What is 3/9 plus 8/19? (Answer: 43/57)

Exact Answer

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Problem: What is 3/9 plus 8/19?
Formula / Expression: 3/9 + 8/19
Final Answer: 43/57
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 3/9 by 19, and multiply the numerator and denominator of 8/19 by 9 so both fractions share the common base 171.
Working: 3 × 19/9 × 19 = 57/171 and 8 × 9/19 × 9 = 72/171

Step 3: Add the Numerators
Now add the numerators (57 + 72 = 129) and keep the common denominator 171 unchanged.
Working: 57 + 72/171 = 129/171

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 171, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/171 ÷ 3 = 43/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 57 produces a repeating decimal (approximately 0.754386, or 75.4386%).
Working: 43 ÷ 57 = 0.754386 (75.4386%)

Key Values:
- Simplified Fraction: 43/57
- Mixed Number Form: 43/57
- Decimal Value: 0.754386
- Percentage: 75.4386%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-8-19/
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3/9 + 8/19 = 43/57

Simplified Fraction

43/57

Mixed Number

Proper (43/57)

Decimal Value

0.754386

Percentage

75.4386%

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Step-by-Step Solution: 3/9 + 8/19

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 19) = 171

Step 2

Convert to Equivalent Fractions with Common Denominator 171

Multiply the numerator and denominator of 3/9 by 19, and multiply the numerator and denominator of 8/19 by 9 so both fractions share the common base 171.

3 × 19/9 × 19 = 57/171 and 8 × 9/19 × 9 = 72/171

Step 3

Add the Numerators

Now add the numerators (57 + 72 = 129) and keep the common denominator 171 unchanged.

57 + 72/171 = 129/171

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 171, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/171 ÷ 3 = 43/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 57 produces a repeating decimal (approximately 0.754386, or 75.4386%).

43 ÷ 57 = 0.754386 (75.4386%)

Visual Representation

The diagram below illustrates 3/9 plus 8/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/57`
Mixed Number Form	`43/57`
Decimal Form	`0.754386`
Percentage	`75.4386%`

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Frequently Asked Questions

What is 3/9 plus 8/19 as a fraction?

3/9 + 8/19 in simplest fraction form is 43/57.

What is 3/9 plus 8/19 as a decimal?

3/9 + 8/19 converted to a decimal is 0.754386.

What is 3/9 plus 8/19 as a percentage?

3/9 + 8/19 expressed as a percentage is 75.4386%.

Does 3/9 plus 8/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.754386...) because the denominator contains prime factors other than 2 and 5.