What is 15/27 plus 9/13? (Answer: 146/117)

Exact Answer

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Problem: What is 15/27 plus 9/13?
Formula / Expression: 15/27 + 9/13
Final Answer: 1 29/117 (146/117)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 13 = 351.
Working: LCD(27, 13) = 351

Step 2: Convert to Equivalent Fractions with Common Denominator 351
Multiply the numerator and denominator of 15/27 by 13, and multiply the numerator and denominator of 9/13 by 27 so both fractions share the common base 351.
Working: 15 × 13/27 × 13 = 195/351 and 9 × 27/13 × 27 = 243/351

Step 3: Add the Numerators
Now add the numerators (195 + 243 = 438) and keep the common denominator 351 unchanged.
Working: 195 + 243/351 = 438/351

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 438 and 351, which is 3. Divide both the numerator and denominator by 3.
Working: 438 ÷ 3/351 ÷ 3 = 146/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (146) is greater than the denominator (117), divide 146 by 117: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/117.
Working: 146/117 = 1 29/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 117 produces a repeating decimal (approximately 1.247863, or 124.7863%).
Working: 146 ÷ 117 = 1.247863 (124.7863%)

Key Values:
- Simplified Fraction: 146/117
- Mixed Number Form: 1 29/117
- Decimal Value: 1.247863
- Percentage: 124.7863%

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15/27 + 9/13 = 146/117

Simplified Fraction

146/117

Mixed Number

1 29/117

Decimal Value

1.247863

Percentage

124.7863%

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Step-by-Step Solution: 15/27 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 13 = 351.

LCD(27, 13) = 351

Step 2

Convert to Equivalent Fractions with Common Denominator 351

Multiply the numerator and denominator of 15/27 by 13, and multiply the numerator and denominator of 9/13 by 27 so both fractions share the common base 351.

15 × 13/27 × 13 = 195/351 and 9 × 27/13 × 27 = 243/351

Step 3

Add the Numerators

Now add the numerators (195 + 243 = 438) and keep the common denominator 351 unchanged.

195 + 243/351 = 438/351

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 438 and 351, which is 3. Divide both the numerator and denominator by 3.

438 ÷ 3/351 ÷ 3 = 146/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (146) is greater than the denominator (117), divide 146 by 117: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/117.

146/117 = 129/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 117 produces a repeating decimal (approximately 1.247863, or 124.7863%).

146 ÷ 117 = 1.247863 (124.7863%)

Visual Representation

The diagram below illustrates 15/27 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/117`
Mixed Number Form	`1 29/117`
Decimal Form	`1.247863`
Percentage	`124.7863%`

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Frequently Asked Questions

What is 15/27 plus 9/13 as a fraction?

15/27 + 9/13 in simplest fraction form is 146/117 (or 1 29/117 as a mixed number).

What is 15/27 plus 9/13 as a decimal?

15/27 + 9/13 converted to a decimal is 1.247863.

What is 15/27 plus 9/13 as a percentage?

15/27 + 9/13 expressed as a percentage is 124.7863%.

How do you write 15/27 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 146/117 can be written as the mixed number 1 29/117.

Does 15/27 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.247863...) because the denominator contains prime factors other than 2 and 5.