What is 1/14 plus 2/3? (Answer: 31/42)

Exact Answer

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Problem: What is 1/14 plus 2/3?
Formula / Expression: 1/14 + 2/3
Final Answer: 31/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 3 = 42.
Working: LCD(14, 3) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 1/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.
Working: 1 × 3/14 × 3 = 3/42 and 2 × 14/3 × 14 = 28/42

Step 3: Add the Numerators
Now add the numerators (3 + 28 = 31) and keep the common denominator 42 unchanged.
Working: 3 + 28/42 = 31/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 42 is 1, confirming that 31/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).
Working: 31 ÷ 42 = 0.738095 (73.8095%)

Key Values:
- Simplified Fraction: 31/42
- Mixed Number Form: 31/42
- Decimal Value: 0.738095
- Percentage: 73.8095%

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1/14 + 2/3 = 31/42

Simplified Fraction

31/42

Mixed Number

Proper (31/42)

Decimal Value

0.738095

Percentage

73.8095%

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Step-by-Step Solution: 1/14 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 3 = 42.

LCD(14, 3) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 1/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.

1 × 3/14 × 3 = 3/42 and 2 × 14/3 × 14 = 28/42

Step 3

Add the Numerators

Now add the numerators (3 + 28 = 31) and keep the common denominator 42 unchanged.

3 + 28/42 = 31/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 42 is 1, confirming that 31/42 cannot be reduced further—it is already in its simplest irreducible form.

31/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).

31 ÷ 42 = 0.738095 (73.8095%)

Visual Representation

The diagram below illustrates 1/14 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/42`
Mixed Number Form	`31/42`
Decimal Form	`0.738095`
Percentage	`73.8095%`

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Frequently Asked Questions

What is 1/14 plus 2/3 as a fraction?

1/14 + 2/3 in simplest fraction form is 31/42.

What is 1/14 plus 2/3 as a decimal?

1/14 + 2/3 converted to a decimal is 0.738095.

What is 1/14 plus 2/3 as a percentage?

1/14 + 2/3 expressed as a percentage is 73.8095%.

Does 1/14 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.738095...) because the denominator contains prime factors other than 2 and 5.