What is 8/52 plus 4/13? (Answer: 6/13)

Exact Answer

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Problem: What is 8/52 plus 4/13?
Formula / Expression: 8/52 + 4/13
Final Answer: 6/13
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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 8/52 by 1, and multiply the numerator and denominator of 4/13 by 4 so both fractions share the common base 52.
Working: 8 × 1/52 × 1 = 8/52 and 4 × 4/13 × 4 = 16/52

Step 3: Add the Numerators
Now add the numerators (8 + 16 = 24) and keep the common denominator 52 unchanged.
Working: 8 + 16/52 = 24/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 52, which is 4. Divide both the numerator and denominator by 4.
Working: 24 ÷ 4/52 ÷ 4 = 6/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 13 produces a repeating decimal (approximately 0.461538, or 46.1538%).
Working: 6 ÷ 13 = 0.461538 (46.1538%)

Key Values:
- Simplified Fraction: 6/13
- Mixed Number Form: 6/13
- Decimal Value: 0.461538
- Percentage: 46.1538%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-52-plus-4-13/
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8/52 + 4/13 = 6/13

Simplified Fraction

6/13

Mixed Number

Proper (6/13)

Decimal Value

0.461538

Percentage

46.1538%

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Step-by-Step Solution: 8/52 + 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 8/52 by 1, and multiply the numerator and denominator of 4/13 by 4 so both fractions share the common base 52.

8 × 1/52 × 1 = 8/52 and 4 × 4/13 × 4 = 16/52

Step 3

Add the Numerators

Now add the numerators (8 + 16 = 24) and keep the common denominator 52 unchanged.

8 + 16/52 = 24/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 52, which is 4. Divide both the numerator and denominator by 4.

24 ÷ 4/52 ÷ 4 = 6/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 13 produces a repeating decimal (approximately 0.461538, or 46.1538%).

6 ÷ 13 = 0.461538 (46.1538%)

Visual Representation

The diagram below illustrates 8/52 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/13`
Mixed Number Form	`6/13`
Decimal Form	`0.461538`
Percentage	`46.1538%`

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Frequently Asked Questions

What is 8/52 plus 4/13 as a fraction?

8/52 + 4/13 in simplest fraction form is 6/13.

What is 8/52 plus 4/13 as a decimal?

8/52 + 4/13 converted to a decimal is 0.461538.

What is 8/52 plus 4/13 as a percentage?

8/52 + 4/13 expressed as a percentage is 46.1538%.

Does 8/52 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.461538...) because the denominator contains prime factors other than 2 and 5.