What is 17/39 plus 7/13? (Answer: 38/39)

Exact Answer

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Problem: What is 17/39 plus 7/13?
Formula / Expression: 17/39 + 7/13
Final Answer: 38/39
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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 17/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.
Working: 17 × 1/39 × 1 = 17/39 and 7 × 3/13 × 3 = 21/39

Step 3: Add the Numerators
Now add the numerators (17 + 21 = 38) and keep the common denominator 39 unchanged.
Working: 17 + 21/39 = 38/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 38 and 39 is 1, confirming that 38/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 38/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 39 produces a repeating decimal (approximately 0.974359, or 97.4359%).
Working: 38 ÷ 39 = 0.974359 (97.4359%)

Key Values:
- Simplified Fraction: 38/39
- Mixed Number Form: 38/39
- Decimal Value: 0.974359
- Percentage: 97.4359%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-17-39-plus-7-13/
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17/39 + 7/13 = 38/39

Simplified Fraction

38/39

Mixed Number

Proper (38/39)

Decimal Value

0.974359

Percentage

97.4359%

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Step-by-Step Solution: 17/39 + 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 17/39 by 1, and multiply the numerator and denominator of 7/13 by 3 so both fractions share the common base 39.

17 × 1/39 × 1 = 17/39 and 7 × 3/13 × 3 = 21/39

Step 3

Add the Numerators

Now add the numerators (17 + 21 = 38) and keep the common denominator 39 unchanged.

17 + 21/39 = 38/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 38 and 39 is 1, confirming that 38/39 cannot be reduced further—it is already in its simplest irreducible form.

38/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 39 produces a repeating decimal (approximately 0.974359, or 97.4359%).

38 ÷ 39 = 0.974359 (97.4359%)

Visual Representation

The diagram below illustrates 17/39 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/39`
Mixed Number Form	`38/39`
Decimal Form	`0.974359`
Percentage	`97.4359%`

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Frequently Asked Questions

What is 17/39 plus 7/13 as a fraction?

17/39 + 7/13 in simplest fraction form is 38/39.

What is 17/39 plus 7/13 as a decimal?

17/39 + 7/13 converted to a decimal is 0.974359.

What is 17/39 plus 7/13 as a percentage?

17/39 + 7/13 expressed as a percentage is 97.4359%.

Does 17/39 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.974359...) because the denominator contains prime factors other than 2 and 5.