What is 3/7 plus 1/2? (Answer: 13/14)

Exact Answer

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Problem: What is 3/7 plus 1/2?
Formula / Expression: 3/7 + 1/2
Final Answer: 13/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 2 = 14.
Working: LCD(7, 2) = 14

Step 2: Convert to Equivalent Fractions with Common Denominator 14
Multiply the numerator and denominator of 3/7 by 2, and multiply the numerator and denominator of 1/2 by 7 so both fractions share the common base 14.
Working: 3 × 2/7 × 2 = 6/14 and 1 × 7/2 × 7 = 7/14

Step 3: Add the Numerators
Now add the numerators (6 + 7 = 13) and keep the common denominator 14 unchanged.
Working: 6 + 7/14 = 13/14

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 14 is 1, confirming that 13/14 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).
Working: 13 ÷ 14 = 0.928571 (92.8571%)

Key Values:
- Simplified Fraction: 13/14
- Mixed Number Form: 13/14
- Decimal Value: 0.928571
- Percentage: 92.8571%

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3/7 + 1/2 = 13/14

Simplified Fraction

13/14

Mixed Number

Proper (13/14)

Decimal Value

0.928571

Percentage

92.8571%

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Step-by-Step Solution: 3/7 + 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 2 = 14.

LCD(7, 2) = 14

Step 2

Convert to Equivalent Fractions with Common Denominator 14

Multiply the numerator and denominator of 3/7 by 2, and multiply the numerator and denominator of 1/2 by 7 so both fractions share the common base 14.

3 × 2/7 × 2 = 6/14 and 1 × 7/2 × 7 = 7/14

Step 3

Add the Numerators

Now add the numerators (6 + 7 = 13) and keep the common denominator 14 unchanged.

6 + 7/14 = 13/14

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 14 is 1, confirming that 13/14 cannot be reduced further—it is already in its simplest irreducible form.

13/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).

13 ÷ 14 = 0.928571 (92.8571%)

Visual Representation

The diagram below illustrates 3/7 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/14`
Mixed Number Form	`13/14`
Decimal Form	`0.928571`
Percentage	`92.8571%`

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Frequently Asked Questions

What is 3/7 plus 1/2 as a fraction?

3/7 + 1/2 in simplest fraction form is 13/14.

What is 3/7 plus 1/2 as a decimal?

3/7 + 1/2 converted to a decimal is 0.928571.

What is 3/7 plus 1/2 as a percentage?

3/7 + 1/2 expressed as a percentage is 92.8571%.

Does 3/7 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.928571...) because the denominator contains prime factors other than 2 and 5.