What is 3/52 plus 4/13? (Answer: 19/52)

Exact Answer

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Problem: What is 3/52 plus 4/13?
Formula / Expression: 3/52 + 4/13
Final Answer: 19/52
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.
Working: LCD(52, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 3/52 by 1, and multiply the numerator and denominator of 4/13 by 4 so both fractions share the common base 52.
Working: 3 × 1/52 × 1 = 3/52 and 4 × 4/13 × 4 = 16/52

Step 3: Add the Numerators
Now add the numerators (3 + 16 = 19) and keep the common denominator 52 unchanged.
Working: 3 + 16/52 = 19/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 52 is 1, confirming that 19/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 52 produces a repeating decimal (approximately 0.365385, or 36.5385%).
Working: 19 ÷ 52 = 0.365385 (36.5385%)

Key Values:
- Simplified Fraction: 19/52
- Mixed Number Form: 19/52
- Decimal Value: 0.365385
- Percentage: 36.5385%

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Solved with FractionsCalc:
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3/52 + 4/13 = 19/52

Simplified Fraction

19/52

Mixed Number

Proper (19/52)

Decimal Value

0.365385

Percentage

36.5385%

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Step-by-Step Solution: 3/52 + 4/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.

LCD(52, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 3/52 by 1, and multiply the numerator and denominator of 4/13 by 4 so both fractions share the common base 52.

3 × 1/52 × 1 = 3/52 and 4 × 4/13 × 4 = 16/52

Step 3

Add the Numerators

Now add the numerators (3 + 16 = 19) and keep the common denominator 52 unchanged.

3 + 16/52 = 19/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 52 is 1, confirming that 19/52 cannot be reduced further—it is already in its simplest irreducible form.

19/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 52 produces a repeating decimal (approximately 0.365385, or 36.5385%).

19 ÷ 52 = 0.365385 (36.5385%)

Visual Representation

The diagram below illustrates 3/52 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/52`
Mixed Number Form	`19/52`
Decimal Form	`0.365385`
Percentage	`36.5385%`

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Frequently Asked Questions

What is 3/52 plus 4/13 as a fraction?

3/52 + 4/13 in simplest fraction form is 19/52.

What is 3/52 plus 4/13 as a decimal?

3/52 + 4/13 converted to a decimal is 0.365385.

What is 3/52 plus 4/13 as a percentage?

3/52 + 4/13 expressed as a percentage is 36.5385%.

Does 3/52 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.365385...) because the denominator contains prime factors other than 2 and 5.