What is 5/13 plus 10/25? (Answer: 51/65)

Exact Answer

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Problem: What is 5/13 plus 10/25?
Formula / Expression: 5/13 + 10/25
Final Answer: 51/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 25 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 25 = 325.
Working: LCD(13, 25) = 325

Step 2: Convert to Equivalent Fractions with Common Denominator 325
Multiply the numerator and denominator of 5/13 by 25, and multiply the numerator and denominator of 10/25 by 13 so both fractions share the common base 325.
Working: 5 × 25/13 × 25 = 125/325 and 10 × 13/25 × 13 = 130/325

Step 3: Add the Numerators
Now add the numerators (125 + 130 = 255) and keep the common denominator 325 unchanged.
Working: 125 + 130/325 = 255/325

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 255 and 325, which is 5. Divide both the numerator and denominator by 5.
Working: 255 ÷ 5/325 ÷ 5 = 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-10-25/
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5/13 + 10/25 = 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 + 10/25

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 25 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 25 = 325.

LCD(13, 25) = 325

Step 2

Convert to Equivalent Fractions with Common Denominator 325

Multiply the numerator and denominator of 5/13 by 25, and multiply the numerator and denominator of 10/25 by 13 so both fractions share the common base 325.

5 × 25/13 × 25 = 125/325 and 10 × 13/25 × 13 = 130/325

Step 3

Add the Numerators

Now add the numerators (125 + 130 = 255) and keep the common denominator 325 unchanged.

125 + 130/325 = 255/325

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 255 and 325, which is 5. Divide both the numerator and denominator by 5.

255 ÷ 5/325 ÷ 5 = 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 10/25 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 10/25 as a fraction?

5/13 + 10/25 in simplest fraction form is 51/65.

What is 5/13 plus 10/25 as a decimal?

5/13 + 10/25 converted to a decimal is 0.784615.

What is 5/13 plus 10/25 as a percentage?

5/13 + 10/25 expressed as a percentage is 78.4615%.

Does 5/13 plus 10/25 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.