What is 7/61 plus 2/13? (Answer: 213/793)

Exact Answer

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Problem: What is 7/61 plus 2/13?
Formula / Expression: 7/61 + 2/13
Final Answer: 213/793
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 61 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 61 × 13 = 793.
Working: LCD(61, 13) = 793

Step 2: Convert to Equivalent Fractions with Common Denominator 793
Multiply the numerator and denominator of 7/61 by 13, and multiply the numerator and denominator of 2/13 by 61 so both fractions share the common base 793.
Working: 7 × 13/61 × 13 = 91/793 and 2 × 61/13 × 61 = 122/793

Step 3: Add the Numerators
Now add the numerators (91 + 122 = 213) and keep the common denominator 793 unchanged.
Working: 91 + 122/793 = 213/793

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 213 and 793 is 1, confirming that 213/793 cannot be reduced further—it is already in its simplest irreducible form.
Working: 213/793

Step 5: Decimal & Percentage Representation
Dividing the numerator 213 by denominator 793 produces a repeating decimal (approximately 0.2686, or 26.86%).
Working: 213 ÷ 793 = 0.2686 (26.86%)

Key Values:
- Simplified Fraction: 213/793
- Mixed Number Form: 213/793
- Decimal Value: 0.2686
- Percentage: 26.86%

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Solved with FractionsCalc:
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7/61 + 2/13 = 213/793

Simplified Fraction

213/793

Mixed Number

Proper (213/793)

Decimal Value

0.2686

Percentage

26.86%

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Step-by-Step Solution: 7/61 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 61 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 61 × 13 = 793.

LCD(61, 13) = 793

Step 2

Convert to Equivalent Fractions with Common Denominator 793

Multiply the numerator and denominator of 7/61 by 13, and multiply the numerator and denominator of 2/13 by 61 so both fractions share the common base 793.

7 × 13/61 × 13 = 91/793 and 2 × 61/13 × 61 = 122/793

Step 3

Add the Numerators

Now add the numerators (91 + 122 = 213) and keep the common denominator 793 unchanged.

91 + 122/793 = 213/793

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 213 and 793 is 1, confirming that 213/793 cannot be reduced further—it is already in its simplest irreducible form.

213/793

Step 5

Decimal & Percentage Representation

Dividing the numerator 213 by denominator 793 produces a repeating decimal (approximately 0.2686, or 26.86%).

213 ÷ 793 = 0.2686 (26.86%)

Visual Representation

The diagram below illustrates 7/61 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`213/793`
Mixed Number Form	`213/793`
Decimal Form	`0.2686`
Percentage	`26.86%`

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Frequently Asked Questions

What is 7/61 plus 2/13 as a fraction?

7/61 + 2/13 in simplest fraction form is 213/793.

What is 7/61 plus 2/13 as a decimal?

7/61 + 2/13 converted to a decimal is 0.2686.

What is 7/61 plus 2/13 as a percentage?

7/61 + 2/13 expressed as a percentage is 26.86%.

Does 7/61 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.2686...) because the denominator contains prime factors other than 2 and 5.