What is 1/4 plus 8/13? (Answer: 45/52)

Exact Answer

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Problem: What is 1/4 plus 8/13?
Formula / Expression: 1/4 + 8/13
Final Answer: 45/52
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.
Working: LCD(4, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 1/4 by 13, and multiply the numerator and denominator of 8/13 by 4 so both fractions share the common base 52.
Working: 1 × 13/4 × 13 = 13/52 and 8 × 4/13 × 4 = 32/52

Step 3: Add the Numerators
Now add the numerators (13 + 32 = 45) and keep the common denominator 52 unchanged.
Working: 13 + 32/52 = 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-1-4-plus-8-13/
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1/4 + 8/13 = 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: 1/4 + 8/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.

LCD(4, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 1/4 by 13, and multiply the numerator and denominator of 8/13 by 4 so both fractions share the common base 52.

1 × 13/4 × 13 = 13/52 and 8 × 4/13 × 4 = 32/52

Step 3

Add the Numerators

Now add the numerators (13 + 32 = 45) and keep the common denominator 52 unchanged.

13 + 32/52 = 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 1/4 plus 8/13 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 1/4 plus 8/13 as a fraction?

1/4 + 8/13 in simplest fraction form is 45/52.

What is 1/4 plus 8/13 as a decimal?

1/4 + 8/13 converted to a decimal is 0.865385.

What is 1/4 plus 8/13 as a percentage?

1/4 + 8/13 expressed as a percentage is 86.5385%.

Does 1/4 plus 8/13 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.