What is 5/52 plus 3/13? (Answer: 17/52)

Exact Answer

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Problem: What is 5/52 plus 3/13?
Formula / Expression: 5/52 + 3/13
Final Answer: 17/52
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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 5/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.
Working: 5 × 1/52 × 1 = 5/52 and 3 × 4/13 × 4 = 12/52

Step 3: Add the Numerators
Now add the numerators (5 + 12 = 17) and keep the common denominator 52 unchanged.
Working: 5 + 12/52 = 17/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 52 is 1, confirming that 17/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 52 produces a repeating decimal (approximately 0.326923, or 32.6923%).
Working: 17 ÷ 52 = 0.326923 (32.6923%)

Key Values:
- Simplified Fraction: 17/52
- Mixed Number Form: 17/52
- Decimal Value: 0.326923
- Percentage: 32.6923%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-52-plus-3-13/
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5/52 + 3/13 = 17/52

Simplified Fraction

17/52

Mixed Number

Proper (17/52)

Decimal Value

0.326923

Percentage

32.6923%

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Step-by-Step Solution: 5/52 + 3/13

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 5/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.

5 × 1/52 × 1 = 5/52 and 3 × 4/13 × 4 = 12/52

Step 3

Add the Numerators

Now add the numerators (5 + 12 = 17) and keep the common denominator 52 unchanged.

5 + 12/52 = 17/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 52 is 1, confirming that 17/52 cannot be reduced further—it is already in its simplest irreducible form.

17/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 52 produces a repeating decimal (approximately 0.326923, or 32.6923%).

17 ÷ 52 = 0.326923 (32.6923%)

Visual Representation

The diagram below illustrates 5/52 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/52`
Mixed Number Form	`17/52`
Decimal Form	`0.326923`
Percentage	`32.6923%`

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Frequently Asked Questions

What is 5/52 plus 3/13 as a fraction?

5/52 + 3/13 in simplest fraction form is 17/52.

What is 5/52 plus 3/13 as a decimal?

5/52 + 3/13 converted to a decimal is 0.326923.

What is 5/52 plus 3/13 as a percentage?

5/52 + 3/13 expressed as a percentage is 32.6923%.

Does 5/52 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.326923...) because the denominator contains prime factors other than 2 and 5.