What is 4/13 plus 3/4? (Answer: 55/52)

Exact Answer

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Problem: What is 4/13 plus 3/4?
Formula / Expression: 4/13 + 3/4
Final Answer: 1 3/52 (55/52)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 4/13 by 4, and multiply the numerator and denominator of 3/4 by 13 so both fractions share the common base 52.
Working: 4 × 4/13 × 4 = 16/52 and 3 × 13/4 × 13 = 39/52

Step 3: Add the Numerators
Now add the numerators (16 + 39 = 55) and keep the common denominator 52 unchanged.
Working: 16 + 39/52 = 55/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 52 is 1, confirming that 55/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/52

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (55) is greater than the denominator (52), divide 55 by 52: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/52.
Working: 55/52 = 1 3/52

Step 6: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 52 produces a repeating decimal (approximately 1.057692, or 105.7692%).
Working: 55 ÷ 52 = 1.057692 (105.7692%)

Key Values:
- Simplified Fraction: 55/52
- Mixed Number Form: 1 3/52
- Decimal Value: 1.057692
- Percentage: 105.7692%

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Solved with FractionsCalc:
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4/13 + 3/4 = 55/52

Simplified Fraction

55/52

Mixed Number

1 3/52

Decimal Value

1.057692

Percentage

105.7692%

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Step-by-Step Solution: 4/13 + 3/4

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 4) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

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

4 × 4/13 × 4 = 16/52 and 3 × 13/4 × 13 = 39/52

Step 3

Add the Numerators

Now add the numerators (16 + 39 = 55) and keep the common denominator 52 unchanged.

16 + 39/52 = 55/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 52 is 1, confirming that 55/52 cannot be reduced further—it is already in its simplest irreducible form.

55/52

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (55) is greater than the denominator (52), divide 55 by 52: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/52.

55/52 = 13/52

Step 6

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 52 produces a repeating decimal (approximately 1.057692, or 105.7692%).

55 ÷ 52 = 1.057692 (105.7692%)

Visual Representation

The diagram below illustrates 4/13 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/52`
Mixed Number Form	`1 3/52`
Decimal Form	`1.057692`
Percentage	`105.7692%`

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Frequently Asked Questions

What is 4/13 plus 3/4 as a fraction?

4/13 + 3/4 in simplest fraction form is 55/52 (or 1 3/52 as a mixed number).

What is 4/13 plus 3/4 as a decimal?

4/13 + 3/4 converted to a decimal is 1.057692.

What is 4/13 plus 3/4 as a percentage?

4/13 + 3/4 expressed as a percentage is 105.7692%.

How do you write 4/13 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 55/52 can be written as the mixed number 1 3/52.

Does 4/13 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.057692...) because the denominator contains prime factors other than 2 and 5.