What is 3/14 plus 2/3? (Answer: 37/42)

Exact Answer

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Problem: What is 3/14 plus 2/3?
Formula / Expression: 3/14 + 2/3
Final Answer: 37/42
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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 3/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.
Working: 3 × 3/14 × 3 = 9/42 and 2 × 14/3 × 14 = 28/42

Step 3: Add the Numerators
Now add the numerators (9 + 28 = 37) and keep the common denominator 42 unchanged.
Working: 9 + 28/42 = 37/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 42 is 1, confirming that 37/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 42 produces a repeating decimal (approximately 0.880952, or 88.0952%).
Working: 37 ÷ 42 = 0.880952 (88.0952%)

Key Values:
- Simplified Fraction: 37/42
- Mixed Number Form: 37/42
- Decimal Value: 0.880952
- Percentage: 88.0952%

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Solved with FractionsCalc:
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3/14 + 2/3 = 37/42

Simplified Fraction

37/42

Mixed Number

Proper (37/42)

Decimal Value

0.880952

Percentage

88.0952%

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Step-by-Step Solution: 3/14 + 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 3/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.

3 × 3/14 × 3 = 9/42 and 2 × 14/3 × 14 = 28/42

Step 3

Add the Numerators

Now add the numerators (9 + 28 = 37) and keep the common denominator 42 unchanged.

9 + 28/42 = 37/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 42 is 1, confirming that 37/42 cannot be reduced further—it is already in its simplest irreducible form.

37/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 42 produces a repeating decimal (approximately 0.880952, or 88.0952%).

37 ÷ 42 = 0.880952 (88.0952%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/42`
Mixed Number Form	`37/42`
Decimal Form	`0.880952`
Percentage	`88.0952%`

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Frequently Asked Questions

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

3/14 + 2/3 in simplest fraction form is 37/42.

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

3/14 + 2/3 converted to a decimal is 0.880952.

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

3/14 + 2/3 expressed as a percentage is 88.0952%.

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

It results in a repeating decimal (approximately 0.880952...) because the denominator contains prime factors other than 2 and 5.