What is 3/66 plus 2/13? (Answer: 57/286)

Exact Answer

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Problem: What is 3/66 plus 2/13?
Formula / Expression: 3/66 + 2/13
Final Answer: 57/286
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 66 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 66 × 13 = 858.
Working: LCD(66, 13) = 858

Step 2: Convert to Equivalent Fractions with Common Denominator 858
Multiply the numerator and denominator of 3/66 by 13, and multiply the numerator and denominator of 2/13 by 66 so both fractions share the common base 858.
Working: 3 × 13/66 × 13 = 39/858 and 2 × 66/13 × 66 = 132/858

Step 3: Add the Numerators
Now add the numerators (39 + 132 = 171) and keep the common denominator 858 unchanged.
Working: 39 + 132/858 = 171/858

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 171 and 858, which is 3. Divide both the numerator and denominator by 3.
Working: 171 ÷ 3/858 ÷ 3 = 57/286

Step 5: Decimal & Percentage Representation
Dividing the numerator 57 by denominator 286 produces a repeating decimal (approximately 0.199301, or 19.9301%).
Working: 57 ÷ 286 = 0.199301 (19.9301%)

Key Values:
- Simplified Fraction: 57/286
- Mixed Number Form: 57/286
- Decimal Value: 0.199301
- Percentage: 19.9301%

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Solved with FractionsCalc:
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3/66 + 2/13 = 57/286

Simplified Fraction

57/286

Mixed Number

Proper (57/286)

Decimal Value

0.199301

Percentage

19.9301%

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Step-by-Step Solution: 3/66 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 66 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 66 × 13 = 858.

LCD(66, 13) = 858

Step 2

Convert to Equivalent Fractions with Common Denominator 858

Multiply the numerator and denominator of 3/66 by 13, and multiply the numerator and denominator of 2/13 by 66 so both fractions share the common base 858.

3 × 13/66 × 13 = 39/858 and 2 × 66/13 × 66 = 132/858

Step 3

Add the Numerators

Now add the numerators (39 + 132 = 171) and keep the common denominator 858 unchanged.

39 + 132/858 = 171/858

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 171 and 858, which is 3. Divide both the numerator and denominator by 3.

171 ÷ 3/858 ÷ 3 = 57/286

Step 5

Decimal & Percentage Representation

Dividing the numerator 57 by denominator 286 produces a repeating decimal (approximately 0.199301, or 19.9301%).

57 ÷ 286 = 0.199301 (19.9301%)

Visual Representation

The diagram below illustrates 3/66 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`57/286`
Mixed Number Form	`57/286`
Decimal Form	`0.199301`
Percentage	`19.9301%`

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Frequently Asked Questions

What is 3/66 plus 2/13 as a fraction?

3/66 + 2/13 in simplest fraction form is 57/286.

What is 3/66 plus 2/13 as a decimal?

3/66 + 2/13 converted to a decimal is 0.199301.

What is 3/66 plus 2/13 as a percentage?

3/66 + 2/13 expressed as a percentage is 19.9301%.

Does 3/66 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.199301...) because the denominator contains prime factors other than 2 and 5.