What is 5/13 plus 14/35? (Answer: 51/65)

Exact Answer

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Problem: What is 5/13 plus 14/35?
Formula / Expression: 5/13 + 14/35
Final Answer: 51/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 35 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 35 = 455.
Working: LCD(13, 35) = 455

Step 2: Convert to Equivalent Fractions with Common Denominator 455
Multiply the numerator and denominator of 5/13 by 35, and multiply the numerator and denominator of 14/35 by 13 so both fractions share the common base 455.
Working: 5 × 35/13 × 35 = 175/455 and 14 × 13/35 × 13 = 182/455

Step 3: Add the Numerators
Now add the numerators (175 + 182 = 357) and keep the common denominator 455 unchanged.
Working: 175 + 182/455 = 357/455

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 357 and 455, which is 7. Divide both the numerator and denominator by 7.
Working: 357 ÷ 7/455 ÷ 7 = 51/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 65 produces a repeating decimal (approximately 0.784615, or 78.4615%).
Working: 51 ÷ 65 = 0.784615 (78.4615%)

Key Values:
- Simplified Fraction: 51/65
- Mixed Number Form: 51/65
- Decimal Value: 0.784615
- Percentage: 78.4615%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-13-plus-14-35/
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5/13 + 14/35 = 51/65

Simplified Fraction

51/65

Mixed Number

Proper (51/65)

Decimal Value

0.784615

Percentage

78.4615%

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Step-by-Step Solution: 5/13 + 14/35

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 35 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 35 = 455.

LCD(13, 35) = 455

Step 2

Convert to Equivalent Fractions with Common Denominator 455

Multiply the numerator and denominator of 5/13 by 35, and multiply the numerator and denominator of 14/35 by 13 so both fractions share the common base 455.

5 × 35/13 × 35 = 175/455 and 14 × 13/35 × 13 = 182/455

Step 3

Add the Numerators

Now add the numerators (175 + 182 = 357) and keep the common denominator 455 unchanged.

175 + 182/455 = 357/455

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 357 and 455, which is 7. Divide both the numerator and denominator by 7.

357 ÷ 7/455 ÷ 7 = 51/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 65 produces a repeating decimal (approximately 0.784615, or 78.4615%).

51 ÷ 65 = 0.784615 (78.4615%)

Visual Representation

The diagram below illustrates 5/13 plus 14/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/65`
Mixed Number Form	`51/65`
Decimal Form	`0.784615`
Percentage	`78.4615%`

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Frequently Asked Questions

What is 5/13 plus 14/35 as a fraction?

5/13 + 14/35 in simplest fraction form is 51/65.

What is 5/13 plus 14/35 as a decimal?

5/13 + 14/35 converted to a decimal is 0.784615.

What is 5/13 plus 14/35 as a percentage?

5/13 + 14/35 expressed as a percentage is 78.4615%.

Does 5/13 plus 14/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.784615...) because the denominator contains prime factors other than 2 and 5.