What is 3/17 plus 10/13? (Answer: 209/221)

Exact Answer

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Problem: What is 3/17 plus 10/13?
Formula / Expression: 3/17 + 10/13
Final Answer: 209/221
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 221
Multiply the numerator and denominator of 3/17 by 13, and multiply the numerator and denominator of 10/13 by 17 so both fractions share the common base 221.
Working: 3 × 13/17 × 13 = 39/221 and 10 × 17/13 × 17 = 170/221

Step 3: Add the Numerators
Now add the numerators (39 + 170 = 209) and keep the common denominator 221 unchanged.
Working: 39 + 170/221 = 209/221

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 221 is 1, confirming that 209/221 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/221

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 221 produces a repeating decimal (approximately 0.945701, or 94.5701%).
Working: 209 ÷ 221 = 0.945701 (94.5701%)

Key Values:
- Simplified Fraction: 209/221
- Mixed Number Form: 209/221
- Decimal Value: 0.945701
- Percentage: 94.5701%

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Solved with FractionsCalc:
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3/17 + 10/13 = 209/221

Simplified Fraction

209/221

Mixed Number

Proper (209/221)

Decimal Value

0.945701

Percentage

94.5701%

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Step-by-Step Solution: 3/17 + 10/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(17, 13) = 221

Step 2

Convert to Equivalent Fractions with Common Denominator 221

Multiply the numerator and denominator of 3/17 by 13, and multiply the numerator and denominator of 10/13 by 17 so both fractions share the common base 221.

3 × 13/17 × 13 = 39/221 and 10 × 17/13 × 17 = 170/221

Step 3

Add the Numerators

Now add the numerators (39 + 170 = 209) and keep the common denominator 221 unchanged.

39 + 170/221 = 209/221

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 221 is 1, confirming that 209/221 cannot be reduced further—it is already in its simplest irreducible form.

209/221

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 221 produces a repeating decimal (approximately 0.945701, or 94.5701%).

209 ÷ 221 = 0.945701 (94.5701%)

Visual Representation

The diagram below illustrates 3/17 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/221`
Mixed Number Form	`209/221`
Decimal Form	`0.945701`
Percentage	`94.5701%`

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Frequently Asked Questions

What is 3/17 plus 10/13 as a fraction?

3/17 + 10/13 in simplest fraction form is 209/221.

What is 3/17 plus 10/13 as a decimal?

3/17 + 10/13 converted to a decimal is 0.945701.

What is 3/17 plus 10/13 as a percentage?

3/17 + 10/13 expressed as a percentage is 94.5701%.

Does 3/17 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.945701...) because the denominator contains prime factors other than 2 and 5.