What is 10/49 plus 3/13? (Answer: 277/637)

Exact Answer

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Problem: What is 10/49 plus 3/13?
Formula / Expression: 10/49 + 3/13
Final Answer: 277/637
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 13 = 637.
Working: LCD(49, 13) = 637

Step 2: Convert to Equivalent Fractions with Common Denominator 637
Multiply the numerator and denominator of 10/49 by 13, and multiply the numerator and denominator of 3/13 by 49 so both fractions share the common base 637.
Working: 10 × 13/49 × 13 = 130/637 and 3 × 49/13 × 49 = 147/637

Step 3: Add the Numerators
Now add the numerators (130 + 147 = 277) and keep the common denominator 637 unchanged.
Working: 130 + 147/637 = 277/637

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 277 and 637 is 1, confirming that 277/637 cannot be reduced further—it is already in its simplest irreducible form.
Working: 277/637

Step 5: Decimal & Percentage Representation
Dividing the numerator 277 by denominator 637 produces a repeating decimal (approximately 0.434851, or 43.4851%).
Working: 277 ÷ 637 = 0.434851 (43.4851%)

Key Values:
- Simplified Fraction: 277/637
- Mixed Number Form: 277/637
- Decimal Value: 0.434851
- Percentage: 43.4851%

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Solved with FractionsCalc:
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10/49 + 3/13 = 277/637

Simplified Fraction

277/637

Mixed Number

Proper (277/637)

Decimal Value

0.434851

Percentage

43.4851%

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Step-by-Step Solution: 10/49 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 13 = 637.

LCD(49, 13) = 637

Step 2

Convert to Equivalent Fractions with Common Denominator 637

Multiply the numerator and denominator of 10/49 by 13, and multiply the numerator and denominator of 3/13 by 49 so both fractions share the common base 637.

10 × 13/49 × 13 = 130/637 and 3 × 49/13 × 49 = 147/637

Step 3

Add the Numerators

Now add the numerators (130 + 147 = 277) and keep the common denominator 637 unchanged.

130 + 147/637 = 277/637

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 277 and 637 is 1, confirming that 277/637 cannot be reduced further—it is already in its simplest irreducible form.

277/637

Step 5

Decimal & Percentage Representation

Dividing the numerator 277 by denominator 637 produces a repeating decimal (approximately 0.434851, or 43.4851%).

277 ÷ 637 = 0.434851 (43.4851%)

Visual Representation

The diagram below illustrates 10/49 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`277/637`
Mixed Number Form	`277/637`
Decimal Form	`0.434851`
Percentage	`43.4851%`

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Frequently Asked Questions

What is 10/49 plus 3/13 as a fraction?

10/49 + 3/13 in simplest fraction form is 277/637.

What is 10/49 plus 3/13 as a decimal?

10/49 + 3/13 converted to a decimal is 0.434851.

What is 10/49 plus 3/13 as a percentage?

10/49 + 3/13 expressed as a percentage is 43.4851%.

Does 10/49 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.434851...) because the denominator contains prime factors other than 2 and 5.