What is 3/19 plus 3/4? (Answer: 69/76)

Exact Answer

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Problem: What is 3/19 plus 3/4?
Formula / Expression: 3/19 + 3/4
Final Answer: 69/76
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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 3/19 by 4, and multiply the numerator and denominator of 3/4 by 19 so both fractions share the common base 76.
Working: 3 × 4/19 × 4 = 12/76 and 3 × 19/4 × 19 = 57/76

Step 3: Add the Numerators
Now add the numerators (12 + 57 = 69) and keep the common denominator 76 unchanged.
Working: 12 + 57/76 = 69/76

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 76 is 1, confirming that 69/76 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/76

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 76 produces a repeating decimal (approximately 0.907895, or 90.7895%).
Working: 69 ÷ 76 = 0.907895 (90.7895%)

Key Values:
- Simplified Fraction: 69/76
- Mixed Number Form: 69/76
- Decimal Value: 0.907895
- Percentage: 90.7895%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-19-plus-3-4/
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3/19 + 3/4 = 69/76

Simplified Fraction

69/76

Mixed Number

Proper (69/76)

Decimal Value

0.907895

Percentage

90.7895%

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Step-by-Step Solution: 3/19 + 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 3/19 by 4, and multiply the numerator and denominator of 3/4 by 19 so both fractions share the common base 76.

3 × 4/19 × 4 = 12/76 and 3 × 19/4 × 19 = 57/76

Step 3

Add the Numerators

Now add the numerators (12 + 57 = 69) and keep the common denominator 76 unchanged.

12 + 57/76 = 69/76

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 76 is 1, confirming that 69/76 cannot be reduced further—it is already in its simplest irreducible form.

69/76

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 76 produces a repeating decimal (approximately 0.907895, or 90.7895%).

69 ÷ 76 = 0.907895 (90.7895%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/76`
Mixed Number Form	`69/76`
Decimal Form	`0.907895`
Percentage	`90.7895%`

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Frequently Asked Questions

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

3/19 + 3/4 in simplest fraction form is 69/76.

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

3/19 + 3/4 converted to a decimal is 0.907895.

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

3/19 + 3/4 expressed as a percentage is 90.7895%.

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

It results in a repeating decimal (approximately 0.907895...) because the denominator contains prime factors other than 2 and 5.