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

Exact Answer

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

Step 3: Add the Numerators
Now add the numerators (4 + 12 = 16) and keep the common denominator 52 unchanged.
Working: 4 + 12/52 = 16/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 16 and 52, which is 4. Divide both the numerator and denominator by 4.
Working: 16 ÷ 4/52 ÷ 4 = 4/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 13 produces a repeating decimal (approximately 0.307692, or 30.7692%).
Working: 4 ÷ 13 = 0.307692 (30.7692%)

Key Values:
- Simplified Fraction: 4/13
- Mixed Number Form: 4/13
- Decimal Value: 0.307692
- Percentage: 30.7692%

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

Simplified Fraction

4/13

Mixed Number

Proper (4/13)

Decimal Value

0.307692

Percentage

30.7692%

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Step-by-Step Solution: 4/52 + 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 4/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.

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

Step 3

Add the Numerators

Now add the numerators (4 + 12 = 16) and keep the common denominator 52 unchanged.

4 + 12/52 = 16/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 16 and 52, which is 4. Divide both the numerator and denominator by 4.

16 ÷ 4/52 ÷ 4 = 4/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 13 produces a repeating decimal (approximately 0.307692, or 30.7692%).

4 ÷ 13 = 0.307692 (30.7692%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/13`
Mixed Number Form	`4/13`
Decimal Form	`0.307692`
Percentage	`30.7692%`

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Frequently Asked Questions

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

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

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

4/52 + 3/13 converted to a decimal is 0.307692.

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

4/52 + 3/13 expressed as a percentage is 30.7692%.

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

It results in a repeating decimal (approximately 0.307692...) because the denominator contains prime factors other than 2 and 5.