What is 3/69 plus 2/13? (Answer: 59/299)

Exact Answer

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Problem: What is 3/69 plus 2/13?
Formula / Expression: 3/69 + 2/13
Final Answer: 59/299
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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 3/69 by 13, and multiply the numerator and denominator of 2/13 by 69 so both fractions share the common base 897.
Working: 3 × 13/69 × 13 = 39/897 and 2 × 69/13 × 69 = 138/897

Step 3: Add the Numerators
Now add the numerators (39 + 138 = 177) and keep the common denominator 897 unchanged.
Working: 39 + 138/897 = 177/897

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 177 and 897, which is 3. Divide both the numerator and denominator by 3.
Working: 177 ÷ 3/897 ÷ 3 = 59/299

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 299 produces a repeating decimal (approximately 0.197324, or 19.7324%).
Working: 59 ÷ 299 = 0.197324 (19.7324%)

Key Values:
- Simplified Fraction: 59/299
- Mixed Number Form: 59/299
- Decimal Value: 0.197324
- Percentage: 19.7324%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-69-plus-2-13/
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3/69 + 2/13 = 59/299

Simplified Fraction

59/299

Mixed Number

Proper (59/299)

Decimal Value

0.197324

Percentage

19.7324%

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Step-by-Step Solution: 3/69 + 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 3/69 by 13, and multiply the numerator and denominator of 2/13 by 69 so both fractions share the common base 897.

3 × 13/69 × 13 = 39/897 and 2 × 69/13 × 69 = 138/897

Step 3

Add the Numerators

Now add the numerators (39 + 138 = 177) and keep the common denominator 897 unchanged.

39 + 138/897 = 177/897

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 177 and 897, which is 3. Divide both the numerator and denominator by 3.

177 ÷ 3/897 ÷ 3 = 59/299

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 299 produces a repeating decimal (approximately 0.197324, or 19.7324%).

59 ÷ 299 = 0.197324 (19.7324%)

Visual Representation

The diagram below illustrates 3/69 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/299`
Mixed Number Form	`59/299`
Decimal Form	`0.197324`
Percentage	`19.7324%`

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Frequently Asked Questions

What is 3/69 plus 2/13 as a fraction?

3/69 + 2/13 in simplest fraction form is 59/299.

What is 3/69 plus 2/13 as a decimal?

3/69 + 2/13 converted to a decimal is 0.197324.

What is 3/69 plus 2/13 as a percentage?

3/69 + 2/13 expressed as a percentage is 19.7324%.

Does 3/69 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.197324...) because the denominator contains prime factors other than 2 and 5.