What is 6/52 plus 3/13? (Answer: 9/26)

Exact Answer

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Problem: What is 6/52 plus 3/13?
Formula / Expression: 6/52 + 3/13
Final Answer: 9/26
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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 6/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.
Working: 6 × 1/52 × 1 = 6/52 and 3 × 4/13 × 4 = 12/52

Step 3: Add the Numerators
Now add the numerators (6 + 12 = 18) and keep the common denominator 52 unchanged.
Working: 6 + 12/52 = 18/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 52, which is 2. Divide both the numerator and denominator by 2.
Working: 18 ÷ 2/52 ÷ 2 = 9/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 26 produces a repeating decimal (approximately 0.346154, or 34.6154%).
Working: 9 ÷ 26 = 0.346154 (34.6154%)

Key Values:
- Simplified Fraction: 9/26
- Mixed Number Form: 9/26
- Decimal Value: 0.346154
- Percentage: 34.6154%

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Solved with FractionsCalc:
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6/52 + 3/13 = 9/26

Simplified Fraction

9/26

Mixed Number

Proper (9/26)

Decimal Value

0.346154

Percentage

34.6154%

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Step-by-Step Solution: 6/52 + 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 6/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.

6 × 1/52 × 1 = 6/52 and 3 × 4/13 × 4 = 12/52

Step 3

Add the Numerators

Now add the numerators (6 + 12 = 18) and keep the common denominator 52 unchanged.

6 + 12/52 = 18/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 52, which is 2. Divide both the numerator and denominator by 2.

18 ÷ 2/52 ÷ 2 = 9/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 26 produces a repeating decimal (approximately 0.346154, or 34.6154%).

9 ÷ 26 = 0.346154 (34.6154%)

Visual Representation

The diagram below illustrates 6/52 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/26`
Mixed Number Form	`9/26`
Decimal Form	`0.346154`
Percentage	`34.6154%`

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Frequently Asked Questions

What is 6/52 plus 3/13 as a fraction?

6/52 + 3/13 in simplest fraction form is 9/26.

What is 6/52 plus 3/13 as a decimal?

6/52 + 3/13 converted to a decimal is 0.346154.

What is 6/52 plus 3/13 as a percentage?

6/52 + 3/13 expressed as a percentage is 34.6154%.

Does 6/52 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.346154...) because the denominator contains prime factors other than 2 and 5.