What is 8/52 plus 5/13? (Answer: 7/13)

Exact Answer

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Problem: What is 8/52 plus 5/13?
Formula / Expression: 8/52 + 5/13
Final Answer: 7/13
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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 5/13 by 4 so both fractions share the common base 52.
Working: 8 × 1/52 × 1 = 8/52 and 5 × 4/13 × 4 = 20/52

Step 3: Add the Numerators
Now add the numerators (8 + 20 = 28) and keep the common denominator 52 unchanged.
Working: 8 + 20/52 = 28/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 52, which is 4. Divide both the numerator and denominator by 4.
Working: 28 ÷ 4/52 ÷ 4 = 7/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 13 produces a repeating decimal (approximately 0.538462, or 53.8462%).
Working: 7 ÷ 13 = 0.538462 (53.8462%)

Key Values:
- Simplified Fraction: 7/13
- Mixed Number Form: 7/13
- Decimal Value: 0.538462
- Percentage: 53.8462%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-52-plus-5-13/
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8/52 + 5/13 = 7/13

Simplified Fraction

7/13

Mixed Number

Proper (7/13)

Decimal Value

0.538462

Percentage

53.8462%

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Step-by-Step Solution: 8/52 + 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 8/52 by 1, and multiply the numerator and denominator of 5/13 by 4 so both fractions share the common base 52.

8 × 1/52 × 1 = 8/52 and 5 × 4/13 × 4 = 20/52

Step 3

Add the Numerators

Now add the numerators (8 + 20 = 28) and keep the common denominator 52 unchanged.

8 + 20/52 = 28/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 52, which is 4. Divide both the numerator and denominator by 4.

28 ÷ 4/52 ÷ 4 = 7/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 13 produces a repeating decimal (approximately 0.538462, or 53.8462%).

7 ÷ 13 = 0.538462 (53.8462%)

Visual Representation

The diagram below illustrates 8/52 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/13`
Mixed Number Form	`7/13`
Decimal Form	`0.538462`
Percentage	`53.8462%`

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Frequently Asked Questions

What is 8/52 plus 5/13 as a fraction?

8/52 + 5/13 in simplest fraction form is 7/13.

What is 8/52 plus 5/13 as a decimal?

8/52 + 5/13 converted to a decimal is 0.538462.

What is 8/52 plus 5/13 as a percentage?

8/52 + 5/13 expressed as a percentage is 53.8462%.

Does 8/52 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.538462...) because the denominator contains prime factors other than 2 and 5.