What is 3/16 plus 9/39? (Answer: 87/208)

Exact Answer

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Problem: What is 3/16 plus 9/39?
Formula / Expression: 3/16 + 9/39
Final Answer: 87/208
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 39 = 624.
Working: LCD(16, 39) = 624

Step 2: Convert to Equivalent Fractions with Common Denominator 624
Multiply the numerator and denominator of 3/16 by 39, and multiply the numerator and denominator of 9/39 by 16 so both fractions share the common base 624.
Working: 3 × 39/16 × 39 = 117/624 and 9 × 16/39 × 16 = 144/624

Step 3: Add the Numerators
Now add the numerators (117 + 144 = 261) and keep the common denominator 624 unchanged.
Working: 117 + 144/624 = 261/624

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 261 and 624, which is 3. Divide both the numerator and denominator by 3.
Working: 261 ÷ 3/624 ÷ 3 = 87/208

Step 5: Decimal & Percentage Representation
Dividing the numerator 87 by denominator 208 produces a repeating decimal (approximately 0.418269, or 41.8269%).
Working: 87 ÷ 208 = 0.418269 (41.8269%)

Key Values:
- Simplified Fraction: 87/208
- Mixed Number Form: 87/208
- Decimal Value: 0.418269
- Percentage: 41.8269%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-16-plus-9-39/
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3/16 + 9/39 = 87/208

Simplified Fraction

87/208

Mixed Number

Proper (87/208)

Decimal Value

0.418269

Percentage

41.8269%

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Step-by-Step Solution: 3/16 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 39 = 624.

LCD(16, 39) = 624

Step 2

Convert to Equivalent Fractions with Common Denominator 624

Multiply the numerator and denominator of 3/16 by 39, and multiply the numerator and denominator of 9/39 by 16 so both fractions share the common base 624.

3 × 39/16 × 39 = 117/624 and 9 × 16/39 × 16 = 144/624

Step 3

Add the Numerators

Now add the numerators (117 + 144 = 261) and keep the common denominator 624 unchanged.

117 + 144/624 = 261/624

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 261 and 624, which is 3. Divide both the numerator and denominator by 3.

261 ÷ 3/624 ÷ 3 = 87/208

Step 5

Decimal & Percentage Representation

Dividing the numerator 87 by denominator 208 produces a repeating decimal (approximately 0.418269, or 41.8269%).

87 ÷ 208 = 0.418269 (41.8269%)

Visual Representation

The diagram below illustrates 3/16 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`87/208`
Mixed Number Form	`87/208`
Decimal Form	`0.418269`
Percentage	`41.8269%`

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Frequently Asked Questions

What is 3/16 plus 9/39 as a fraction?

3/16 + 9/39 in simplest fraction form is 87/208.

What is 3/16 plus 9/39 as a decimal?

3/16 + 9/39 converted to a decimal is 0.418269.

What is 3/16 plus 9/39 as a percentage?

3/16 + 9/39 expressed as a percentage is 41.8269%.

Does 3/16 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.418269...) because the denominator contains prime factors other than 2 and 5.