What is 3/9 plus 9/19? (Answer: 46/57)

Exact Answer

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Problem: What is 3/9 plus 9/19?
Formula / Expression: 3/9 + 9/19
Final Answer: 46/57
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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 9/19 by 9 so both fractions share the common base 171.
Working: 3 × 19/9 × 19 = 57/171 and 9 × 9/19 × 9 = 81/171

Step 3: Add the Numerators
Now add the numerators (57 + 81 = 138) and keep the common denominator 171 unchanged.
Working: 57 + 81/171 = 138/171

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 171, which is 3. Divide both the numerator and denominator by 3.
Working: 138 ÷ 3/171 ÷ 3 = 46/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 57 produces a repeating decimal (approximately 0.807018, or 80.7018%).
Working: 46 ÷ 57 = 0.807018 (80.7018%)

Key Values:
- Simplified Fraction: 46/57
- Mixed Number Form: 46/57
- Decimal Value: 0.807018
- Percentage: 80.7018%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-9-19/
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3/9 + 9/19 = 46/57

Simplified Fraction

46/57

Mixed Number

Proper (46/57)

Decimal Value

0.807018

Percentage

80.7018%

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

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 9/19 by 9 so both fractions share the common base 171.

3 × 19/9 × 19 = 57/171 and 9 × 9/19 × 9 = 81/171

Step 3

Add the Numerators

Now add the numerators (57 + 81 = 138) and keep the common denominator 171 unchanged.

57 + 81/171 = 138/171

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 171, which is 3. Divide both the numerator and denominator by 3.

138 ÷ 3/171 ÷ 3 = 46/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 57 produces a repeating decimal (approximately 0.807018, or 80.7018%).

46 ÷ 57 = 0.807018 (80.7018%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/57`
Mixed Number Form	`46/57`
Decimal Form	`0.807018`
Percentage	`80.7018%`

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Frequently Asked Questions

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

3/9 + 9/19 in simplest fraction form is 46/57.

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

3/9 + 9/19 converted to a decimal is 0.807018.

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

3/9 + 9/19 expressed as a percentage is 80.7018%.

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

It results in a repeating decimal (approximately 0.807018...) because the denominator contains prime factors other than 2 and 5.