What is 2/21 plus 6/55?
2/21 plus 6/55 equals 236/1155 (or 0.204329 in decimal form). Learn the step-by-step solution to add 2/21 and 6/55 using Least Common Denominator and simplification.
Exact Answer
2/21 + 6/55 = 236/1155
Simplified Fraction
236/1155
Mixed Number
Proper (236/1155)
Decimal Value
0.204329
Percentage
20.4329%
Step-by-Step Solution: 2/21 + 6/55
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 55 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 55 = 1155.
LCD(21, 55) = 1155
Step 2
Convert to Equivalent Fractions with Common Denominator 1155
Multiply the numerator and denominator of 2/21 by 55, and multiply the numerator and denominator of 6/55 by 21 so both fractions share the common base 1155.
2 × 55/21 × 55 = 110/1155 and 6 × 21/55 × 21 = 126/1155
Step 3
Add the Numerators
Now add the numerators (110 + 126 = 236) and keep the common denominator 1155 unchanged.
110 + 126/1155 = 236/1155
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 236 and 1155 is 1, confirming that 236/1155 cannot be reduced further—it is already in its simplest irreducible form.
236/1155
Step 5
Decimal & Percentage Representation
Dividing the numerator 236 by denominator 1155 produces a repeating decimal (approximately 0.204329, or 20.4329%).
236 ÷ 1155 = 0.204329 (20.4329%)
Visual Representation
The diagram below illustrates 2/21 plus 6/55 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 236/1155 |
| Mixed Number Form | 236/1155 |
| Decimal Form | 0.204329 |
| Percentage | 20.4329% |
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Frequently Asked Questions
What is 2/21 plus 6/55 as a fraction?
2/21 + 6/55 in simplest fraction form is 236/1155.
What is 2/21 plus 6/55 as a decimal?
2/21 + 6/55 converted to a decimal is 0.204329.
What is 2/21 plus 6/55 as a percentage?
2/21 + 6/55 expressed as a percentage is 20.4329%.
Does 2/21 plus 6/55 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.204329...) because the denominator contains prime factors other than 2 and 5.