What is 3/30 plus 4/13? (Answer: 53/130)

Exact Answer

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Problem: What is 3/30 plus 4/13?
Formula / Expression: 3/30 + 4/13
Final Answer: 53/130
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 30 × 13 = 390.
Working: LCD(30, 13) = 390

Step 2: Convert to Equivalent Fractions with Common Denominator 390
Multiply the numerator and denominator of 3/30 by 13, and multiply the numerator and denominator of 4/13 by 30 so both fractions share the common base 390.
Working: 3 × 13/30 × 13 = 39/390 and 4 × 30/13 × 30 = 120/390

Step 3: Add the Numerators
Now add the numerators (39 + 120 = 159) and keep the common denominator 390 unchanged.
Working: 39 + 120/390 = 159/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 159 and 390, which is 3. Divide both the numerator and denominator by 3.
Working: 159 ÷ 3/390 ÷ 3 = 53/130

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 130 produces a repeating decimal (approximately 0.407692, or 40.7692%).
Working: 53 ÷ 130 = 0.407692 (40.7692%)

Key Values:
- Simplified Fraction: 53/130
- Mixed Number Form: 53/130
- Decimal Value: 0.407692
- Percentage: 40.7692%

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3/30 + 4/13 = 53/130

Simplified Fraction

53/130

Mixed Number

Proper (53/130)

Decimal Value

0.407692

Percentage

40.7692%

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Step-by-Step Solution: 3/30 + 4/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 30 × 13 = 390.

LCD(30, 13) = 390

Step 2

Convert to Equivalent Fractions with Common Denominator 390

Multiply the numerator and denominator of 3/30 by 13, and multiply the numerator and denominator of 4/13 by 30 so both fractions share the common base 390.

3 × 13/30 × 13 = 39/390 and 4 × 30/13 × 30 = 120/390

Step 3

Add the Numerators

Now add the numerators (39 + 120 = 159) and keep the common denominator 390 unchanged.

39 + 120/390 = 159/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 159 and 390, which is 3. Divide both the numerator and denominator by 3.

159 ÷ 3/390 ÷ 3 = 53/130

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 130 produces a repeating decimal (approximately 0.407692, or 40.7692%).

53 ÷ 130 = 0.407692 (40.7692%)

Visual Representation

The diagram below illustrates 3/30 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/130`
Mixed Number Form	`53/130`
Decimal Form	`0.407692`
Percentage	`40.7692%`

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Frequently Asked Questions

What is 3/30 plus 4/13 as a fraction?

3/30 + 4/13 in simplest fraction form is 53/130.

What is 3/30 plus 4/13 as a decimal?

3/30 + 4/13 converted to a decimal is 0.407692.

What is 3/30 plus 4/13 as a percentage?

3/30 + 4/13 expressed as a percentage is 40.7692%.

Does 3/30 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.407692...) because the denominator contains prime factors other than 2 and 5.