What is 2/24 plus 4/39? (Answer: 29/156)

Exact Answer

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Problem: What is 2/24 plus 4/39?
Formula / Expression: 2/24 + 4/39
Final Answer: 29/156
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 312 (which is smaller than their product 24 × 39 = 936, keeping the calculation simpler).
Working: LCD(24, 39) = 312

Step 2: Convert to Equivalent Fractions with Common Denominator 312
Multiply the numerator and denominator of 2/24 by 13, and multiply the numerator and denominator of 4/39 by 8 so both fractions share the common base 312.
Working: 2 × 13/24 × 13 = 26/312 and 4 × 8/39 × 8 = 32/312

Step 3: Add the Numerators
Now add the numerators (26 + 32 = 58) and keep the common denominator 312 unchanged.
Working: 26 + 32/312 = 58/312

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 312, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/312 ÷ 2 = 29/156

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 156 produces a repeating decimal (approximately 0.185897, or 18.5897%).
Working: 29 ÷ 156 = 0.185897 (18.5897%)

Key Values:
- Simplified Fraction: 29/156
- Mixed Number Form: 29/156
- Decimal Value: 0.185897
- Percentage: 18.5897%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-24-plus-4-39/
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2/24 + 4/39 = 29/156

Simplified Fraction

29/156

Mixed Number

Proper (29/156)

Decimal Value

0.185897

Percentage

18.5897%

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Step-by-Step Solution: 2/24 + 4/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 312 (which is smaller than their product 24 × 39 = 936, keeping the calculation simpler).

LCD(24, 39) = 312

Step 2

Convert to Equivalent Fractions with Common Denominator 312

Multiply the numerator and denominator of 2/24 by 13, and multiply the numerator and denominator of 4/39 by 8 so both fractions share the common base 312.

2 × 13/24 × 13 = 26/312 and 4 × 8/39 × 8 = 32/312

Step 3

Add the Numerators

Now add the numerators (26 + 32 = 58) and keep the common denominator 312 unchanged.

26 + 32/312 = 58/312

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 312, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/312 ÷ 2 = 29/156

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 156 produces a repeating decimal (approximately 0.185897, or 18.5897%).

29 ÷ 156 = 0.185897 (18.5897%)

Visual Representation

The diagram below illustrates 2/24 plus 4/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/156`
Mixed Number Form	`29/156`
Decimal Form	`0.185897`
Percentage	`18.5897%`

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Frequently Asked Questions

What is 2/24 plus 4/39 as a fraction?

2/24 + 4/39 in simplest fraction form is 29/156.

What is 2/24 plus 4/39 as a decimal?

2/24 + 4/39 converted to a decimal is 0.185897.

What is 2/24 plus 4/39 as a percentage?

2/24 + 4/39 expressed as a percentage is 18.5897%.

Does 2/24 plus 4/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.185897...) because the denominator contains prime factors other than 2 and 5.