What is 1/5 plus 10/13? (Answer: 63/65)

Exact Answer

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Problem: What is 1/5 plus 10/13?
Formula / Expression: 1/5 + 10/13
Final Answer: 63/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.
Working: LCD(5, 13) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 1/5 by 13, and multiply the numerator and denominator of 10/13 by 5 so both fractions share the common base 65.
Working: 1 × 13/5 × 13 = 13/65 and 10 × 5/13 × 5 = 50/65

Step 3: Add the Numerators
Now add the numerators (13 + 50 = 63) and keep the common denominator 65 unchanged.
Working: 13 + 50/65 = 63/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 63 and 65 is 1, confirming that 63/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 63/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 63 by denominator 65 produces a repeating decimal (approximately 0.969231, or 96.9231%).
Working: 63 ÷ 65 = 0.969231 (96.9231%)

Key Values:
- Simplified Fraction: 63/65
- Mixed Number Form: 63/65
- Decimal Value: 0.969231
- Percentage: 96.9231%

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Solved with FractionsCalc:
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1/5 + 10/13 = 63/65

Simplified Fraction

63/65

Mixed Number

Proper (63/65)

Decimal Value

0.969231

Percentage

96.9231%

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Step-by-Step Solution: 1/5 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.

LCD(5, 13) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 1/5 by 13, and multiply the numerator and denominator of 10/13 by 5 so both fractions share the common base 65.

1 × 13/5 × 13 = 13/65 and 10 × 5/13 × 5 = 50/65

Step 3

Add the Numerators

Now add the numerators (13 + 50 = 63) and keep the common denominator 65 unchanged.

13 + 50/65 = 63/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 63 and 65 is 1, confirming that 63/65 cannot be reduced further—it is already in its simplest irreducible form.

63/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 63 by denominator 65 produces a repeating decimal (approximately 0.969231, or 96.9231%).

63 ÷ 65 = 0.969231 (96.9231%)

Visual Representation

The diagram below illustrates 1/5 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`63/65`
Mixed Number Form	`63/65`
Decimal Form	`0.969231`
Percentage	`96.9231%`

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Frequently Asked Questions

What is 1/5 plus 10/13 as a fraction?

1/5 + 10/13 in simplest fraction form is 63/65.

What is 1/5 plus 10/13 as a decimal?

1/5 + 10/13 converted to a decimal is 0.969231.

What is 1/5 plus 10/13 as a percentage?

1/5 + 10/13 expressed as a percentage is 96.9231%.

Does 1/5 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.969231...) because the denominator contains prime factors other than 2 and 5.