What is 5/52 plus 7/13? (Answer: 33/52)

Exact Answer

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Problem: What is 5/52 plus 7/13?
Formula / Expression: 5/52 + 7/13
Final Answer: 33/52
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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 5/52 by 1, and multiply the numerator and denominator of 7/13 by 4 so both fractions share the common base 52.
Working: 5 × 1/52 × 1 = 5/52 and 7 × 4/13 × 4 = 28/52

Step 3: Add the Numerators
Now add the numerators (5 + 28 = 33) and keep the common denominator 52 unchanged.
Working: 5 + 28/52 = 33/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 33 and 52 is 1, confirming that 33/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 33/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 52 produces a repeating decimal (approximately 0.634615, or 63.4615%).
Working: 33 ÷ 52 = 0.634615 (63.4615%)

Key Values:
- Simplified Fraction: 33/52
- Mixed Number Form: 33/52
- Decimal Value: 0.634615
- Percentage: 63.4615%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-52-plus-7-13/
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5/52 + 7/13 = 33/52

Simplified Fraction

33/52

Mixed Number

Proper (33/52)

Decimal Value

0.634615

Percentage

63.4615%

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Step-by-Step Solution: 5/52 + 7/13

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 5/52 by 1, and multiply the numerator and denominator of 7/13 by 4 so both fractions share the common base 52.

5 × 1/52 × 1 = 5/52 and 7 × 4/13 × 4 = 28/52

Step 3

Add the Numerators

Now add the numerators (5 + 28 = 33) and keep the common denominator 52 unchanged.

5 + 28/52 = 33/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 33 and 52 is 1, confirming that 33/52 cannot be reduced further—it is already in its simplest irreducible form.

33/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 52 produces a repeating decimal (approximately 0.634615, or 63.4615%).

33 ÷ 52 = 0.634615 (63.4615%)

Visual Representation

The diagram below illustrates 5/52 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/52`
Mixed Number Form	`33/52`
Decimal Form	`0.634615`
Percentage	`63.4615%`

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Frequently Asked Questions

What is 5/52 plus 7/13 as a fraction?

5/52 + 7/13 in simplest fraction form is 33/52.

What is 5/52 plus 7/13 as a decimal?

5/52 + 7/13 converted to a decimal is 0.634615.

What is 5/52 plus 7/13 as a percentage?

5/52 + 7/13 expressed as a percentage is 63.4615%.

Does 5/52 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.634615...) because the denominator contains prime factors other than 2 and 5.