What is 15/40 plus 9/13? (Answer: 111/104)

Exact Answer

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Problem: What is 15/40 plus 9/13?
Formula / Expression: 15/40 + 9/13
Final Answer: 1 7/104 (111/104)
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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 15/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.
Working: 15 × 13/40 × 13 = 195/520 and 9 × 40/13 × 40 = 360/520

Step 3: Add the Numerators
Now add the numerators (195 + 360 = 555) and keep the common denominator 520 unchanged.
Working: 195 + 360/520 = 555/520

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 555 and 520, which is 5. Divide both the numerator and denominator by 5.
Working: 555 ÷ 5/520 ÷ 5 = 111/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (111) is greater than the denominator (104), divide 111 by 104: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/104.
Working: 111/104 = 1 7/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 111 by denominator 104 produces a repeating decimal (approximately 1.067308, or 106.7308%).
Working: 111 ÷ 104 = 1.067308 (106.7308%)

Key Values:
- Simplified Fraction: 111/104
- Mixed Number Form: 1 7/104
- Decimal Value: 1.067308
- Percentage: 106.7308%

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Solved with FractionsCalc:
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15/40 + 9/13 = 111/104

Simplified Fraction

111/104

Mixed Number

1 7/104

Decimal Value

1.067308

Percentage

106.7308%

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Step-by-Step Solution: 15/40 + 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 15/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.

15 × 13/40 × 13 = 195/520 and 9 × 40/13 × 40 = 360/520

Step 3

Add the Numerators

Now add the numerators (195 + 360 = 555) and keep the common denominator 520 unchanged.

195 + 360/520 = 555/520

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 555 and 520, which is 5. Divide both the numerator and denominator by 5.

555 ÷ 5/520 ÷ 5 = 111/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (111) is greater than the denominator (104), divide 111 by 104: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/104.

111/104 = 17/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 111 by denominator 104 produces a repeating decimal (approximately 1.067308, or 106.7308%).

111 ÷ 104 = 1.067308 (106.7308%)

Visual Representation

The diagram below illustrates 15/40 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`111/104`
Mixed Number Form	`1 7/104`
Decimal Form	`1.067308`
Percentage	`106.7308%`

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Frequently Asked Questions

What is 15/40 plus 9/13 as a fraction?

15/40 + 9/13 in simplest fraction form is 111/104 (or 1 7/104 as a mixed number).

What is 15/40 plus 9/13 as a decimal?

15/40 + 9/13 converted to a decimal is 1.067308.

What is 15/40 plus 9/13 as a percentage?

15/40 + 9/13 expressed as a percentage is 106.7308%.

How do you write 15/40 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 111/104 can be written as the mixed number 1 7/104.

Does 15/40 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.067308...) because the denominator contains prime factors other than 2 and 5.