What is 7/13 plus 2/3? (Answer: 47/39)

Exact Answer

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Problem: What is 7/13 plus 2/3?
Formula / Expression: 7/13 + 2/3
Final Answer: 1 8/39 (47/39)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.
Working: LCD(13, 3) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 7/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.
Working: 7 × 3/13 × 3 = 21/39 and 2 × 13/3 × 13 = 26/39

Step 3: Add the Numerators
Now add the numerators (21 + 26 = 47) and keep the common denominator 39 unchanged.
Working: 21 + 26/39 = 47/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 39 is 1, confirming that 47/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/39

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (47) is greater than the denominator (39), divide 47 by 39: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/39.
Working: 47/39 = 1 8/39

Step 6: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 39 produces a repeating decimal (approximately 1.205128, or 120.5128%).
Working: 47 ÷ 39 = 1.205128 (120.5128%)

Key Values:
- Simplified Fraction: 47/39
- Mixed Number Form: 1 8/39
- Decimal Value: 1.205128
- Percentage: 120.5128%

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Solved with FractionsCalc:
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7/13 + 2/3 = 47/39

Simplified Fraction

47/39

Mixed Number

1 8/39

Decimal Value

1.205128

Percentage

120.5128%

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Step-by-Step Solution: 7/13 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.

LCD(13, 3) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 7/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.

7 × 3/13 × 3 = 21/39 and 2 × 13/3 × 13 = 26/39

Step 3

Add the Numerators

Now add the numerators (21 + 26 = 47) and keep the common denominator 39 unchanged.

21 + 26/39 = 47/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 39 is 1, confirming that 47/39 cannot be reduced further—it is already in its simplest irreducible form.

47/39

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (47) is greater than the denominator (39), divide 47 by 39: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/39.

47/39 = 18/39

Step 6

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 39 produces a repeating decimal (approximately 1.205128, or 120.5128%).

47 ÷ 39 = 1.205128 (120.5128%)

Visual Representation

The diagram below illustrates 7/13 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/39`
Mixed Number Form	`1 8/39`
Decimal Form	`1.205128`
Percentage	`120.5128%`

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Frequently Asked Questions

What is 7/13 plus 2/3 as a fraction?

7/13 + 2/3 in simplest fraction form is 47/39 (or 1 8/39 as a mixed number).

What is 7/13 plus 2/3 as a decimal?

7/13 + 2/3 converted to a decimal is 1.205128.

What is 7/13 plus 2/3 as a percentage?

7/13 + 2/3 expressed as a percentage is 120.5128%.

How do you write 7/13 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 47/39 can be written as the mixed number 1 8/39.

Does 7/13 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.205128...) because the denominator contains prime factors other than 2 and 5.