What is 1/14 plus 2/9? (Answer: 37/126)

Exact Answer

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Problem: What is 1/14 plus 2/9?
Formula / Expression: 1/14 + 2/9
Final Answer: 37/126
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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 1/14 by 9, and multiply the numerator and denominator of 2/9 by 14 so both fractions share the common base 126.
Working: 1 × 9/14 × 9 = 9/126 and 2 × 14/9 × 14 = 28/126

Step 3: Add the Numerators
Now add the numerators (9 + 28 = 37) and keep the common denominator 126 unchanged.
Working: 9 + 28/126 = 37/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 126 is 1, confirming that 37/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 126 produces a repeating decimal (approximately 0.293651, or 29.3651%).
Working: 37 ÷ 126 = 0.293651 (29.3651%)

Key Values:
- Simplified Fraction: 37/126
- Mixed Number Form: 37/126
- Decimal Value: 0.293651
- Percentage: 29.3651%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-14-plus-2-9/
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1/14 + 2/9 = 37/126

Simplified Fraction

37/126

Mixed Number

Proper (37/126)

Decimal Value

0.293651

Percentage

29.3651%

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Step-by-Step Solution: 1/14 + 2/9

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 1/14 by 9, and multiply the numerator and denominator of 2/9 by 14 so both fractions share the common base 126.

1 × 9/14 × 9 = 9/126 and 2 × 14/9 × 14 = 28/126

Step 3

Add the Numerators

Now add the numerators (9 + 28 = 37) and keep the common denominator 126 unchanged.

9 + 28/126 = 37/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 126 is 1, confirming that 37/126 cannot be reduced further—it is already in its simplest irreducible form.

37/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 126 produces a repeating decimal (approximately 0.293651, or 29.3651%).

37 ÷ 126 = 0.293651 (29.3651%)

Visual Representation

The diagram below illustrates 1/14 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/126`
Mixed Number Form	`37/126`
Decimal Form	`0.293651`
Percentage	`29.3651%`

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Frequently Asked Questions

What is 1/14 plus 2/9 as a fraction?

1/14 + 2/9 in simplest fraction form is 37/126.

What is 1/14 plus 2/9 as a decimal?

1/14 + 2/9 converted to a decimal is 0.293651.

What is 1/14 plus 2/9 as a percentage?

1/14 + 2/9 expressed as a percentage is 29.3651%.

Does 1/14 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.293651...) because the denominator contains prime factors other than 2 and 5.