What is 10/30 plus 7/13? (Answer: 34/39)

Exact Answer

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Problem: What is 10/30 plus 7/13?
Formula / Expression: 10/30 + 7/13
Final Answer: 34/39
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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 10/30 by 13, and multiply the numerator and denominator of 7/13 by 30 so both fractions share the common base 390.
Working: 10 × 13/30 × 13 = 130/390 and 7 × 30/13 × 30 = 210/390

Step 3: Add the Numerators
Now add the numerators (130 + 210 = 340) and keep the common denominator 390 unchanged.
Working: 130 + 210/390 = 340/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 340 and 390, which is 10. Divide both the numerator and denominator by 10.
Working: 340 ÷ 10/390 ÷ 10 = 34/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 39 produces a repeating decimal (approximately 0.871795, or 87.1795%).
Working: 34 ÷ 39 = 0.871795 (87.1795%)

Key Values:
- Simplified Fraction: 34/39
- Mixed Number Form: 34/39
- Decimal Value: 0.871795
- Percentage: 87.1795%

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Solved with FractionsCalc:
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10/30 + 7/13 = 34/39

Simplified Fraction

34/39

Mixed Number

Proper (34/39)

Decimal Value

0.871795

Percentage

87.1795%

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Step-by-Step Solution: 10/30 + 7/13

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 10/30 by 13, and multiply the numerator and denominator of 7/13 by 30 so both fractions share the common base 390.

10 × 13/30 × 13 = 130/390 and 7 × 30/13 × 30 = 210/390

Step 3

Add the Numerators

Now add the numerators (130 + 210 = 340) and keep the common denominator 390 unchanged.

130 + 210/390 = 340/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 340 and 390, which is 10. Divide both the numerator and denominator by 10.

340 ÷ 10/390 ÷ 10 = 34/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 39 produces a repeating decimal (approximately 0.871795, or 87.1795%).

34 ÷ 39 = 0.871795 (87.1795%)

Visual Representation

The diagram below illustrates 10/30 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/39`
Mixed Number Form	`34/39`
Decimal Form	`0.871795`
Percentage	`87.1795%`

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Frequently Asked Questions

What is 10/30 plus 7/13 as a fraction?

10/30 + 7/13 in simplest fraction form is 34/39.

What is 10/30 plus 7/13 as a decimal?

10/30 + 7/13 converted to a decimal is 0.871795.

What is 10/30 plus 7/13 as a percentage?

10/30 + 7/13 expressed as a percentage is 87.1795%.

Does 10/30 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.871795...) because the denominator contains prime factors other than 2 and 5.