What is 1/52 plus 3/13? (Answer: 1/4)

Exact Answer

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Problem: What is 1/52 plus 3/13?
Formula / Expression: 1/52 + 3/13
Final Answer: 1/4
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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 1/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.
Working: 1 × 1/52 × 1 = 1/52 and 3 × 4/13 × 4 = 12/52

Step 3: Add the Numerators
Now add the numerators (1 + 12 = 13) and keep the common denominator 52 unchanged.
Working: 1 + 12/52 = 13/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 13 and 52, which is 13. Divide both the numerator and denominator by 13.
Working: 13 ÷ 13/52 ÷ 13 = 1/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 4 yields an exact terminating decimal of 0.25 (or 25%).
Working: 1 ÷ 4 = 0.25 (25%)

Key Values:
- Simplified Fraction: 1/4
- Mixed Number Form: 1/4
- Decimal Value: 0.25
- Percentage: 25%

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Solved with FractionsCalc:
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1/52 + 3/13 = 1/4

Simplified Fraction

1/4

Mixed Number

Proper (1/4)

Decimal Value

0.25

Percentage

25%

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Step-by-Step Solution: 1/52 + 3/13

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 1/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.

1 × 1/52 × 1 = 1/52 and 3 × 4/13 × 4 = 12/52

Step 3

Add the Numerators

Now add the numerators (1 + 12 = 13) and keep the common denominator 52 unchanged.

1 + 12/52 = 13/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 13 and 52, which is 13. Divide both the numerator and denominator by 13.

13 ÷ 13/52 ÷ 13 = 1/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 4 yields an exact terminating decimal of 0.25 (or 25%).

1 ÷ 4 = 0.25 (25%)

Visual Representation

The diagram below illustrates 1/52 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/4`
Mixed Number Form	`1/4`
Decimal Form	`0.25`
Percentage	`25%`

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Frequently Asked Questions

What is 1/52 plus 3/13 as a fraction?

1/52 + 3/13 in simplest fraction form is 1/4.

What is 1/52 plus 3/13 as a decimal?

1/52 + 3/13 converted to a decimal is 0.25.

What is 1/52 plus 3/13 as a percentage?

1/52 + 3/13 expressed as a percentage is 25%.

Does 1/52 plus 3/13 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.25) because the denominator in simplest terms contains only prime factors 2 and/or 5.