What is 2/13 plus 10/65? (Answer: 4/13)

Exact Answer

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Problem: What is 2/13 plus 10/65?
Formula / Expression: 2/13 + 10/65
Final Answer: 4/13
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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(13, 65) = 65

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

Step 3: Add the Numerators
Now add the numerators (10 + 10 = 20) and keep the common denominator 65 unchanged.
Working: 10 + 10/65 = 20/65

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 65, which is 5. Divide both the numerator and denominator by 5.
Working: 20 ÷ 5/65 ÷ 5 = 4/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 13 produces a repeating decimal (approximately 0.307692, or 30.7692%).
Working: 4 ÷ 13 = 0.307692 (30.7692%)

Key Values:
- Simplified Fraction: 4/13
- Mixed Number Form: 4/13
- Decimal Value: 0.307692
- Percentage: 30.7692%

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Solved with FractionsCalc:
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2/13 + 10/65 = 4/13

Simplified Fraction

4/13

Mixed Number

Proper (4/13)

Decimal Value

0.307692

Percentage

30.7692%

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Step-by-Step Solution: 2/13 + 10/65

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(13, 65) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 2/13 by 5, and multiply the numerator and denominator of 10/65 by 1 so both fractions share the common base 65.

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

Step 3

Add the Numerators

Now add the numerators (10 + 10 = 20) and keep the common denominator 65 unchanged.

10 + 10/65 = 20/65

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 20 and 65, which is 5. Divide both the numerator and denominator by 5.

20 ÷ 5/65 ÷ 5 = 4/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 13 produces a repeating decimal (approximately 0.307692, or 30.7692%).

4 ÷ 13 = 0.307692 (30.7692%)

Visual Representation

The diagram below illustrates 2/13 plus 10/65 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/13`
Mixed Number Form	`4/13`
Decimal Form	`0.307692`
Percentage	`30.7692%`

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Frequently Asked Questions

What is 2/13 plus 10/65 as a fraction?

2/13 + 10/65 in simplest fraction form is 4/13.

What is 2/13 plus 10/65 as a decimal?

2/13 + 10/65 converted to a decimal is 0.307692.

What is 2/13 plus 10/65 as a percentage?

2/13 + 10/65 expressed as a percentage is 30.7692%.

Does 2/13 plus 10/65 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.307692...) because the denominator contains prime factors other than 2 and 5.