What is 3/14 plus 3/9? (Answer: 23/42)

Exact Answer

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Problem: What is 3/14 plus 3/9?
Formula / Expression: 3/14 + 3/9
Final Answer: 23/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 9 = 126.
Working: LCD(14, 9) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 3/14 by 9, and multiply the numerator and denominator of 3/9 by 14 so both fractions share the common base 126.
Working: 3 × 9/14 × 9 = 27/126 and 3 × 14/9 × 14 = 42/126

Step 3: Add the Numerators
Now add the numerators (27 + 42 = 69) and keep the common denominator 126 unchanged.
Working: 27 + 42/126 = 69/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 126, which is 3. Divide both the numerator and denominator by 3.
Working: 69 ÷ 3/126 ÷ 3 = 23/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 42 produces a repeating decimal (approximately 0.547619, or 54.7619%).
Working: 23 ÷ 42 = 0.547619 (54.7619%)

Key Values:
- Simplified Fraction: 23/42
- Mixed Number Form: 23/42
- Decimal Value: 0.547619
- Percentage: 54.7619%

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Solved with FractionsCalc:
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3/14 + 3/9 = 23/42

Simplified Fraction

23/42

Mixed Number

Proper (23/42)

Decimal Value

0.547619

Percentage

54.7619%

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Step-by-Step Solution: 3/14 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 9 = 126.

LCD(14, 9) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 3/14 by 9, and multiply the numerator and denominator of 3/9 by 14 so both fractions share the common base 126.

3 × 9/14 × 9 = 27/126 and 3 × 14/9 × 14 = 42/126

Step 3

Add the Numerators

Now add the numerators (27 + 42 = 69) and keep the common denominator 126 unchanged.

27 + 42/126 = 69/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 69 and 126, which is 3. Divide both the numerator and denominator by 3.

69 ÷ 3/126 ÷ 3 = 23/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 42 produces a repeating decimal (approximately 0.547619, or 54.7619%).

23 ÷ 42 = 0.547619 (54.7619%)

Visual Representation

The diagram below illustrates 3/14 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/42`
Mixed Number Form	`23/42`
Decimal Form	`0.547619`
Percentage	`54.7619%`

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Frequently Asked Questions

What is 3/14 plus 3/9 as a fraction?

3/14 + 3/9 in simplest fraction form is 23/42.

What is 3/14 plus 3/9 as a decimal?

3/14 + 3/9 converted to a decimal is 0.547619.

What is 3/14 plus 3/9 as a percentage?

3/14 + 3/9 expressed as a percentage is 54.7619%.

Does 3/14 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.547619...) because the denominator contains prime factors other than 2 and 5.