What is 2/9 plus 4/14? (Answer: 32/63)

Exact Answer

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Problem: What is 2/9 plus 4/14?
Formula / Expression: 2/9 + 4/14
Final Answer: 32/63
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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 2/9 by 14, and multiply the numerator and denominator of 4/14 by 9 so both fractions share the common base 126.
Working: 2 × 14/9 × 14 = 28/126 and 4 × 9/14 × 9 = 36/126

Step 3: Add the Numerators
Now add the numerators (28 + 36 = 64) and keep the common denominator 126 unchanged.
Working: 28 + 36/126 = 64/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 64 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 64 ÷ 2/126 ÷ 2 = 32/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 63 produces a repeating decimal (approximately 0.507937, or 50.7937%).
Working: 32 ÷ 63 = 0.507937 (50.7937%)

Key Values:
- Simplified Fraction: 32/63
- Mixed Number Form: 32/63
- Decimal Value: 0.507937
- Percentage: 50.7937%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-4-14/
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2/9 + 4/14 = 32/63

Simplified Fraction

32/63

Mixed Number

Proper (32/63)

Decimal Value

0.507937

Percentage

50.7937%

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Step-by-Step Solution: 2/9 + 4/14

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 2/9 by 14, and multiply the numerator and denominator of 4/14 by 9 so both fractions share the common base 126.

2 × 14/9 × 14 = 28/126 and 4 × 9/14 × 9 = 36/126

Step 3

Add the Numerators

Now add the numerators (28 + 36 = 64) and keep the common denominator 126 unchanged.

28 + 36/126 = 64/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 64 and 126, which is 2. Divide both the numerator and denominator by 2.

64 ÷ 2/126 ÷ 2 = 32/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 63 produces a repeating decimal (approximately 0.507937, or 50.7937%).

32 ÷ 63 = 0.507937 (50.7937%)

Visual Representation

The diagram below illustrates 2/9 plus 4/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/63`
Mixed Number Form	`32/63`
Decimal Form	`0.507937`
Percentage	`50.7937%`

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Frequently Asked Questions

What is 2/9 plus 4/14 as a fraction?

2/9 + 4/14 in simplest fraction form is 32/63.

What is 2/9 plus 4/14 as a decimal?

2/9 + 4/14 converted to a decimal is 0.507937.

What is 2/9 plus 4/14 as a percentage?

2/9 + 4/14 expressed as a percentage is 50.7937%.

Does 2/9 plus 4/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.507937...) because the denominator contains prime factors other than 2 and 5.