What is 2/14 plus 6/9? (Answer: 17/21)

Exact Answer

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Problem: What is 2/14 plus 6/9?
Formula / Expression: 2/14 + 6/9
Final Answer: 17/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 9 = 126.
Working: LCD(14, 9) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 2/14 by 9, and multiply the numerator and denominator of 6/9 by 14 so both fractions share the common base 126.
Working: 2 × 9/14 × 9 = 18/126 and 6 × 14/9 × 14 = 84/126

Step 3: Add the Numerators
Now add the numerators (18 + 84 = 102) and keep the common denominator 126 unchanged.
Working: 18 + 84/126 = 102/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 126, which is 6. Divide both the numerator and denominator by 6.
Working: 102 ÷ 6/126 ÷ 6 = 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-14-plus-6-9/
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2/14 + 6/9 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

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Step-by-Step Solution: 2/14 + 6/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 9 = 126.

LCD(14, 9) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 2/14 by 9, and multiply the numerator and denominator of 6/9 by 14 so both fractions share the common base 126.

2 × 9/14 × 9 = 18/126 and 6 × 14/9 × 14 = 84/126

Step 3

Add the Numerators

Now add the numerators (18 + 84 = 102) and keep the common denominator 126 unchanged.

18 + 84/126 = 102/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 126, which is 6. Divide both the numerator and denominator by 6.

102 ÷ 6/126 ÷ 6 = 17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

The diagram below illustrates 2/14 plus 6/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

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Frequently Asked Questions

What is 2/14 plus 6/9 as a fraction?

2/14 + 6/9 in simplest fraction form is 17/21.

What is 2/14 plus 6/9 as a decimal?

2/14 + 6/9 converted to a decimal is 0.809524.

What is 2/14 plus 6/9 as a percentage?

2/14 + 6/9 expressed as a percentage is 80.9524%.

Does 2/14 plus 6/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.