What is 3/14 plus 2/8? (Answer: 13/28)

Exact Answer

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Problem: What is 3/14 plus 2/8?
Formula / Expression: 3/14 + 2/8
Final Answer: 13/28
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 56 (which is smaller than their product 14 × 8 = 112, keeping the calculation simpler).
Working: LCD(14, 8) = 56

Step 2: Convert to Equivalent Fractions with Common Denominator 56
Multiply the numerator and denominator of 3/14 by 4, and multiply the numerator and denominator of 2/8 by 7 so both fractions share the common base 56.
Working: 3 × 4/14 × 4 = 12/56 and 2 × 7/8 × 7 = 14/56

Step 3: Add the Numerators
Now add the numerators (12 + 14 = 26) and keep the common denominator 56 unchanged.
Working: 12 + 14/56 = 26/56

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 56, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/56 ÷ 2 = 13/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).
Working: 13 ÷ 28 = 0.464286 (46.4286%)

Key Values:
- Simplified Fraction: 13/28
- Mixed Number Form: 13/28
- Decimal Value: 0.464286
- Percentage: 46.4286%

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Solved with FractionsCalc:
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3/14 + 2/8 = 13/28

Simplified Fraction

13/28

Mixed Number

Proper (13/28)

Decimal Value

0.464286

Percentage

46.4286%

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Step-by-Step Solution: 3/14 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 56 (which is smaller than their product 14 × 8 = 112, keeping the calculation simpler).

LCD(14, 8) = 56

Step 2

Convert to Equivalent Fractions with Common Denominator 56

Multiply the numerator and denominator of 3/14 by 4, and multiply the numerator and denominator of 2/8 by 7 so both fractions share the common base 56.

3 × 4/14 × 4 = 12/56 and 2 × 7/8 × 7 = 14/56

Step 3

Add the Numerators

Now add the numerators (12 + 14 = 26) and keep the common denominator 56 unchanged.

12 + 14/56 = 26/56

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 56, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/56 ÷ 2 = 13/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).

13 ÷ 28 = 0.464286 (46.4286%)

Visual Representation

The diagram below illustrates 3/14 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/28`
Mixed Number Form	`13/28`
Decimal Form	`0.464286`
Percentage	`46.4286%`

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Frequently Asked Questions

What is 3/14 plus 2/8 as a fraction?

3/14 + 2/8 in simplest fraction form is 13/28.

What is 3/14 plus 2/8 as a decimal?

3/14 + 2/8 converted to a decimal is 0.464286.

What is 3/14 plus 2/8 as a percentage?

3/14 + 2/8 expressed as a percentage is 46.4286%.

Does 3/14 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.464286...) because the denominator contains prime factors other than 2 and 5.