What is 3/14 plus 1/2? (Answer: 5/7)

Exact Answer

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Problem: What is 3/14 plus 1/2?
Formula / Expression: 3/14 + 1/2
Final Answer: 5/7
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (3 + 7 = 10) and keep the common denominator 14 unchanged.
Working: 3 + 7/14 = 10/14

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 14, which is 2. Divide both the numerator and denominator by 2.
Working: 10 ÷ 2/14 ÷ 2 = 5/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 7 produces a repeating decimal (approximately 0.714286, or 71.4286%).
Working: 5 ÷ 7 = 0.714286 (71.4286%)

Key Values:
- Simplified Fraction: 5/7
- Mixed Number Form: 5/7
- Decimal Value: 0.714286
- Percentage: 71.4286%

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Solved with FractionsCalc:
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3/14 + 1/2 = 5/7

Simplified Fraction

5/7

Mixed Number

Proper (5/7)

Decimal Value

0.714286

Percentage

71.4286%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(14, 2) = 14

Step 2

Convert to Equivalent Fractions with Common Denominator 14

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

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

Step 3

Add the Numerators

Now add the numerators (3 + 7 = 10) and keep the common denominator 14 unchanged.

3 + 7/14 = 10/14

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 14, which is 2. Divide both the numerator and denominator by 2.

10 ÷ 2/14 ÷ 2 = 5/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 7 produces a repeating decimal (approximately 0.714286, or 71.4286%).

5 ÷ 7 = 0.714286 (71.4286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/7`
Mixed Number Form	`5/7`
Decimal Form	`0.714286`
Percentage	`71.4286%`

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Frequently Asked Questions

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

3/14 + 1/2 in simplest fraction form is 5/7.

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

3/14 + 1/2 converted to a decimal is 0.714286.

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

3/14 + 1/2 expressed as a percentage is 71.4286%.

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

It results in a repeating decimal (approximately 0.714286...) because the denominator contains prime factors other than 2 and 5.