What is 2/14 plus 8/9?
2/14 plus 8/9 equals 65/63 (or 1 2/63 as a mixed number) (or 1.031746 in decimal form). Learn the step-by-step solution to add 2/14 and 8/9 using Least Common Denominator and simplification.
Exact Answer
2/14 + 8/9 = 65/63
Simplified Fraction
65/63
Mixed Number
1 2/63
Decimal Value
1.031746
Percentage
103.1746%
Step-by-Step Solution: 2/14 + 8/9
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 8/9 by 14 so both fractions share the common base 126.
2 × 9/14 × 9 = 18/126 and 8 × 14/9 × 14 = 112/126
Step 3
Add the Numerators
Now add the numerators (18 + 112 = 130) and keep the common denominator 126 unchanged.
18 + 112/126 = 130/126
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 130 and 126, which is 2. Divide both the numerator and denominator by 2.
130 ÷ 2/126 ÷ 2 = 65/63
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (65) is greater than the denominator (63), divide 65 by 63: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/63.
65/63 = 12/63
Step 6
Decimal & Percentage Representation
Dividing the numerator 65 by denominator 63 produces a repeating decimal (approximately 1.031746, or 103.1746%).
65 ÷ 63 = 1.031746 (103.1746%)
Visual Representation
The diagram below illustrates 2/14 plus 8/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 65/63 |
| Mixed Number Form | 1 2/63 |
| Decimal Form | 1.031746 |
| Percentage | 103.1746% |
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Frequently Asked Questions
What is 2/14 plus 8/9 as a fraction?
2/14 + 8/9 in simplest fraction form is 65/63 (or 1 2/63 as a mixed number).
What is 2/14 plus 8/9 as a decimal?
2/14 + 8/9 converted to a decimal is 1.031746.
What is 2/14 plus 8/9 as a percentage?
2/14 + 8/9 expressed as a percentage is 103.1746%.
How do you write 2/14 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 65/63 can be written as the mixed number 1 2/63.
Does 2/14 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.031746...) because the denominator contains prime factors other than 2 and 5.