What is 3/20 plus 7/39? (Answer: 257/780)

Exact Answer

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Problem: What is 3/20 plus 7/39?
Formula / Expression: 3/20 + 7/39
Final Answer: 257/780
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 39 = 780.
Working: LCD(20, 39) = 780

Step 2: Convert to Equivalent Fractions with Common Denominator 780
Multiply the numerator and denominator of 3/20 by 39, and multiply the numerator and denominator of 7/39 by 20 so both fractions share the common base 780.
Working: 3 × 39/20 × 39 = 117/780 and 7 × 20/39 × 20 = 140/780

Step 3: Add the Numerators
Now add the numerators (117 + 140 = 257) and keep the common denominator 780 unchanged.
Working: 117 + 140/780 = 257/780

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 257 and 780 is 1, confirming that 257/780 cannot be reduced further—it is already in its simplest irreducible form.
Working: 257/780

Step 5: Decimal & Percentage Representation
Dividing the numerator 257 by denominator 780 produces a repeating decimal (approximately 0.329487, or 32.9487%).
Working: 257 ÷ 780 = 0.329487 (32.9487%)

Key Values:
- Simplified Fraction: 257/780
- Mixed Number Form: 257/780
- Decimal Value: 0.329487
- Percentage: 32.9487%

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Solved with FractionsCalc:
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3/20 + 7/39 = 257/780

Simplified Fraction

257/780

Mixed Number

Proper (257/780)

Decimal Value

0.329487

Percentage

32.9487%

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Step-by-Step Solution: 3/20 + 7/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 39 = 780.

LCD(20, 39) = 780

Step 2

Convert to Equivalent Fractions with Common Denominator 780

Multiply the numerator and denominator of 3/20 by 39, and multiply the numerator and denominator of 7/39 by 20 so both fractions share the common base 780.

3 × 39/20 × 39 = 117/780 and 7 × 20/39 × 20 = 140/780

Step 3

Add the Numerators

Now add the numerators (117 + 140 = 257) and keep the common denominator 780 unchanged.

117 + 140/780 = 257/780

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 257 and 780 is 1, confirming that 257/780 cannot be reduced further—it is already in its simplest irreducible form.

257/780

Step 5

Decimal & Percentage Representation

Dividing the numerator 257 by denominator 780 produces a repeating decimal (approximately 0.329487, or 32.9487%).

257 ÷ 780 = 0.329487 (32.9487%)

Visual Representation

The diagram below illustrates 3/20 plus 7/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`257/780`
Mixed Number Form	`257/780`
Decimal Form	`0.329487`
Percentage	`32.9487%`

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Frequently Asked Questions

What is 3/20 plus 7/39 as a fraction?

3/20 + 7/39 in simplest fraction form is 257/780.

What is 3/20 plus 7/39 as a decimal?

3/20 + 7/39 converted to a decimal is 0.329487.

What is 3/20 plus 7/39 as a percentage?

3/20 + 7/39 expressed as a percentage is 32.9487%.

Does 3/20 plus 7/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.329487...) because the denominator contains prime factors other than 2 and 5.