What is 1/9 plus 2/14? (Answer: 16/63)

Exact Answer

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Problem: What is 1/9 plus 2/14?
Formula / Expression: 1/9 + 2/14
Final Answer: 16/63
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 1/9 by 14, and multiply the numerator and denominator of 2/14 by 9 so both fractions share the common base 126.
Working: 1 × 14/9 × 14 = 14/126 and 2 × 9/14 × 9 = 18/126

Step 3: Add the Numerators
Now add the numerators (14 + 18 = 32) and keep the common denominator 126 unchanged.
Working: 14 + 18/126 = 32/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 32 ÷ 2/126 ÷ 2 = 16/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 63 produces a repeating decimal (approximately 0.253968, or 25.3968%).
Working: 16 ÷ 63 = 0.253968 (25.3968%)

Key Values:
- Simplified Fraction: 16/63
- Mixed Number Form: 16/63
- Decimal Value: 0.253968
- Percentage: 25.3968%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-2-14/
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1/9 + 2/14 = 16/63

Simplified Fraction

16/63

Mixed Number

Proper (16/63)

Decimal Value

0.253968

Percentage

25.3968%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 14) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

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

1 × 14/9 × 14 = 14/126 and 2 × 9/14 × 9 = 18/126

Step 3

Add the Numerators

Now add the numerators (14 + 18 = 32) and keep the common denominator 126 unchanged.

14 + 18/126 = 32/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 126, which is 2. Divide both the numerator and denominator by 2.

32 ÷ 2/126 ÷ 2 = 16/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 63 produces a repeating decimal (approximately 0.253968, or 25.3968%).

16 ÷ 63 = 0.253968 (25.3968%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/63`
Mixed Number Form	`16/63`
Decimal Form	`0.253968`
Percentage	`25.3968%`

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Frequently Asked Questions

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

1/9 + 2/14 in simplest fraction form is 16/63.

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

1/9 + 2/14 converted to a decimal is 0.253968.

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

1/9 + 2/14 expressed as a percentage is 25.3968%.

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

It results in a repeating decimal (approximately 0.253968...) because the denominator contains prime factors other than 2 and 5.