What is 2/15 plus 10/13? (Answer: 176/195)

Exact Answer

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Problem: What is 2/15 plus 10/13?
Formula / Expression: 2/15 + 10/13
Final Answer: 176/195
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 13 = 195.
Working: LCD(15, 13) = 195

Step 2: Convert to Equivalent Fractions with Common Denominator 195
Multiply the numerator and denominator of 2/15 by 13, and multiply the numerator and denominator of 10/13 by 15 so both fractions share the common base 195.
Working: 2 × 13/15 × 13 = 26/195 and 10 × 15/13 × 15 = 150/195

Step 3: Add the Numerators
Now add the numerators (26 + 150 = 176) and keep the common denominator 195 unchanged.
Working: 26 + 150/195 = 176/195

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 176 and 195 is 1, confirming that 176/195 cannot be reduced further—it is already in its simplest irreducible form.
Working: 176/195

Step 5: Decimal & Percentage Representation
Dividing the numerator 176 by denominator 195 produces a repeating decimal (approximately 0.902564, or 90.2564%).
Working: 176 ÷ 195 = 0.902564 (90.2564%)

Key Values:
- Simplified Fraction: 176/195
- Mixed Number Form: 176/195
- Decimal Value: 0.902564
- Percentage: 90.2564%

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Solved with FractionsCalc:
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2/15 + 10/13 = 176/195

Simplified Fraction

176/195

Mixed Number

Proper (176/195)

Decimal Value

0.902564

Percentage

90.2564%

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Step-by-Step Solution: 2/15 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 13 = 195.

LCD(15, 13) = 195

Step 2

Convert to Equivalent Fractions with Common Denominator 195

Multiply the numerator and denominator of 2/15 by 13, and multiply the numerator and denominator of 10/13 by 15 so both fractions share the common base 195.

2 × 13/15 × 13 = 26/195 and 10 × 15/13 × 15 = 150/195

Step 3

Add the Numerators

Now add the numerators (26 + 150 = 176) and keep the common denominator 195 unchanged.

26 + 150/195 = 176/195

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 176 and 195 is 1, confirming that 176/195 cannot be reduced further—it is already in its simplest irreducible form.

176/195

Step 5

Decimal & Percentage Representation

Dividing the numerator 176 by denominator 195 produces a repeating decimal (approximately 0.902564, or 90.2564%).

176 ÷ 195 = 0.902564 (90.2564%)

Visual Representation

The diagram below illustrates 2/15 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`176/195`
Mixed Number Form	`176/195`
Decimal Form	`0.902564`
Percentage	`90.2564%`

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Frequently Asked Questions

What is 2/15 plus 10/13 as a fraction?

2/15 + 10/13 in simplest fraction form is 176/195.

What is 2/15 plus 10/13 as a decimal?

2/15 + 10/13 converted to a decimal is 0.902564.

What is 2/15 plus 10/13 as a percentage?

2/15 + 10/13 expressed as a percentage is 90.2564%.

Does 2/15 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.902564...) because the denominator contains prime factors other than 2 and 5.