What is 4/13 plus 10/31? (Answer: 254/403)

Exact Answer

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Problem: What is 4/13 plus 10/31?
Formula / Expression: 4/13 + 10/31
Final Answer: 254/403
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 31 = 403.
Working: LCD(13, 31) = 403

Step 2: Convert to Equivalent Fractions with Common Denominator 403
Multiply the numerator and denominator of 4/13 by 31, and multiply the numerator and denominator of 10/31 by 13 so both fractions share the common base 403.
Working: 4 × 31/13 × 31 = 124/403 and 10 × 13/31 × 13 = 130/403

Step 3: Add the Numerators
Now add the numerators (124 + 130 = 254) and keep the common denominator 403 unchanged.
Working: 124 + 130/403 = 254/403

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 254 and 403 is 1, confirming that 254/403 cannot be reduced further—it is already in its simplest irreducible form.
Working: 254/403

Step 5: Decimal & Percentage Representation
Dividing the numerator 254 by denominator 403 produces a repeating decimal (approximately 0.630273, or 63.0273%).
Working: 254 ÷ 403 = 0.630273 (63.0273%)

Key Values:
- Simplified Fraction: 254/403
- Mixed Number Form: 254/403
- Decimal Value: 0.630273
- Percentage: 63.0273%

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4/13 + 10/31 = 254/403

Simplified Fraction

254/403

Mixed Number

Proper (254/403)

Decimal Value

0.630273

Percentage

63.0273%

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Step-by-Step Solution: 4/13 + 10/31

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 31 = 403.

LCD(13, 31) = 403

Step 2

Convert to Equivalent Fractions with Common Denominator 403

Multiply the numerator and denominator of 4/13 by 31, and multiply the numerator and denominator of 10/31 by 13 so both fractions share the common base 403.

4 × 31/13 × 31 = 124/403 and 10 × 13/31 × 13 = 130/403

Step 3

Add the Numerators

Now add the numerators (124 + 130 = 254) and keep the common denominator 403 unchanged.

124 + 130/403 = 254/403

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 254 and 403 is 1, confirming that 254/403 cannot be reduced further—it is already in its simplest irreducible form.

254/403

Step 5

Decimal & Percentage Representation

Dividing the numerator 254 by denominator 403 produces a repeating decimal (approximately 0.630273, or 63.0273%).

254 ÷ 403 = 0.630273 (63.0273%)

Visual Representation

The diagram below illustrates 4/13 plus 10/31 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`254/403`
Mixed Number Form	`254/403`
Decimal Form	`0.630273`
Percentage	`63.0273%`

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Frequently Asked Questions

What is 4/13 plus 10/31 as a fraction?

4/13 + 10/31 in simplest fraction form is 254/403.

What is 4/13 plus 10/31 as a decimal?

4/13 + 10/31 converted to a decimal is 0.630273.

What is 4/13 plus 10/31 as a percentage?

4/13 + 10/31 expressed as a percentage is 63.0273%.

Does 4/13 plus 10/31 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.630273...) because the denominator contains prime factors other than 2 and 5.