What is 10/35 plus 5/13? (Answer: 61/91)

Exact Answer

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Problem: What is 10/35 plus 5/13?
Formula / Expression: 10/35 + 5/13
Final Answer: 61/91
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 455
Multiply the numerator and denominator of 10/35 by 13, and multiply the numerator and denominator of 5/13 by 35 so both fractions share the common base 455.
Working: 10 × 13/35 × 13 = 130/455 and 5 × 35/13 × 35 = 175/455

Step 3: Add the Numerators
Now add the numerators (130 + 175 = 305) and keep the common denominator 455 unchanged.
Working: 130 + 175/455 = 305/455

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 305 and 455, which is 5. Divide both the numerator and denominator by 5.
Working: 305 ÷ 5/455 ÷ 5 = 61/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 91 produces a repeating decimal (approximately 0.67033, or 67.033%).
Working: 61 ÷ 91 = 0.67033 (67.033%)

Key Values:
- Simplified Fraction: 61/91
- Mixed Number Form: 61/91
- Decimal Value: 0.67033
- Percentage: 67.033%

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Solved with FractionsCalc:
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10/35 + 5/13 = 61/91

Simplified Fraction

61/91

Mixed Number

Proper (61/91)

Decimal Value

0.67033

Percentage

67.033%

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Step-by-Step Solution: 10/35 + 5/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(35, 13) = 455

Step 2

Convert to Equivalent Fractions with Common Denominator 455

Multiply the numerator and denominator of 10/35 by 13, and multiply the numerator and denominator of 5/13 by 35 so both fractions share the common base 455.

10 × 13/35 × 13 = 130/455 and 5 × 35/13 × 35 = 175/455

Step 3

Add the Numerators

Now add the numerators (130 + 175 = 305) and keep the common denominator 455 unchanged.

130 + 175/455 = 305/455

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 305 and 455, which is 5. Divide both the numerator and denominator by 5.

305 ÷ 5/455 ÷ 5 = 61/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 91 produces a repeating decimal (approximately 0.67033, or 67.033%).

61 ÷ 91 = 0.67033 (67.033%)

Visual Representation

The diagram below illustrates 10/35 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/91`
Mixed Number Form	`61/91`
Decimal Form	`0.67033`
Percentage	`67.033%`

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Frequently Asked Questions

What is 10/35 plus 5/13 as a fraction?

10/35 + 5/13 in simplest fraction form is 61/91.

What is 10/35 plus 5/13 as a decimal?

10/35 + 5/13 converted to a decimal is 0.67033.

What is 10/35 plus 5/13 as a percentage?

10/35 + 5/13 expressed as a percentage is 67.033%.

Does 10/35 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.67033...) because the denominator contains prime factors other than 2 and 5.