What is 9/52 plus 9/13? (Answer: 45/52)

Exact Answer

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Problem: What is 9/52 plus 9/13?
Formula / Expression: 9/52 + 9/13
Final Answer: 45/52
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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 9/52 by 1, and multiply the numerator and denominator of 9/13 by 4 so both fractions share the common base 52.
Working: 9 × 1/52 × 1 = 9/52 and 9 × 4/13 × 4 = 36/52

Step 3: Add the Numerators
Now add the numerators (9 + 36 = 45) and keep the common denominator 52 unchanged.
Working: 9 + 36/52 = 45/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 45 and 52 is 1, confirming that 45/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 45/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 52 produces a repeating decimal (approximately 0.865385, or 86.5385%).
Working: 45 ÷ 52 = 0.865385 (86.5385%)

Key Values:
- Simplified Fraction: 45/52
- Mixed Number Form: 45/52
- Decimal Value: 0.865385
- Percentage: 86.5385%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-52-plus-9-13/
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9/52 + 9/13 = 45/52

Simplified Fraction

45/52

Mixed Number

Proper (45/52)

Decimal Value

0.865385

Percentage

86.5385%

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Step-by-Step Solution: 9/52 + 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 9/52 by 1, and multiply the numerator and denominator of 9/13 by 4 so both fractions share the common base 52.

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

Step 3

Add the Numerators

Now add the numerators (9 + 36 = 45) and keep the common denominator 52 unchanged.

9 + 36/52 = 45/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 45 and 52 is 1, confirming that 45/52 cannot be reduced further—it is already in its simplest irreducible form.

45/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 52 produces a repeating decimal (approximately 0.865385, or 86.5385%).

45 ÷ 52 = 0.865385 (86.5385%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/52`
Mixed Number Form	`45/52`
Decimal Form	`0.865385`
Percentage	`86.5385%`

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Frequently Asked Questions

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

9/52 + 9/13 in simplest fraction form is 45/52.

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

9/52 + 9/13 converted to a decimal is 0.865385.

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

9/52 + 9/13 expressed as a percentage is 86.5385%.

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

It results in a repeating decimal (approximately 0.865385...) because the denominator contains prime factors other than 2 and 5.