What is 3/63 plus 2/13? (Answer: 55/273)

Exact Answer

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Problem: What is 3/63 plus 2/13?
Formula / Expression: 3/63 + 2/13
Final Answer: 55/273
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 63 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 63 × 13 = 819.
Working: LCD(63, 13) = 819

Step 2: Convert to Equivalent Fractions with Common Denominator 819
Multiply the numerator and denominator of 3/63 by 13, and multiply the numerator and denominator of 2/13 by 63 so both fractions share the common base 819.
Working: 3 × 13/63 × 13 = 39/819 and 2 × 63/13 × 63 = 126/819

Step 3: Add the Numerators
Now add the numerators (39 + 126 = 165) and keep the common denominator 819 unchanged.
Working: 39 + 126/819 = 165/819

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 165 and 819, which is 3. Divide both the numerator and denominator by 3.
Working: 165 ÷ 3/819 ÷ 3 = 55/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 273 produces a repeating decimal (approximately 0.201465, or 20.1465%).
Working: 55 ÷ 273 = 0.201465 (20.1465%)

Key Values:
- Simplified Fraction: 55/273
- Mixed Number Form: 55/273
- Decimal Value: 0.201465
- Percentage: 20.1465%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-63-plus-2-13/
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3/63 + 2/13 = 55/273

Simplified Fraction

55/273

Mixed Number

Proper (55/273)

Decimal Value

0.201465

Percentage

20.1465%

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Step-by-Step Solution: 3/63 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 63 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 63 × 13 = 819.

LCD(63, 13) = 819

Step 2

Convert to Equivalent Fractions with Common Denominator 819

Multiply the numerator and denominator of 3/63 by 13, and multiply the numerator and denominator of 2/13 by 63 so both fractions share the common base 819.

3 × 13/63 × 13 = 39/819 and 2 × 63/13 × 63 = 126/819

Step 3

Add the Numerators

Now add the numerators (39 + 126 = 165) and keep the common denominator 819 unchanged.

39 + 126/819 = 165/819

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 165 and 819, which is 3. Divide both the numerator and denominator by 3.

165 ÷ 3/819 ÷ 3 = 55/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 273 produces a repeating decimal (approximately 0.201465, or 20.1465%).

55 ÷ 273 = 0.201465 (20.1465%)

Visual Representation

The diagram below illustrates 3/63 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/273`
Mixed Number Form	`55/273`
Decimal Form	`0.201465`
Percentage	`20.1465%`

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Frequently Asked Questions

What is 3/63 plus 2/13 as a fraction?

3/63 + 2/13 in simplest fraction form is 55/273.

What is 3/63 plus 2/13 as a decimal?

3/63 + 2/13 converted to a decimal is 0.201465.

What is 3/63 plus 2/13 as a percentage?

3/63 + 2/13 expressed as a percentage is 20.1465%.

Does 3/63 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.201465...) because the denominator contains prime factors other than 2 and 5.