What is 2/24 plus 9/39? (Answer: 49/156)

Exact Answer

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Problem: What is 2/24 plus 9/39?
Formula / Expression: 2/24 + 9/39
Final Answer: 49/156
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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 9/39 by 8 so both fractions share the common base 312.
Working: 2 × 13/24 × 13 = 26/312 and 9 × 8/39 × 8 = 72/312

Step 3: Add the Numerators
Now add the numerators (26 + 72 = 98) and keep the common denominator 312 unchanged.
Working: 26 + 72/312 = 98/312

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 98 and 312, which is 2. Divide both the numerator and denominator by 2.
Working: 98 ÷ 2/312 ÷ 2 = 49/156

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 156 produces a repeating decimal (approximately 0.314103, or 31.4103%).
Working: 49 ÷ 156 = 0.314103 (31.4103%)

Key Values:
- Simplified Fraction: 49/156
- Mixed Number Form: 49/156
- Decimal Value: 0.314103
- Percentage: 31.4103%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-24-plus-9-39/
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2/24 + 9/39 = 49/156

Simplified Fraction

49/156

Mixed Number

Proper (49/156)

Decimal Value

0.314103

Percentage

31.4103%

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Step-by-Step Solution: 2/24 + 9/39

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 9/39 by 8 so both fractions share the common base 312.

2 × 13/24 × 13 = 26/312 and 9 × 8/39 × 8 = 72/312

Step 3

Add the Numerators

Now add the numerators (26 + 72 = 98) and keep the common denominator 312 unchanged.

26 + 72/312 = 98/312

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 98 and 312, which is 2. Divide both the numerator and denominator by 2.

98 ÷ 2/312 ÷ 2 = 49/156

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 156 produces a repeating decimal (approximately 0.314103, or 31.4103%).

49 ÷ 156 = 0.314103 (31.4103%)

Visual Representation

The diagram below illustrates 2/24 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/156`
Mixed Number Form	`49/156`
Decimal Form	`0.314103`
Percentage	`31.4103%`

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Frequently Asked Questions

What is 2/24 plus 9/39 as a fraction?

2/24 + 9/39 in simplest fraction form is 49/156.

What is 2/24 plus 9/39 as a decimal?

2/24 + 9/39 converted to a decimal is 0.314103.

What is 2/24 plus 9/39 as a percentage?

2/24 + 9/39 expressed as a percentage is 31.4103%.

Does 2/24 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.314103...) because the denominator contains prime factors other than 2 and 5.