What is 8/52 plus 9/13? (Answer: 11/13)

Exact Answer

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Problem: What is 8/52 plus 9/13?
Formula / Expression: 8/52 + 9/13
Final Answer: 11/13
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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 9/13 by 4 so both fractions share the common base 52.
Working: 8 × 1/52 × 1 = 8/52 and 9 × 4/13 × 4 = 36/52

Step 3: Add the Numerators
Now add the numerators (8 + 36 = 44) and keep the common denominator 52 unchanged.
Working: 8 + 36/52 = 44/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 44 and 52, which is 4. Divide both the numerator and denominator by 4.
Working: 44 ÷ 4/52 ÷ 4 = 11/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 13 produces a repeating decimal (approximately 0.846154, or 84.6154%).
Working: 11 ÷ 13 = 0.846154 (84.6154%)

Key Values:
- Simplified Fraction: 11/13
- Mixed Number Form: 11/13
- Decimal Value: 0.846154
- Percentage: 84.6154%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-52-plus-9-13/
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8/52 + 9/13 = 11/13

Simplified Fraction

11/13

Mixed Number

Proper (11/13)

Decimal Value

0.846154

Percentage

84.6154%

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Step-by-Step Solution: 8/52 + 9/13

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 9/13 by 4 so both fractions share the common base 52.

8 × 1/52 × 1 = 8/52 and 9 × 4/13 × 4 = 36/52

Step 3

Add the Numerators

Now add the numerators (8 + 36 = 44) and keep the common denominator 52 unchanged.

8 + 36/52 = 44/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 44 and 52, which is 4. Divide both the numerator and denominator by 4.

44 ÷ 4/52 ÷ 4 = 11/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 13 produces a repeating decimal (approximately 0.846154, or 84.6154%).

11 ÷ 13 = 0.846154 (84.6154%)

Visual Representation

The diagram below illustrates 8/52 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/13`
Mixed Number Form	`11/13`
Decimal Form	`0.846154`
Percentage	`84.6154%`

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Frequently Asked Questions

What is 8/52 plus 9/13 as a fraction?

8/52 + 9/13 in simplest fraction form is 11/13.

What is 8/52 plus 9/13 as a decimal?

8/52 + 9/13 converted to a decimal is 0.846154.

What is 8/52 plus 9/13 as a percentage?

8/52 + 9/13 expressed as a percentage is 84.6154%.

Does 8/52 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.846154...) because the denominator contains prime factors other than 2 and 5.