What is 7/39 plus 7/13? (Answer: 28/39)

Exact Answer

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Problem: What is 7/39 plus 7/13?
Formula / Expression: 7/39 + 7/13
Final Answer: 28/39
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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 7/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.
Working: 7 × 1/39 × 1 = 7/39 and 7 × 3/13 × 3 = 21/39

Step 3: Add the Numerators
Now add the numerators (7 + 21 = 28) and keep the common denominator 39 unchanged.
Working: 7 + 21/39 = 28/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 28 and 39 is 1, confirming that 28/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 28/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 28 by denominator 39 produces a repeating decimal (approximately 0.717949, or 71.7949%).
Working: 28 ÷ 39 = 0.717949 (71.7949%)

Key Values:
- Simplified Fraction: 28/39
- Mixed Number Form: 28/39
- Decimal Value: 0.717949
- Percentage: 71.7949%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-39-plus-7-13/
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7/39 + 7/13 = 28/39

Simplified Fraction

28/39

Mixed Number

Proper (28/39)

Decimal Value

0.717949

Percentage

71.7949%

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Step-by-Step Solution: 7/39 + 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 7/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.

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

Step 3

Add the Numerators

Now add the numerators (7 + 21 = 28) and keep the common denominator 39 unchanged.

7 + 21/39 = 28/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 28 and 39 is 1, confirming that 28/39 cannot be reduced further—it is already in its simplest irreducible form.

28/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 28 by denominator 39 produces a repeating decimal (approximately 0.717949, or 71.7949%).

28 ÷ 39 = 0.717949 (71.7949%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`28/39`
Mixed Number Form	`28/39`
Decimal Form	`0.717949`
Percentage	`71.7949%`

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Frequently Asked Questions

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

7/39 + 7/13 in simplest fraction form is 28/39.

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

7/39 + 7/13 converted to a decimal is 0.717949.

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

7/39 + 7/13 expressed as a percentage is 71.7949%.

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

It results in a repeating decimal (approximately 0.717949...) because the denominator contains prime factors other than 2 and 5.