What is 3/52 plus 5/13? (Answer: 23/52)

Exact Answer

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Problem: What is 3/52 plus 5/13?
Formula / Expression: 3/52 + 5/13
Final Answer: 23/52
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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 5/13 by 4 so both fractions share the common base 52.
Working: 3 × 1/52 × 1 = 3/52 and 5 × 4/13 × 4 = 20/52

Step 3: Add the Numerators
Now add the numerators (3 + 20 = 23) and keep the common denominator 52 unchanged.
Working: 3 + 20/52 = 23/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 52 is 1, confirming that 23/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 52 produces a repeating decimal (approximately 0.442308, or 44.2308%).
Working: 23 ÷ 52 = 0.442308 (44.2308%)

Key Values:
- Simplified Fraction: 23/52
- Mixed Number Form: 23/52
- Decimal Value: 0.442308
- Percentage: 44.2308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-52-plus-5-13/
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3/52 + 5/13 = 23/52

Simplified Fraction

23/52

Mixed Number

Proper (23/52)

Decimal Value

0.442308

Percentage

44.2308%

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

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 5/13 by 4 so both fractions share the common base 52.

3 × 1/52 × 1 = 3/52 and 5 × 4/13 × 4 = 20/52

Step 3

Add the Numerators

Now add the numerators (3 + 20 = 23) and keep the common denominator 52 unchanged.

3 + 20/52 = 23/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 52 is 1, confirming that 23/52 cannot be reduced further—it is already in its simplest irreducible form.

23/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 52 produces a repeating decimal (approximately 0.442308, or 44.2308%).

23 ÷ 52 = 0.442308 (44.2308%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/52`
Mixed Number Form	`23/52`
Decimal Form	`0.442308`
Percentage	`44.2308%`

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Frequently Asked Questions

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

3/52 + 5/13 in simplest fraction form is 23/52.

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

3/52 + 5/13 converted to a decimal is 0.442308.

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

3/52 + 5/13 expressed as a percentage is 44.2308%.

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

It results in a repeating decimal (approximately 0.442308...) because the denominator contains prime factors other than 2 and 5.