What is 3/24 plus 9/39? (Answer: 37/104)

Exact Answer

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Problem: What is 3/24 plus 9/39?
Formula / Expression: 3/24 + 9/39
Final Answer: 37/104
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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 3/24 by 13, and multiply the numerator and denominator of 9/39 by 8 so both fractions share the common base 312.
Working: 3 × 13/24 × 13 = 39/312 and 9 × 8/39 × 8 = 72/312

Step 3: Add the Numerators
Now add the numerators (39 + 72 = 111) and keep the common denominator 312 unchanged.
Working: 39 + 72/312 = 111/312

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 312, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/312 ÷ 3 = 37/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 104 produces a repeating decimal (approximately 0.355769, or 35.5769%).
Working: 37 ÷ 104 = 0.355769 (35.5769%)

Key Values:
- Simplified Fraction: 37/104
- Mixed Number Form: 37/104
- Decimal Value: 0.355769
- Percentage: 35.5769%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-24-plus-9-39/
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3/24 + 9/39 = 37/104

Simplified Fraction

37/104

Mixed Number

Proper (37/104)

Decimal Value

0.355769

Percentage

35.5769%

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Step-by-Step Solution: 3/24 + 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 3/24 by 13, and multiply the numerator and denominator of 9/39 by 8 so both fractions share the common base 312.

3 × 13/24 × 13 = 39/312 and 9 × 8/39 × 8 = 72/312

Step 3

Add the Numerators

Now add the numerators (39 + 72 = 111) and keep the common denominator 312 unchanged.

39 + 72/312 = 111/312

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 312, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/312 ÷ 3 = 37/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 104 produces a repeating decimal (approximately 0.355769, or 35.5769%).

37 ÷ 104 = 0.355769 (35.5769%)

Visual Representation

The diagram below illustrates 3/24 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/104`
Mixed Number Form	`37/104`
Decimal Form	`0.355769`
Percentage	`35.5769%`

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Frequently Asked Questions

What is 3/24 plus 9/39 as a fraction?

3/24 + 9/39 in simplest fraction form is 37/104.

What is 3/24 plus 9/39 as a decimal?

3/24 + 9/39 converted to a decimal is 0.355769.

What is 3/24 plus 9/39 as a percentage?

3/24 + 9/39 expressed as a percentage is 35.5769%.

Does 3/24 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.355769...) because the denominator contains prime factors other than 2 and 5.