What is 7/29 plus 10/13? (Answer: 381/377)

Exact Answer

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Problem: What is 7/29 plus 10/13?
Formula / Expression: 7/29 + 10/13
Final Answer: 1 4/377 (381/377)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 13 = 377.
Working: LCD(29, 13) = 377

Step 2: Convert to Equivalent Fractions with Common Denominator 377
Multiply the numerator and denominator of 7/29 by 13, and multiply the numerator and denominator of 10/13 by 29 so both fractions share the common base 377.
Working: 7 × 13/29 × 13 = 91/377 and 10 × 29/13 × 29 = 290/377

Step 3: Add the Numerators
Now add the numerators (91 + 290 = 381) and keep the common denominator 377 unchanged.
Working: 91 + 290/377 = 381/377

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 381 and 377 is 1, confirming that 381/377 cannot be reduced further—it is already in its simplest irreducible form.
Working: 381/377

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (381) is greater than the denominator (377), divide 381 by 377: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/377.
Working: 381/377 = 1 4/377

Step 6: Decimal & Percentage Representation
Dividing the numerator 381 by denominator 377 produces a repeating decimal (approximately 1.01061, or 101.061%).
Working: 381 ÷ 377 = 1.01061 (101.061%)

Key Values:
- Simplified Fraction: 381/377
- Mixed Number Form: 1 4/377
- Decimal Value: 1.01061
- Percentage: 101.061%

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Solved with FractionsCalc:
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7/29 + 10/13 = 381/377

Simplified Fraction

381/377

Mixed Number

1 4/377

Decimal Value

1.01061

Percentage

101.061%

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Step-by-Step Solution: 7/29 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 13 = 377.

LCD(29, 13) = 377

Step 2

Convert to Equivalent Fractions with Common Denominator 377

Multiply the numerator and denominator of 7/29 by 13, and multiply the numerator and denominator of 10/13 by 29 so both fractions share the common base 377.

7 × 13/29 × 13 = 91/377 and 10 × 29/13 × 29 = 290/377

Step 3

Add the Numerators

Now add the numerators (91 + 290 = 381) and keep the common denominator 377 unchanged.

91 + 290/377 = 381/377

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 381 and 377 is 1, confirming that 381/377 cannot be reduced further—it is already in its simplest irreducible form.

381/377

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (381) is greater than the denominator (377), divide 381 by 377: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/377.

381/377 = 14/377

Step 6

Decimal & Percentage Representation

Dividing the numerator 381 by denominator 377 produces a repeating decimal (approximately 1.01061, or 101.061%).

381 ÷ 377 = 1.01061 (101.061%)

Visual Representation

The diagram below illustrates 7/29 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`381/377`
Mixed Number Form	`1 4/377`
Decimal Form	`1.01061`
Percentage	`101.061%`

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Frequently Asked Questions

What is 7/29 plus 10/13 as a fraction?

7/29 + 10/13 in simplest fraction form is 381/377 (or 1 4/377 as a mixed number).

What is 7/29 plus 10/13 as a decimal?

7/29 + 10/13 converted to a decimal is 1.01061.

What is 7/29 plus 10/13 as a percentage?

7/29 + 10/13 expressed as a percentage is 101.061%.

How do you write 7/29 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 381/377 can be written as the mixed number 1 4/377.

Does 7/29 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.01061...) because the denominator contains prime factors other than 2 and 5.