What is 10/25 plus 9/13? (Answer: 71/65)

Exact Answer

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Problem: What is 10/25 plus 9/13?
Formula / Expression: 10/25 + 9/13
Final Answer: 1 6/65 (71/65)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 325
Multiply the numerator and denominator of 10/25 by 13, and multiply the numerator and denominator of 9/13 by 25 so both fractions share the common base 325.
Working: 10 × 13/25 × 13 = 130/325 and 9 × 25/13 × 25 = 225/325

Step 3: Add the Numerators
Now add the numerators (130 + 225 = 355) and keep the common denominator 325 unchanged.
Working: 130 + 225/325 = 355/325

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 355 and 325, which is 5. Divide both the numerator and denominator by 5.
Working: 355 ÷ 5/325 ÷ 5 = 71/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (65), divide 71 by 65: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/65.
Working: 71/65 = 1 6/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 65 produces a repeating decimal (approximately 1.092308, or 109.2308%).
Working: 71 ÷ 65 = 1.092308 (109.2308%)

Key Values:
- Simplified Fraction: 71/65
- Mixed Number Form: 1 6/65
- Decimal Value: 1.092308
- Percentage: 109.2308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-25-plus-9-13/
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10/25 + 9/13 = 71/65

Simplified Fraction

71/65

Mixed Number

1 6/65

Decimal Value

1.092308

Percentage

109.2308%

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Step-by-Step Solution: 10/25 + 9/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(25, 13) = 325

Step 2

Convert to Equivalent Fractions with Common Denominator 325

Multiply the numerator and denominator of 10/25 by 13, and multiply the numerator and denominator of 9/13 by 25 so both fractions share the common base 325.

10 × 13/25 × 13 = 130/325 and 9 × 25/13 × 25 = 225/325

Step 3

Add the Numerators

Now add the numerators (130 + 225 = 355) and keep the common denominator 325 unchanged.

130 + 225/325 = 355/325

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 355 and 325, which is 5. Divide both the numerator and denominator by 5.

355 ÷ 5/325 ÷ 5 = 71/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (65), divide 71 by 65: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/65.

71/65 = 16/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 65 produces a repeating decimal (approximately 1.092308, or 109.2308%).

71 ÷ 65 = 1.092308 (109.2308%)

Visual Representation

The diagram below illustrates 10/25 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/65`
Mixed Number Form	`1 6/65`
Decimal Form	`1.092308`
Percentage	`109.2308%`

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Frequently Asked Questions

What is 10/25 plus 9/13 as a fraction?

10/25 + 9/13 in simplest fraction form is 71/65 (or 1 6/65 as a mixed number).

What is 10/25 plus 9/13 as a decimal?

10/25 + 9/13 converted to a decimal is 1.092308.

What is 10/25 plus 9/13 as a percentage?

10/25 + 9/13 expressed as a percentage is 109.2308%.

How do you write 10/25 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/65 can be written as the mixed number 1 6/65.

Does 10/25 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.092308...) because the denominator contains prime factors other than 2 and 5.