What is 5/24 plus 9/39? (Answer: 137/312)

Exact Answer

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Problem: What is 5/24 plus 9/39?
Formula / Expression: 5/24 + 9/39
Final Answer: 137/312
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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 5/24 by 13, and multiply the numerator and denominator of 9/39 by 8 so both fractions share the common base 312.
Working: 5 × 13/24 × 13 = 65/312 and 9 × 8/39 × 8 = 72/312

Step 3: Add the Numerators
Now add the numerators (65 + 72 = 137) and keep the common denominator 312 unchanged.
Working: 65 + 72/312 = 137/312

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 137 and 312 is 1, confirming that 137/312 cannot be reduced further—it is already in its simplest irreducible form.
Working: 137/312

Step 5: Decimal & Percentage Representation
Dividing the numerator 137 by denominator 312 produces a repeating decimal (approximately 0.439103, or 43.9103%).
Working: 137 ÷ 312 = 0.439103 (43.9103%)

Key Values:
- Simplified Fraction: 137/312
- Mixed Number Form: 137/312
- Decimal Value: 0.439103
- Percentage: 43.9103%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-24-plus-9-39/
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5/24 + 9/39 = 137/312

Simplified Fraction

137/312

Mixed Number

Proper (137/312)

Decimal Value

0.439103

Percentage

43.9103%

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Step-by-Step Solution: 5/24 + 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 5/24 by 13, and multiply the numerator and denominator of 9/39 by 8 so both fractions share the common base 312.

5 × 13/24 × 13 = 65/312 and 9 × 8/39 × 8 = 72/312

Step 3

Add the Numerators

Now add the numerators (65 + 72 = 137) and keep the common denominator 312 unchanged.

65 + 72/312 = 137/312

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 137 and 312 is 1, confirming that 137/312 cannot be reduced further—it is already in its simplest irreducible form.

137/312

Step 5

Decimal & Percentage Representation

Dividing the numerator 137 by denominator 312 produces a repeating decimal (approximately 0.439103, or 43.9103%).

137 ÷ 312 = 0.439103 (43.9103%)

Visual Representation

The diagram below illustrates 5/24 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`137/312`
Mixed Number Form	`137/312`
Decimal Form	`0.439103`
Percentage	`43.9103%`

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Frequently Asked Questions

What is 5/24 plus 9/39 as a fraction?

5/24 + 9/39 in simplest fraction form is 137/312.

What is 5/24 plus 9/39 as a decimal?

5/24 + 9/39 converted to a decimal is 0.439103.

What is 5/24 plus 9/39 as a percentage?

5/24 + 9/39 expressed as a percentage is 43.9103%.

Does 5/24 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.439103...) because the denominator contains prime factors other than 2 and 5.