What is 5/13 plus 7/17? (Answer: 176/221)

Exact Answer

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Problem: What is 5/13 plus 7/17?
Formula / Expression: 5/13 + 7/17
Final Answer: 176/221
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 17 = 221.
Working: LCD(13, 17) = 221

Step 2: Convert to Equivalent Fractions with Common Denominator 221
Multiply the numerator and denominator of 5/13 by 17, and multiply the numerator and denominator of 7/17 by 13 so both fractions share the common base 221.
Working: 5 × 17/13 × 17 = 85/221 and 7 × 13/17 × 13 = 91/221

Step 3: Add the Numerators
Now add the numerators (85 + 91 = 176) and keep the common denominator 221 unchanged.
Working: 85 + 91/221 = 176/221

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 176 and 221 is 1, confirming that 176/221 cannot be reduced further—it is already in its simplest irreducible form.
Working: 176/221

Step 5: Decimal & Percentage Representation
Dividing the numerator 176 by denominator 221 produces a repeating decimal (approximately 0.79638, or 79.638%).
Working: 176 ÷ 221 = 0.79638 (79.638%)

Key Values:
- Simplified Fraction: 176/221
- Mixed Number Form: 176/221
- Decimal Value: 0.79638
- Percentage: 79.638%

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Solved with FractionsCalc:
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5/13 + 7/17 = 176/221

Simplified Fraction

176/221

Mixed Number

Proper (176/221)

Decimal Value

0.79638

Percentage

79.638%

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Step-by-Step Solution: 5/13 + 7/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 17 = 221.

LCD(13, 17) = 221

Step 2

Convert to Equivalent Fractions with Common Denominator 221

Multiply the numerator and denominator of 5/13 by 17, and multiply the numerator and denominator of 7/17 by 13 so both fractions share the common base 221.

5 × 17/13 × 17 = 85/221 and 7 × 13/17 × 13 = 91/221

Step 3

Add the Numerators

Now add the numerators (85 + 91 = 176) and keep the common denominator 221 unchanged.

85 + 91/221 = 176/221

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 176 and 221 is 1, confirming that 176/221 cannot be reduced further—it is already in its simplest irreducible form.

176/221

Step 5

Decimal & Percentage Representation

Dividing the numerator 176 by denominator 221 produces a repeating decimal (approximately 0.79638, or 79.638%).

176 ÷ 221 = 0.79638 (79.638%)

Visual Representation

The diagram below illustrates 5/13 plus 7/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`176/221`
Mixed Number Form	`176/221`
Decimal Form	`0.79638`
Percentage	`79.638%`

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Frequently Asked Questions

What is 5/13 plus 7/17 as a fraction?

5/13 + 7/17 in simplest fraction form is 176/221.

What is 5/13 plus 7/17 as a decimal?

5/13 + 7/17 converted to a decimal is 0.79638.

What is 5/13 plus 7/17 as a percentage?

5/13 + 7/17 expressed as a percentage is 79.638%.

Does 5/13 plus 7/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.79638...) because the denominator contains prime factors other than 2 and 5.