What is 3/13 plus 3/7? (Answer: 60/91)

Exact Answer

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Problem: What is 3/13 plus 3/7?
Formula / Expression: 3/13 + 3/7
Final Answer: 60/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.
Working: LCD(13, 7) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 3/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.
Working: 3 × 7/13 × 7 = 21/91 and 3 × 13/7 × 13 = 39/91

Step 3: Add the Numerators
Now add the numerators (21 + 39 = 60) and keep the common denominator 91 unchanged.
Working: 21 + 39/91 = 60/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 60 and 91 is 1, confirming that 60/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 60/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 60 by denominator 91 produces a repeating decimal (approximately 0.659341, or 65.9341%).
Working: 60 ÷ 91 = 0.659341 (65.9341%)

Key Values:
- Simplified Fraction: 60/91
- Mixed Number Form: 60/91
- Decimal Value: 0.659341
- Percentage: 65.9341%

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Solved with FractionsCalc:
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3/13 + 3/7 = 60/91

Simplified Fraction

60/91

Mixed Number

Proper (60/91)

Decimal Value

0.659341

Percentage

65.9341%

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Step-by-Step Solution: 3/13 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.

LCD(13, 7) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 3/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.

3 × 7/13 × 7 = 21/91 and 3 × 13/7 × 13 = 39/91

Step 3

Add the Numerators

Now add the numerators (21 + 39 = 60) and keep the common denominator 91 unchanged.

21 + 39/91 = 60/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 60 and 91 is 1, confirming that 60/91 cannot be reduced further—it is already in its simplest irreducible form.

60/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 60 by denominator 91 produces a repeating decimal (approximately 0.659341, or 65.9341%).

60 ÷ 91 = 0.659341 (65.9341%)

Visual Representation

The diagram below illustrates 3/13 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`60/91`
Mixed Number Form	`60/91`
Decimal Form	`0.659341`
Percentage	`65.9341%`

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Frequently Asked Questions

What is 3/13 plus 3/7 as a fraction?

3/13 + 3/7 in simplest fraction form is 60/91.

What is 3/13 plus 3/7 as a decimal?

3/13 + 3/7 converted to a decimal is 0.659341.

What is 3/13 plus 3/7 as a percentage?

3/13 + 3/7 expressed as a percentage is 65.9341%.

Does 3/13 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.659341...) because the denominator contains prime factors other than 2 and 5.