What is 3/13 plus 12/49? (Answer: 303/637)

Exact Answer

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Problem: What is 3/13 plus 12/49?
Formula / Expression: 3/13 + 12/49
Final Answer: 303/637
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 637
Multiply the numerator and denominator of 3/13 by 49, and multiply the numerator and denominator of 12/49 by 13 so both fractions share the common base 637.
Working: 3 × 49/13 × 49 = 147/637 and 12 × 13/49 × 13 = 156/637

Step 3: Add the Numerators
Now add the numerators (147 + 156 = 303) and keep the common denominator 637 unchanged.
Working: 147 + 156/637 = 303/637

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 303 and 637 is 1, confirming that 303/637 cannot be reduced further—it is already in its simplest irreducible form.
Working: 303/637

Step 5: Decimal & Percentage Representation
Dividing the numerator 303 by denominator 637 produces a repeating decimal (approximately 0.475667, or 47.5667%).
Working: 303 ÷ 637 = 0.475667 (47.5667%)

Key Values:
- Simplified Fraction: 303/637
- Mixed Number Form: 303/637
- Decimal Value: 0.475667
- Percentage: 47.5667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-13-plus-12-49/
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3/13 + 12/49 = 303/637

Simplified Fraction

303/637

Mixed Number

Proper (303/637)

Decimal Value

0.475667

Percentage

47.5667%

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Step-by-Step Solution: 3/13 + 12/49

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 49) = 637

Step 2

Convert to Equivalent Fractions with Common Denominator 637

Multiply the numerator and denominator of 3/13 by 49, and multiply the numerator and denominator of 12/49 by 13 so both fractions share the common base 637.

3 × 49/13 × 49 = 147/637 and 12 × 13/49 × 13 = 156/637

Step 3

Add the Numerators

Now add the numerators (147 + 156 = 303) and keep the common denominator 637 unchanged.

147 + 156/637 = 303/637

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 303 and 637 is 1, confirming that 303/637 cannot be reduced further—it is already in its simplest irreducible form.

303/637

Step 5

Decimal & Percentage Representation

Dividing the numerator 303 by denominator 637 produces a repeating decimal (approximately 0.475667, or 47.5667%).

303 ÷ 637 = 0.475667 (47.5667%)

Visual Representation

The diagram below illustrates 3/13 plus 12/49 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`303/637`
Mixed Number Form	`303/637`
Decimal Form	`0.475667`
Percentage	`47.5667%`

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Frequently Asked Questions

What is 3/13 plus 12/49 as a fraction?

3/13 + 12/49 in simplest fraction form is 303/637.

What is 3/13 plus 12/49 as a decimal?

3/13 + 12/49 converted to a decimal is 0.475667.

What is 3/13 plus 12/49 as a percentage?

3/13 + 12/49 expressed as a percentage is 47.5667%.

Does 3/13 plus 12/49 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.475667...) because the denominator contains prime factors other than 2 and 5.