What is 3/54 plus 3/13? (Answer: 67/234)

Exact Answer

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Problem: What is 3/54 plus 3/13?
Formula / Expression: 3/54 + 3/13
Final Answer: 67/234
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 54 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 54 × 13 = 702.
Working: LCD(54, 13) = 702

Step 2: Convert to Equivalent Fractions with Common Denominator 702
Multiply the numerator and denominator of 3/54 by 13, and multiply the numerator and denominator of 3/13 by 54 so both fractions share the common base 702.
Working: 3 × 13/54 × 13 = 39/702 and 3 × 54/13 × 54 = 162/702

Step 3: Add the Numerators
Now add the numerators (39 + 162 = 201) and keep the common denominator 702 unchanged.
Working: 39 + 162/702 = 201/702

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 201 and 702, which is 3. Divide both the numerator and denominator by 3.
Working: 201 ÷ 3/702 ÷ 3 = 67/234

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 234 produces a repeating decimal (approximately 0.286325, or 28.6325%).
Working: 67 ÷ 234 = 0.286325 (28.6325%)

Key Values:
- Simplified Fraction: 67/234
- Mixed Number Form: 67/234
- Decimal Value: 0.286325
- Percentage: 28.6325%

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Solved with FractionsCalc:
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3/54 + 3/13 = 67/234

Simplified Fraction

67/234

Mixed Number

Proper (67/234)

Decimal Value

0.286325

Percentage

28.6325%

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Step-by-Step Solution: 3/54 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 54 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 54 × 13 = 702.

LCD(54, 13) = 702

Step 2

Convert to Equivalent Fractions with Common Denominator 702

Multiply the numerator and denominator of 3/54 by 13, and multiply the numerator and denominator of 3/13 by 54 so both fractions share the common base 702.

3 × 13/54 × 13 = 39/702 and 3 × 54/13 × 54 = 162/702

Step 3

Add the Numerators

Now add the numerators (39 + 162 = 201) and keep the common denominator 702 unchanged.

39 + 162/702 = 201/702

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 201 and 702, which is 3. Divide both the numerator and denominator by 3.

201 ÷ 3/702 ÷ 3 = 67/234

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 234 produces a repeating decimal (approximately 0.286325, or 28.6325%).

67 ÷ 234 = 0.286325 (28.6325%)

Visual Representation

The diagram below illustrates 3/54 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/234`
Mixed Number Form	`67/234`
Decimal Form	`0.286325`
Percentage	`28.6325%`

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Frequently Asked Questions

What is 3/54 plus 3/13 as a fraction?

3/54 + 3/13 in simplest fraction form is 67/234.

What is 3/54 plus 3/13 as a decimal?

3/54 + 3/13 converted to a decimal is 0.286325.

What is 3/54 plus 3/13 as a percentage?

3/54 + 3/13 expressed as a percentage is 28.6325%.

Does 3/54 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.286325...) because the denominator contains prime factors other than 2 and 5.