What is 7/27 plus 10/13? (Answer: 361/351)

Exact Answer

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Problem: What is 7/27 plus 10/13?
Formula / Expression: 7/27 + 10/13
Final Answer: 1 10/351 (361/351)
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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 7/27 by 13, and multiply the numerator and denominator of 10/13 by 27 so both fractions share the common base 351.
Working: 7 × 13/27 × 13 = 91/351 and 10 × 27/13 × 27 = 270/351

Step 3: Add the Numerators
Now add the numerators (91 + 270 = 361) and keep the common denominator 351 unchanged.
Working: 91 + 270/351 = 361/351

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 361 and 351 is 1, confirming that 361/351 cannot be reduced further—it is already in its simplest irreducible form.
Working: 361/351

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (361) is greater than the denominator (351), divide 361 by 351: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/351.
Working: 361/351 = 1 10/351

Step 6: Decimal & Percentage Representation
Dividing the numerator 361 by denominator 351 produces a repeating decimal (approximately 1.02849, or 102.849%).
Working: 361 ÷ 351 = 1.02849 (102.849%)

Key Values:
- Simplified Fraction: 361/351
- Mixed Number Form: 1 10/351
- Decimal Value: 1.02849
- Percentage: 102.849%

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Solved with FractionsCalc:
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7/27 + 10/13 = 361/351

Simplified Fraction

361/351

Mixed Number

1 10/351

Decimal Value

1.02849

Percentage

102.849%

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Step-by-Step Solution: 7/27 + 10/13

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 7/27 by 13, and multiply the numerator and denominator of 10/13 by 27 so both fractions share the common base 351.

7 × 13/27 × 13 = 91/351 and 10 × 27/13 × 27 = 270/351

Step 3

Add the Numerators

Now add the numerators (91 + 270 = 361) and keep the common denominator 351 unchanged.

91 + 270/351 = 361/351

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 361 and 351 is 1, confirming that 361/351 cannot be reduced further—it is already in its simplest irreducible form.

361/351

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (361) is greater than the denominator (351), divide 361 by 351: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/351.

361/351 = 110/351

Step 6

Decimal & Percentage Representation

Dividing the numerator 361 by denominator 351 produces a repeating decimal (approximately 1.02849, or 102.849%).

361 ÷ 351 = 1.02849 (102.849%)

Visual Representation

The diagram below illustrates 7/27 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`361/351`
Mixed Number Form	`1 10/351`
Decimal Form	`1.02849`
Percentage	`102.849%`

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Frequently Asked Questions

What is 7/27 plus 10/13 as a fraction?

7/27 + 10/13 in simplest fraction form is 361/351 (or 1 10/351 as a mixed number).

What is 7/27 plus 10/13 as a decimal?

7/27 + 10/13 converted to a decimal is 1.02849.

What is 7/27 plus 10/13 as a percentage?

7/27 + 10/13 expressed as a percentage is 102.849%.

How do you write 7/27 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 361/351 can be written as the mixed number 1 10/351.

Does 7/27 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.02849...) because the denominator contains prime factors other than 2 and 5.