What is 10/27 plus 7/13? (Answer: 319/351)

Exact Answer

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Problem: What is 10/27 plus 7/13?
Formula / Expression: 10/27 + 7/13
Final Answer: 319/351
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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 10/27 by 13, and multiply the numerator and denominator of 7/13 by 27 so both fractions share the common base 351.
Working: 10 × 13/27 × 13 = 130/351 and 7 × 27/13 × 27 = 189/351

Step 3: Add the Numerators
Now add the numerators (130 + 189 = 319) and keep the common denominator 351 unchanged.
Working: 130 + 189/351 = 319/351

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 319 and 351 is 1, confirming that 319/351 cannot be reduced further—it is already in its simplest irreducible form.
Working: 319/351

Step 5: Decimal & Percentage Representation
Dividing the numerator 319 by denominator 351 produces a repeating decimal (approximately 0.908832, or 90.8832%).
Working: 319 ÷ 351 = 0.908832 (90.8832%)

Key Values:
- Simplified Fraction: 319/351
- Mixed Number Form: 319/351
- Decimal Value: 0.908832
- Percentage: 90.8832%

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Solved with FractionsCalc:
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10/27 + 7/13 = 319/351

Simplified Fraction

319/351

Mixed Number

Proper (319/351)

Decimal Value

0.908832

Percentage

90.8832%

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

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

10 × 13/27 × 13 = 130/351 and 7 × 27/13 × 27 = 189/351

Step 3

Add the Numerators

Now add the numerators (130 + 189 = 319) and keep the common denominator 351 unchanged.

130 + 189/351 = 319/351

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 319 and 351 is 1, confirming that 319/351 cannot be reduced further—it is already in its simplest irreducible form.

319/351

Step 5

Decimal & Percentage Representation

Dividing the numerator 319 by denominator 351 produces a repeating decimal (approximately 0.908832, or 90.8832%).

319 ÷ 351 = 0.908832 (90.8832%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`319/351`
Mixed Number Form	`319/351`
Decimal Form	`0.908832`
Percentage	`90.8832%`

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Frequently Asked Questions

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

10/27 + 7/13 in simplest fraction form is 319/351.

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

10/27 + 7/13 converted to a decimal is 0.908832.

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

10/27 + 7/13 expressed as a percentage is 90.8832%.

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

It results in a repeating decimal (approximately 0.908832...) because the denominator contains prime factors other than 2 and 5.