What is 3/65 plus 2/13? (Answer: 1/5)

Exact Answer

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Problem: What is 3/65 plus 2/13?
Formula / Expression: 3/65 + 2/13
Final Answer: 1/5
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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 3/65 by 1, and multiply the numerator and denominator of 2/13 by 5 so both fractions share the common base 65.
Working: 3 × 1/65 × 1 = 3/65 and 2 × 5/13 × 5 = 10/65

Step 3: Add the Numerators
Now add the numerators (3 + 10 = 13) and keep the common denominator 65 unchanged.
Working: 3 + 10/65 = 13/65

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 13 and 65, which is 13. Divide both the numerator and denominator by 13.
Working: 13 ÷ 13/65 ÷ 13 = 1/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 5 yields an exact terminating decimal of 0.2 (or 20%).
Working: 1 ÷ 5 = 0.2 (20%)

Key Values:
- Simplified Fraction: 1/5
- Mixed Number Form: 1/5
- Decimal Value: 0.2
- Percentage: 20%

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Solved with FractionsCalc:
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3/65 + 2/13 = 1/5

Simplified Fraction

1/5

Mixed Number

Proper (1/5)

Decimal Value

0.2

Percentage

20%

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Step-by-Step Solution: 3/65 + 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 3/65 by 1, and multiply the numerator and denominator of 2/13 by 5 so both fractions share the common base 65.

3 × 1/65 × 1 = 3/65 and 2 × 5/13 × 5 = 10/65

Step 3

Add the Numerators

Now add the numerators (3 + 10 = 13) and keep the common denominator 65 unchanged.

3 + 10/65 = 13/65

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 13 and 65, which is 13. Divide both the numerator and denominator by 13.

13 ÷ 13/65 ÷ 13 = 1/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 5 yields an exact terminating decimal of 0.2 (or 20%).

1 ÷ 5 = 0.2 (20%)

Visual Representation

The diagram below illustrates 3/65 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/5`
Mixed Number Form	`1/5`
Decimal Form	`0.2`
Percentage	`20%`

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Frequently Asked Questions

What is 3/65 plus 2/13 as a fraction?

3/65 + 2/13 in simplest fraction form is 1/5.

What is 3/65 plus 2/13 as a decimal?

3/65 + 2/13 converted to a decimal is 0.2.

What is 3/65 plus 2/13 as a percentage?

3/65 + 2/13 expressed as a percentage is 20%.

Does 3/65 plus 2/13 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.2) because the denominator in simplest terms contains only prime factors 2 and/or 5.