What is 1/4 plus 9/19? (Answer: 55/76)

Exact Answer

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Problem: What is 1/4 plus 9/19?
Formula / Expression: 1/4 + 9/19
Final Answer: 55/76
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 76
Multiply the numerator and denominator of 1/4 by 19, and multiply the numerator and denominator of 9/19 by 4 so both fractions share the common base 76.
Working: 1 × 19/4 × 19 = 19/76 and 9 × 4/19 × 4 = 36/76

Step 3: Add the Numerators
Now add the numerators (19 + 36 = 55) and keep the common denominator 76 unchanged.
Working: 19 + 36/76 = 55/76

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 76 is 1, confirming that 55/76 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/76

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 76 produces a repeating decimal (approximately 0.723684, or 72.3684%).
Working: 55 ÷ 76 = 0.723684 (72.3684%)

Key Values:
- Simplified Fraction: 55/76
- Mixed Number Form: 55/76
- Decimal Value: 0.723684
- Percentage: 72.3684%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-9-19/
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1/4 + 9/19 = 55/76

Simplified Fraction

55/76

Mixed Number

Proper (55/76)

Decimal Value

0.723684

Percentage

72.3684%

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Step-by-Step Solution: 1/4 + 9/19

Step 1

Find the Least Common Denominator (LCD)

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

LCD(4, 19) = 76

Step 2

Convert to Equivalent Fractions with Common Denominator 76

Multiply the numerator and denominator of 1/4 by 19, and multiply the numerator and denominator of 9/19 by 4 so both fractions share the common base 76.

1 × 19/4 × 19 = 19/76 and 9 × 4/19 × 4 = 36/76

Step 3

Add the Numerators

Now add the numerators (19 + 36 = 55) and keep the common denominator 76 unchanged.

19 + 36/76 = 55/76

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 76 is 1, confirming that 55/76 cannot be reduced further—it is already in its simplest irreducible form.

55/76

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 76 produces a repeating decimal (approximately 0.723684, or 72.3684%).

55 ÷ 76 = 0.723684 (72.3684%)

Visual Representation

The diagram below illustrates 1/4 plus 9/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/76`
Mixed Number Form	`55/76`
Decimal Form	`0.723684`
Percentage	`72.3684%`

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Frequently Asked Questions

What is 1/4 plus 9/19 as a fraction?

1/4 + 9/19 in simplest fraction form is 55/76.

What is 1/4 plus 9/19 as a decimal?

1/4 + 9/19 converted to a decimal is 0.723684.

What is 1/4 plus 9/19 as a percentage?

1/4 + 9/19 expressed as a percentage is 72.3684%.

Does 1/4 plus 9/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.723684...) because the denominator contains prime factors other than 2 and 5.