What is 1/14 plus 2/7? (Answer: 5/14)

Exact Answer

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Problem: What is 1/14 plus 2/7?
Formula / Expression: 1/14 + 2/7
Final Answer: 5/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 14 is an exact multiple of 7 (7 × 2 = 14). The Least Common Denominator (LCD) is simply 14, meaning we only need to scale one fraction.
Working: LCD(14, 7) = 14

Step 2: Convert to Equivalent Fractions with Common Denominator 14
Multiply the numerator and denominator of 1/14 by 1, and multiply the numerator and denominator of 2/7 by 2 so both fractions share the common base 14.
Working: 1 × 1/14 × 1 = 1/14 and 2 × 2/7 × 2 = 4/14

Step 3: Add the Numerators
Now add the numerators (1 + 4 = 5) and keep the common denominator 14 unchanged.
Working: 1 + 4/14 = 5/14

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 14 is 1, confirming that 5/14 cannot be reduced further—it is already in its simplest irreducible form.
Working: 5/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).
Working: 5 ÷ 14 = 0.357143 (35.7143%)

Key Values:
- Simplified Fraction: 5/14
- Mixed Number Form: 5/14
- Decimal Value: 0.357143
- Percentage: 35.7143%

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Solved with FractionsCalc:
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1/14 + 2/7 = 5/14

Simplified Fraction

5/14

Mixed Number

Proper (5/14)

Decimal Value

0.357143

Percentage

35.7143%

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Step-by-Step Solution: 1/14 + 2/7

Step 1

Find the Least Common Denominator (LCD)

Notice that 14 is an exact multiple of 7 (7 × 2 = 14). The Least Common Denominator (LCD) is simply 14, meaning we only need to scale one fraction.

LCD(14, 7) = 14

Step 2

Convert to Equivalent Fractions with Common Denominator 14

Multiply the numerator and denominator of 1/14 by 1, and multiply the numerator and denominator of 2/7 by 2 so both fractions share the common base 14.

1 × 1/14 × 1 = 1/14 and 2 × 2/7 × 2 = 4/14

Step 3

Add the Numerators

Now add the numerators (1 + 4 = 5) and keep the common denominator 14 unchanged.

1 + 4/14 = 5/14

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 14 is 1, confirming that 5/14 cannot be reduced further—it is already in its simplest irreducible form.

5/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).

5 ÷ 14 = 0.357143 (35.7143%)

Visual Representation

The diagram below illustrates 1/14 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/14`
Mixed Number Form	`5/14`
Decimal Form	`0.357143`
Percentage	`35.7143%`

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Frequently Asked Questions

What is 1/14 plus 2/7 as a fraction?

1/14 + 2/7 in simplest fraction form is 5/14.

What is 1/14 plus 2/7 as a decimal?

1/14 + 2/7 converted to a decimal is 0.357143.

What is 1/14 plus 2/7 as a percentage?

1/14 + 2/7 expressed as a percentage is 35.7143%.

Does 1/14 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.357143...) because the denominator contains prime factors other than 2 and 5.