What is 5/65 plus 2/13? (Answer: 3/13)

Exact Answer

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Problem: What is 5/65 plus 2/13?
Formula / Expression: 5/65 + 2/13
Final Answer: 3/13
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 65 is an exact multiple of 13 (13 × 5 = 65). The Least Common Denominator (LCD) is simply 65, meaning we only need to scale one fraction.
Working: LCD(65, 13) = 65

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

Step 3: Add the Numerators
Now add the numerators (5 + 10 = 15) and keep the common denominator 65 unchanged.
Working: 5 + 10/65 = 15/65

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 15 and 65, which is 5. Divide both the numerator and denominator by 5.
Working: 15 ÷ 5/65 ÷ 5 = 3/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 13 produces a repeating decimal (approximately 0.230769, or 23.0769%).
Working: 3 ÷ 13 = 0.230769 (23.0769%)

Key Values:
- Simplified Fraction: 3/13
- Mixed Number Form: 3/13
- Decimal Value: 0.230769
- Percentage: 23.0769%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-65-plus-2-13/
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5/65 + 2/13 = 3/13

Simplified Fraction

3/13

Mixed Number

Proper (3/13)

Decimal Value

0.230769

Percentage

23.0769%

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Step-by-Step Solution: 5/65 + 2/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 65 is an exact multiple of 13 (13 × 5 = 65). The Least Common Denominator (LCD) is simply 65, meaning we only need to scale one fraction.

LCD(65, 13) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 5/65 by 1, and multiply the numerator and denominator of 2/13 by 5 so both fractions share the common base 65.

5 × 1/65 × 1 = 5/65 and 2 × 5/13 × 5 = 10/65

Step 3

Add the Numerators

Now add the numerators (5 + 10 = 15) and keep the common denominator 65 unchanged.

5 + 10/65 = 15/65

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 15 and 65, which is 5. Divide both the numerator and denominator by 5.

15 ÷ 5/65 ÷ 5 = 3/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 13 produces a repeating decimal (approximately 0.230769, or 23.0769%).

3 ÷ 13 = 0.230769 (23.0769%)

Visual Representation

The diagram below illustrates 5/65 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/13`
Mixed Number Form	`3/13`
Decimal Form	`0.230769`
Percentage	`23.0769%`

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Frequently Asked Questions

What is 5/65 plus 2/13 as a fraction?

5/65 + 2/13 in simplest fraction form is 3/13.

What is 5/65 plus 2/13 as a decimal?

5/65 + 2/13 converted to a decimal is 0.230769.

What is 5/65 plus 2/13 as a percentage?

5/65 + 2/13 expressed as a percentage is 23.0769%.

Does 5/65 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.230769...) because the denominator contains prime factors other than 2 and 5.