What is 4/19 plus 3/9? (Answer: 31/57)

Exact Answer

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Problem: What is 4/19 plus 3/9?
Formula / Expression: 4/19 + 3/9
Final Answer: 31/57
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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 4/19 by 9, and multiply the numerator and denominator of 3/9 by 19 so both fractions share the common base 171.
Working: 4 × 9/19 × 9 = 36/171 and 3 × 19/9 × 19 = 57/171

Step 3: Add the Numerators
Now add the numerators (36 + 57 = 93) and keep the common denominator 171 unchanged.
Working: 36 + 57/171 = 93/171

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 171, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/171 ÷ 3 = 31/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 57 produces a repeating decimal (approximately 0.54386, or 54.386%).
Working: 31 ÷ 57 = 0.54386 (54.386%)

Key Values:
- Simplified Fraction: 31/57
- Mixed Number Form: 31/57
- Decimal Value: 0.54386
- Percentage: 54.386%

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Solved with FractionsCalc:
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4/19 + 3/9 = 31/57

Simplified Fraction

31/57

Mixed Number

Proper (31/57)

Decimal Value

0.54386

Percentage

54.386%

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Step-by-Step Solution: 4/19 + 3/9

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 4/19 by 9, and multiply the numerator and denominator of 3/9 by 19 so both fractions share the common base 171.

4 × 9/19 × 9 = 36/171 and 3 × 19/9 × 19 = 57/171

Step 3

Add the Numerators

Now add the numerators (36 + 57 = 93) and keep the common denominator 171 unchanged.

36 + 57/171 = 93/171

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 171, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/171 ÷ 3 = 31/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 57 produces a repeating decimal (approximately 0.54386, or 54.386%).

31 ÷ 57 = 0.54386 (54.386%)

Visual Representation

The diagram below illustrates 4/19 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/57`
Mixed Number Form	`31/57`
Decimal Form	`0.54386`
Percentage	`54.386%`

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Frequently Asked Questions

What is 4/19 plus 3/9 as a fraction?

4/19 + 3/9 in simplest fraction form is 31/57.

What is 4/19 plus 3/9 as a decimal?

4/19 + 3/9 converted to a decimal is 0.54386.

What is 4/19 plus 3/9 as a percentage?

4/19 + 3/9 expressed as a percentage is 54.386%.

Does 4/19 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.54386...) because the denominator contains prime factors other than 2 and 5.