What is 3/40 plus 4/13? (Answer: 199/520)

Exact Answer

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Problem: What is 3/40 plus 4/13?
Formula / Expression: 3/40 + 4/13
Final Answer: 199/520
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 3/40 by 13, and multiply the numerator and denominator of 4/13 by 40 so both fractions share the common base 520.
Working: 3 × 13/40 × 13 = 39/520 and 4 × 40/13 × 40 = 160/520

Step 3: Add the Numerators
Now add the numerators (39 + 160 = 199) and keep the common denominator 520 unchanged.
Working: 39 + 160/520 = 199/520

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 199 and 520 is 1, confirming that 199/520 cannot be reduced further—it is already in its simplest irreducible form.
Working: 199/520

Step 5: Decimal & Percentage Representation
Dividing the numerator 199 by denominator 520 produces a repeating decimal (approximately 0.382692, or 38.2692%).
Working: 199 ÷ 520 = 0.382692 (38.2692%)

Key Values:
- Simplified Fraction: 199/520
- Mixed Number Form: 199/520
- Decimal Value: 0.382692
- Percentage: 38.2692%

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3/40 + 4/13 = 199/520

Simplified Fraction

199/520

Mixed Number

Proper (199/520)

Decimal Value

0.382692

Percentage

38.2692%

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Step-by-Step Solution: 3/40 + 4/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.

LCD(40, 13) = 520

Step 2

Convert to Equivalent Fractions with Common Denominator 520

Multiply the numerator and denominator of 3/40 by 13, and multiply the numerator and denominator of 4/13 by 40 so both fractions share the common base 520.

3 × 13/40 × 13 = 39/520 and 4 × 40/13 × 40 = 160/520

Step 3

Add the Numerators

Now add the numerators (39 + 160 = 199) and keep the common denominator 520 unchanged.

39 + 160/520 = 199/520

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 199 and 520 is 1, confirming that 199/520 cannot be reduced further—it is already in its simplest irreducible form.

199/520

Step 5

Decimal & Percentage Representation

Dividing the numerator 199 by denominator 520 produces a repeating decimal (approximately 0.382692, or 38.2692%).

199 ÷ 520 = 0.382692 (38.2692%)

Visual Representation

The diagram below illustrates 3/40 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`199/520`
Mixed Number Form	`199/520`
Decimal Form	`0.382692`
Percentage	`38.2692%`

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Frequently Asked Questions

What is 3/40 plus 4/13 as a fraction?

3/40 + 4/13 in simplest fraction form is 199/520.

What is 3/40 plus 4/13 as a decimal?

3/40 + 4/13 converted to a decimal is 0.382692.

What is 3/40 plus 4/13 as a percentage?

3/40 + 4/13 expressed as a percentage is 38.2692%.

Does 3/40 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.382692...) because the denominator contains prime factors other than 2 and 5.