What is 3/59 plus 3/13? (Answer: 216/767)

Exact Answer

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Problem: What is 3/59 plus 3/13?
Formula / Expression: 3/59 + 3/13
Final Answer: 216/767
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 59 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 59 × 13 = 767.
Working: LCD(59, 13) = 767

Step 2: Convert to Equivalent Fractions with Common Denominator 767
Multiply the numerator and denominator of 3/59 by 13, and multiply the numerator and denominator of 3/13 by 59 so both fractions share the common base 767.
Working: 3 × 13/59 × 13 = 39/767 and 3 × 59/13 × 59 = 177/767

Step 3: Add the Numerators
Now add the numerators (39 + 177 = 216) and keep the common denominator 767 unchanged.
Working: 39 + 177/767 = 216/767

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 216 and 767 is 1, confirming that 216/767 cannot be reduced further—it is already in its simplest irreducible form.
Working: 216/767

Step 5: Decimal & Percentage Representation
Dividing the numerator 216 by denominator 767 produces a repeating decimal (approximately 0.281617, or 28.1617%).
Working: 216 ÷ 767 = 0.281617 (28.1617%)

Key Values:
- Simplified Fraction: 216/767
- Mixed Number Form: 216/767
- Decimal Value: 0.281617
- Percentage: 28.1617%

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Solved with FractionsCalc:
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3/59 + 3/13 = 216/767

Simplified Fraction

216/767

Mixed Number

Proper (216/767)

Decimal Value

0.281617

Percentage

28.1617%

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Step-by-Step Solution: 3/59 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 59 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 59 × 13 = 767.

LCD(59, 13) = 767

Step 2

Convert to Equivalent Fractions with Common Denominator 767

Multiply the numerator and denominator of 3/59 by 13, and multiply the numerator and denominator of 3/13 by 59 so both fractions share the common base 767.

3 × 13/59 × 13 = 39/767 and 3 × 59/13 × 59 = 177/767

Step 3

Add the Numerators

Now add the numerators (39 + 177 = 216) and keep the common denominator 767 unchanged.

39 + 177/767 = 216/767

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 216 and 767 is 1, confirming that 216/767 cannot be reduced further—it is already in its simplest irreducible form.

216/767

Step 5

Decimal & Percentage Representation

Dividing the numerator 216 by denominator 767 produces a repeating decimal (approximately 0.281617, or 28.1617%).

216 ÷ 767 = 0.281617 (28.1617%)

Visual Representation

The diagram below illustrates 3/59 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`216/767`
Mixed Number Form	`216/767`
Decimal Form	`0.281617`
Percentage	`28.1617%`

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Frequently Asked Questions

What is 3/59 plus 3/13 as a fraction?

3/59 + 3/13 in simplest fraction form is 216/767.

What is 3/59 plus 3/13 as a decimal?

3/59 + 3/13 converted to a decimal is 0.281617.

What is 3/59 plus 3/13 as a percentage?

3/59 + 3/13 expressed as a percentage is 28.1617%.

Does 3/59 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.281617...) because the denominator contains prime factors other than 2 and 5.