What is 5/19 plus 3/4? (Answer: 77/76)

Exact Answer

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Problem: What is 5/19 plus 3/4?
Formula / Expression: 5/19 + 3/4
Final Answer: 1 1/76 (77/76)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 4 = 76.
Working: LCD(19, 4) = 76

Step 2: Convert to Equivalent Fractions with Common Denominator 76
Multiply the numerator and denominator of 5/19 by 4, and multiply the numerator and denominator of 3/4 by 19 so both fractions share the common base 76.
Working: 5 × 4/19 × 4 = 20/76 and 3 × 19/4 × 19 = 57/76

Step 3: Add the Numerators
Now add the numerators (20 + 57 = 77) and keep the common denominator 76 unchanged.
Working: 20 + 57/76 = 77/76

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 76 is 1, confirming that 77/76 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/76

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (77) is greater than the denominator (76), divide 77 by 76: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/76.
Working: 77/76 = 1 1/76

Step 6: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 76 produces a repeating decimal (approximately 1.013158, or 101.3158%).
Working: 77 ÷ 76 = 1.013158 (101.3158%)

Key Values:
- Simplified Fraction: 77/76
- Mixed Number Form: 1 1/76
- Decimal Value: 1.013158
- Percentage: 101.3158%

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Solved with FractionsCalc:
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5/19 + 3/4 = 77/76

Simplified Fraction

77/76

Mixed Number

1 1/76

Decimal Value

1.013158

Percentage

101.3158%

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Step-by-Step Solution: 5/19 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 4 = 76.

LCD(19, 4) = 76

Step 2

Convert to Equivalent Fractions with Common Denominator 76

Multiply the numerator and denominator of 5/19 by 4, and multiply the numerator and denominator of 3/4 by 19 so both fractions share the common base 76.

5 × 4/19 × 4 = 20/76 and 3 × 19/4 × 19 = 57/76

Step 3

Add the Numerators

Now add the numerators (20 + 57 = 77) and keep the common denominator 76 unchanged.

20 + 57/76 = 77/76

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 76 is 1, confirming that 77/76 cannot be reduced further—it is already in its simplest irreducible form.

77/76

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (77) is greater than the denominator (76), divide 77 by 76: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/76.

77/76 = 11/76

Step 6

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 76 produces a repeating decimal (approximately 1.013158, or 101.3158%).

77 ÷ 76 = 1.013158 (101.3158%)

Visual Representation

The diagram below illustrates 5/19 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/76`
Mixed Number Form	`1 1/76`
Decimal Form	`1.013158`
Percentage	`101.3158%`

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Frequently Asked Questions

What is 5/19 plus 3/4 as a fraction?

5/19 + 3/4 in simplest fraction form is 77/76 (or 1 1/76 as a mixed number).

What is 5/19 plus 3/4 as a decimal?

5/19 + 3/4 converted to a decimal is 1.013158.

What is 5/19 plus 3/4 as a percentage?

5/19 + 3/4 expressed as a percentage is 101.3158%.

How do you write 5/19 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 77/76 can be written as the mixed number 1 1/76.

Does 5/19 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.013158...) because the denominator contains prime factors other than 2 and 5.