What is 1/4 plus 9/13? (Answer: 49/52)

Exact Answer

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Problem: What is 1/4 plus 9/13?
Formula / Expression: 1/4 + 9/13
Final Answer: 49/52
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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 9/13 by 4 so both fractions share the common base 52.
Working: 1 × 13/4 × 13 = 13/52 and 9 × 4/13 × 4 = 36/52

Step 3: Add the Numerators
Now add the numerators (13 + 36 = 49) and keep the common denominator 52 unchanged.
Working: 13 + 36/52 = 49/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 52 is 1, confirming that 49/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 52 produces a repeating decimal (approximately 0.942308, or 94.2308%).
Working: 49 ÷ 52 = 0.942308 (94.2308%)

Key Values:
- Simplified Fraction: 49/52
- Mixed Number Form: 49/52
- Decimal Value: 0.942308
- Percentage: 94.2308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-9-13/
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1/4 + 9/13 = 49/52

Simplified Fraction

49/52

Mixed Number

Proper (49/52)

Decimal Value

0.942308

Percentage

94.2308%

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Step-by-Step Solution: 1/4 + 9/13

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

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

Step 3

Add the Numerators

Now add the numerators (13 + 36 = 49) and keep the common denominator 52 unchanged.

13 + 36/52 = 49/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 52 is 1, confirming that 49/52 cannot be reduced further—it is already in its simplest irreducible form.

49/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 52 produces a repeating decimal (approximately 0.942308, or 94.2308%).

49 ÷ 52 = 0.942308 (94.2308%)

Visual Representation

The diagram below illustrates 1/4 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/52`
Mixed Number Form	`49/52`
Decimal Form	`0.942308`
Percentage	`94.2308%`

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Frequently Asked Questions

What is 1/4 plus 9/13 as a fraction?

1/4 + 9/13 in simplest fraction form is 49/52.

What is 1/4 plus 9/13 as a decimal?

1/4 + 9/13 converted to a decimal is 0.942308.

What is 1/4 plus 9/13 as a percentage?

1/4 + 9/13 expressed as a percentage is 94.2308%.

Does 1/4 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.942308...) because the denominator contains prime factors other than 2 and 5.