What is 5/19 plus 4/9? (Answer: 121/171)

Exact Answer

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Problem: What is 5/19 plus 4/9?
Formula / Expression: 5/19 + 4/9
Final Answer: 121/171
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 9 = 171.
Working: LCD(19, 9) = 171

Step 2: Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 5/19 by 9, and multiply the numerator and denominator of 4/9 by 19 so both fractions share the common base 171.
Working: 5 × 9/19 × 9 = 45/171 and 4 × 19/9 × 19 = 76/171

Step 3: Add the Numerators
Now add the numerators (45 + 76 = 121) and keep the common denominator 171 unchanged.
Working: 45 + 76/171 = 121/171

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 121 and 171 is 1, confirming that 121/171 cannot be reduced further—it is already in its simplest irreducible form.
Working: 121/171

Step 5: Decimal & Percentage Representation
Dividing the numerator 121 by denominator 171 produces a repeating decimal (approximately 0.707602, or 70.7602%).
Working: 121 ÷ 171 = 0.707602 (70.7602%)

Key Values:
- Simplified Fraction: 121/171
- Mixed Number Form: 121/171
- Decimal Value: 0.707602
- Percentage: 70.7602%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-19-plus-4-9/
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5/19 + 4/9 = 121/171

Simplified Fraction

121/171

Mixed Number

Proper (121/171)

Decimal Value

0.707602

Percentage

70.7602%

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Step-by-Step Solution: 5/19 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 9 = 171.

LCD(19, 9) = 171

Step 2

Convert to Equivalent Fractions with Common Denominator 171

Multiply the numerator and denominator of 5/19 by 9, and multiply the numerator and denominator of 4/9 by 19 so both fractions share the common base 171.

5 × 9/19 × 9 = 45/171 and 4 × 19/9 × 19 = 76/171

Step 3

Add the Numerators

Now add the numerators (45 + 76 = 121) and keep the common denominator 171 unchanged.

45 + 76/171 = 121/171

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 121 and 171 is 1, confirming that 121/171 cannot be reduced further—it is already in its simplest irreducible form.

121/171

Step 5

Decimal & Percentage Representation

Dividing the numerator 121 by denominator 171 produces a repeating decimal (approximately 0.707602, or 70.7602%).

121 ÷ 171 = 0.707602 (70.7602%)

Visual Representation

The diagram below illustrates 5/19 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`121/171`
Mixed Number Form	`121/171`
Decimal Form	`0.707602`
Percentage	`70.7602%`

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Frequently Asked Questions

What is 5/19 plus 4/9 as a fraction?

5/19 + 4/9 in simplest fraction form is 121/171.

What is 5/19 plus 4/9 as a decimal?

5/19 + 4/9 converted to a decimal is 0.707602.

What is 5/19 plus 4/9 as a percentage?

5/19 + 4/9 expressed as a percentage is 70.7602%.

Does 5/19 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.707602...) because the denominator contains prime factors other than 2 and 5.