What is 5/39 plus 7/13? (Answer: 2/3)

Exact Answer

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Problem: What is 5/39 plus 7/13?
Formula / Expression: 5/39 + 7/13
Final Answer: 2/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.
Working: LCD(39, 13) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 5/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.
Working: 5 × 1/39 × 1 = 5/39 and 7 × 3/13 × 3 = 21/39

Step 3: Add the Numerators
Now add the numerators (5 + 21 = 26) and keep the common denominator 39 unchanged.
Working: 5 + 21/39 = 26/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 39, which is 13. Divide both the numerator and denominator by 13.
Working: 26 ÷ 13/39 ÷ 13 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-39-plus-7-13/
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5/39 + 7/13 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 5/39 + 7/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.

LCD(39, 13) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 5/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.

5 × 1/39 × 1 = 5/39 and 7 × 3/13 × 3 = 21/39

Step 3

Add the Numerators

Now add the numerators (5 + 21 = 26) and keep the common denominator 39 unchanged.

5 + 21/39 = 26/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 39, which is 13. Divide both the numerator and denominator by 13.

26 ÷ 13/39 ÷ 13 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 5/39 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 5/39 plus 7/13 as a fraction?

5/39 + 7/13 in simplest fraction form is 2/3.

What is 5/39 plus 7/13 as a decimal?

5/39 + 7/13 converted to a decimal is 0.666667.

What is 5/39 plus 7/13 as a percentage?

5/39 + 7/13 expressed as a percentage is 66.6667%.

Does 5/39 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.