What is 25/40 plus 9/13? (Answer: 137/104)

Exact Answer

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Problem: What is 25/40 plus 9/13?
Formula / Expression: 25/40 + 9/13
Final Answer: 1 33/104 (137/104)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 25/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.
Working: 25 × 13/40 × 13 = 325/520 and 9 × 40/13 × 40 = 360/520

Step 3: Add the Numerators
Now add the numerators (325 + 360 = 685) and keep the common denominator 520 unchanged.
Working: 325 + 360/520 = 685/520

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 685 and 520, which is 5. Divide both the numerator and denominator by 5.
Working: 685 ÷ 5/520 ÷ 5 = 137/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (137) is greater than the denominator (104), divide 137 by 104: it goes in 1 whole time(s) with a remainder of 33, giving the mixed number 1 33/104.
Working: 137/104 = 1 33/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 137 by denominator 104 produces a repeating decimal (approximately 1.317308, or 131.7308%).
Working: 137 ÷ 104 = 1.317308 (131.7308%)

Key Values:
- Simplified Fraction: 137/104
- Mixed Number Form: 1 33/104
- Decimal Value: 1.317308
- Percentage: 131.7308%

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25/40 + 9/13 = 137/104

Simplified Fraction

137/104

Mixed Number

1 33/104

Decimal Value

1.317308

Percentage

131.7308%

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Step-by-Step Solution: 25/40 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.

LCD(40, 13) = 520

Step 2

Convert to Equivalent Fractions with Common Denominator 520

Multiply the numerator and denominator of 25/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.

25 × 13/40 × 13 = 325/520 and 9 × 40/13 × 40 = 360/520

Step 3

Add the Numerators

Now add the numerators (325 + 360 = 685) and keep the common denominator 520 unchanged.

325 + 360/520 = 685/520

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 685 and 520, which is 5. Divide both the numerator and denominator by 5.

685 ÷ 5/520 ÷ 5 = 137/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (137) is greater than the denominator (104), divide 137 by 104: it goes in 1 whole time(s) with a remainder of 33, giving the mixed number 1 33/104.

137/104 = 133/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 137 by denominator 104 produces a repeating decimal (approximately 1.317308, or 131.7308%).

137 ÷ 104 = 1.317308 (131.7308%)

Visual Representation

The diagram below illustrates 25/40 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`137/104`
Mixed Number Form	`1 33/104`
Decimal Form	`1.317308`
Percentage	`131.7308%`

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Frequently Asked Questions

What is 25/40 plus 9/13 as a fraction?

25/40 + 9/13 in simplest fraction form is 137/104 (or 1 33/104 as a mixed number).

What is 25/40 plus 9/13 as a decimal?

25/40 + 9/13 converted to a decimal is 1.317308.

What is 25/40 plus 9/13 as a percentage?

25/40 + 9/13 expressed as a percentage is 131.7308%.

How do you write 25/40 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 137/104 can be written as the mixed number 1 33/104.

Does 25/40 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.317308...) because the denominator contains prime factors other than 2 and 5.