What is 2/9 plus 10/14? (Answer: 59/63)

Exact Answer

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Problem: What is 2/9 plus 10/14?
Formula / Expression: 2/9 + 10/14
Final Answer: 59/63
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 2/9 by 14, and multiply the numerator and denominator of 10/14 by 9 so both fractions share the common base 126.
Working: 2 × 14/9 × 14 = 28/126 and 10 × 9/14 × 9 = 90/126

Step 3: Add the Numerators
Now add the numerators (28 + 90 = 118) and keep the common denominator 126 unchanged.
Working: 28 + 90/126 = 118/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/126 ÷ 2 = 59/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 63 produces a repeating decimal (approximately 0.936508, or 93.6508%).
Working: 59 ÷ 63 = 0.936508 (93.6508%)

Key Values:
- Simplified Fraction: 59/63
- Mixed Number Form: 59/63
- Decimal Value: 0.936508
- Percentage: 93.6508%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-10-14/
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2/9 + 10/14 = 59/63

Simplified Fraction

59/63

Mixed Number

Proper (59/63)

Decimal Value

0.936508

Percentage

93.6508%

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Step-by-Step Solution: 2/9 + 10/14

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 14) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 2/9 by 14, and multiply the numerator and denominator of 10/14 by 9 so both fractions share the common base 126.

2 × 14/9 × 14 = 28/126 and 10 × 9/14 × 9 = 90/126

Step 3

Add the Numerators

Now add the numerators (28 + 90 = 118) and keep the common denominator 126 unchanged.

28 + 90/126 = 118/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 126, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/126 ÷ 2 = 59/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 63 produces a repeating decimal (approximately 0.936508, or 93.6508%).

59 ÷ 63 = 0.936508 (93.6508%)

Visual Representation

The diagram below illustrates 2/9 plus 10/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/63`
Mixed Number Form	`59/63`
Decimal Form	`0.936508`
Percentage	`93.6508%`

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Frequently Asked Questions

What is 2/9 plus 10/14 as a fraction?

2/9 + 10/14 in simplest fraction form is 59/63.

What is 2/9 plus 10/14 as a decimal?

2/9 + 10/14 converted to a decimal is 0.936508.

What is 2/9 plus 10/14 as a percentage?

2/9 + 10/14 expressed as a percentage is 93.6508%.

Does 2/9 plus 10/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.936508...) because the denominator contains prime factors other than 2 and 5.