What is 5/69 plus 2/13? (Answer: 203/897)

Exact Answer

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Problem: What is 5/69 plus 2/13?
Formula / Expression: 5/69 + 2/13
Final Answer: 203/897
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 69 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 69 × 13 = 897.
Working: LCD(69, 13) = 897

Step 2: Convert to Equivalent Fractions with Common Denominator 897
Multiply the numerator and denominator of 5/69 by 13, and multiply the numerator and denominator of 2/13 by 69 so both fractions share the common base 897.
Working: 5 × 13/69 × 13 = 65/897 and 2 × 69/13 × 69 = 138/897

Step 3: Add the Numerators
Now add the numerators (65 + 138 = 203) and keep the common denominator 897 unchanged.
Working: 65 + 138/897 = 203/897

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 203 and 897 is 1, confirming that 203/897 cannot be reduced further—it is already in its simplest irreducible form.
Working: 203/897

Step 5: Decimal & Percentage Representation
Dividing the numerator 203 by denominator 897 produces a repeating decimal (approximately 0.22631, or 22.631%).
Working: 203 ÷ 897 = 0.22631 (22.631%)

Key Values:
- Simplified Fraction: 203/897
- Mixed Number Form: 203/897
- Decimal Value: 0.22631
- Percentage: 22.631%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-69-plus-2-13/
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5/69 + 2/13 = 203/897

Simplified Fraction

203/897

Mixed Number

Proper (203/897)

Decimal Value

0.22631

Percentage

22.631%

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Step-by-Step Solution: 5/69 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 69 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 69 × 13 = 897.

LCD(69, 13) = 897

Step 2

Convert to Equivalent Fractions with Common Denominator 897

Multiply the numerator and denominator of 5/69 by 13, and multiply the numerator and denominator of 2/13 by 69 so both fractions share the common base 897.

5 × 13/69 × 13 = 65/897 and 2 × 69/13 × 69 = 138/897

Step 3

Add the Numerators

Now add the numerators (65 + 138 = 203) and keep the common denominator 897 unchanged.

65 + 138/897 = 203/897

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 203 and 897 is 1, confirming that 203/897 cannot be reduced further—it is already in its simplest irreducible form.

203/897

Step 5

Decimal & Percentage Representation

Dividing the numerator 203 by denominator 897 produces a repeating decimal (approximately 0.22631, or 22.631%).

203 ÷ 897 = 0.22631 (22.631%)

Visual Representation

The diagram below illustrates 5/69 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`203/897`
Mixed Number Form	`203/897`
Decimal Form	`0.22631`
Percentage	`22.631%`

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Frequently Asked Questions

What is 5/69 plus 2/13 as a fraction?

5/69 + 2/13 in simplest fraction form is 203/897.

What is 5/69 plus 2/13 as a decimal?

5/69 + 2/13 converted to a decimal is 0.22631.

What is 5/69 plus 2/13 as a percentage?

5/69 + 2/13 expressed as a percentage is 22.631%.

Does 5/69 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.22631...) because the denominator contains prime factors other than 2 and 5.