What is 2/14 plus 7/9? (Answer: 58/63)

Exact Answer

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Problem: What is 2/14 plus 7/9?
Formula / Expression: 2/14 + 7/9
Final Answer: 58/63
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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 7/9 by 14 so both fractions share the common base 126.
Working: 2 × 9/14 × 9 = 18/126 and 7 × 14/9 × 14 = 98/126

Step 3: Add the Numerators
Now add the numerators (18 + 98 = 116) and keep the common denominator 126 unchanged.
Working: 18 + 98/126 = 116/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 116 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 116 ÷ 2/126 ÷ 2 = 58/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 63 produces a repeating decimal (approximately 0.920635, or 92.0635%).
Working: 58 ÷ 63 = 0.920635 (92.0635%)

Key Values:
- Simplified Fraction: 58/63
- Mixed Number Form: 58/63
- Decimal Value: 0.920635
- Percentage: 92.0635%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-14-plus-7-9/
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2/14 + 7/9 = 58/63

Simplified Fraction

58/63

Mixed Number

Proper (58/63)

Decimal Value

0.920635

Percentage

92.0635%

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Step-by-Step Solution: 2/14 + 7/9

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 7/9 by 14 so both fractions share the common base 126.

2 × 9/14 × 9 = 18/126 and 7 × 14/9 × 14 = 98/126

Step 3

Add the Numerators

Now add the numerators (18 + 98 = 116) and keep the common denominator 126 unchanged.

18 + 98/126 = 116/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 116 and 126, which is 2. Divide both the numerator and denominator by 2.

116 ÷ 2/126 ÷ 2 = 58/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 63 produces a repeating decimal (approximately 0.920635, or 92.0635%).

58 ÷ 63 = 0.920635 (92.0635%)

Visual Representation

The diagram below illustrates 2/14 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/63`
Mixed Number Form	`58/63`
Decimal Form	`0.920635`
Percentage	`92.0635%`

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Frequently Asked Questions

What is 2/14 plus 7/9 as a fraction?

2/14 + 7/9 in simplest fraction form is 58/63.

What is 2/14 plus 7/9 as a decimal?

2/14 + 7/9 converted to a decimal is 0.920635.

What is 2/14 plus 7/9 as a percentage?

2/14 + 7/9 expressed as a percentage is 92.0635%.

Does 2/14 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.920635...) because the denominator contains prime factors other than 2 and 5.