What is 6/17 plus 2/3?
6/17 plus 2/3 equals 52/51 (or 1 1/51 as a mixed number) (or 1.019608 in decimal form). Learn the step-by-step solution to add 6/17 and 2/3 using Least Common Denominator and simplification.
Exact Answer
6/17 + 2/3 = 52/51
Simplified Fraction
52/51
Mixed Number
1 1/51
Decimal Value
1.019608
Percentage
101.9608%
Step-by-Step Solution: 6/17 + 2/3
Step 1
Find the Least Common Denominator (LCD)
The denominators 17 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 3 = 51.
LCD(17, 3) = 51
Step 2
Convert to Equivalent Fractions with Common Denominator 51
Multiply the numerator and denominator of 6/17 by 3, and multiply the numerator and denominator of 2/3 by 17 so both fractions share the common base 51.
6 × 3/17 × 3 = 18/51 and 2 × 17/3 × 17 = 34/51
Step 3
Add the Numerators
Now add the numerators (18 + 34 = 52) and keep the common denominator 51 unchanged.
18 + 34/51 = 52/51
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 52 and 51 is 1, confirming that 52/51 cannot be reduced further—it is already in its simplest irreducible form.
52/51
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (52) is greater than the denominator (51), divide 52 by 51: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/51.
52/51 = 11/51
Step 6
Decimal & Percentage Representation
Dividing the numerator 52 by denominator 51 produces a repeating decimal (approximately 1.019608, or 101.9608%).
52 ÷ 51 = 1.019608 (101.9608%)
Visual Representation
The diagram below illustrates 6/17 plus 2/3 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 52/51 |
| Mixed Number Form | 1 1/51 |
| Decimal Form | 1.019608 |
| Percentage | 101.9608% |
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Frequently Asked Questions
What is 6/17 plus 2/3 as a fraction?
6/17 + 2/3 in simplest fraction form is 52/51 (or 1 1/51 as a mixed number).
What is 6/17 plus 2/3 as a decimal?
6/17 + 2/3 converted to a decimal is 1.019608.
What is 6/17 plus 2/3 as a percentage?
6/17 + 2/3 expressed as a percentage is 101.9608%.
How do you write 6/17 plus 2/3 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 52/51 can be written as the mixed number 1 1/51.
Does 6/17 plus 2/3 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.019608...) because the denominator contains prime factors other than 2 and 5.