What is 6/14 plus 2/3?
6/14 plus 2/3 equals 23/21 (or 1 2/21 as a mixed number) (or 1.095238 in decimal form). Learn the step-by-step solution to add 6/14 and 2/3 using Least Common Denominator and simplification.
Exact Answer
6/14 + 2/3 = 23/21
Simplified Fraction
23/21
Mixed Number
1 2/21
Decimal Value
1.095238
Percentage
109.5238%
Step-by-Step Solution: 6/14 + 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 6/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.
6 × 3/14 × 3 = 18/42 and 2 × 14/3 × 14 = 28/42
Step 3
Add the Numerators
Now add the numerators (18 + 28 = 46) and keep the common denominator 42 unchanged.
18 + 28/42 = 46/42
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 42, which is 2. Divide both the numerator and denominator by 2.
46 ÷ 2/42 ÷ 2 = 23/21
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (23) is greater than the denominator (21), divide 23 by 21: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/21.
23/21 = 12/21
Step 6
Decimal & Percentage Representation
Dividing the numerator 23 by denominator 21 produces a repeating decimal (approximately 1.095238, or 109.5238%).
23 ÷ 21 = 1.095238 (109.5238%)
Visual Representation
The diagram below illustrates 6/14 plus 2/3 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 23/21 |
| Mixed Number Form | 1 2/21 |
| Decimal Form | 1.095238 |
| Percentage | 109.5238% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 6/14 plus 2/3 as a fraction?
6/14 + 2/3 in simplest fraction form is 23/21 (or 1 2/21 as a mixed number).
What is 6/14 plus 2/3 as a decimal?
6/14 + 2/3 converted to a decimal is 1.095238.
What is 6/14 plus 2/3 as a percentage?
6/14 + 2/3 expressed as a percentage is 109.5238%.
How do you write 6/14 plus 2/3 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 23/21 can be written as the mixed number 1 2/21.
Does 6/14 plus 2/3 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.095238...) because the denominator contains prime factors other than 2 and 5.