 expressed as a percentage is 57.6923%.

Does 3/39 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.576923...) because the denominator contains prime factors other than 2 and 5.