What is 6/55 plus 5/21?
6/55 plus 5/21 equals 401/1155 (or 0.347186 in decimal form). Learn the step-by-step solution to add 6/55 and 5/21 using Least Common Denominator and simplification.
Exact Answer
6/55 + 5/21 = 401/1155
Simplified Fraction
401/1155
Mixed Number
Proper (401/1155)
Decimal Value
0.347186
Percentage
34.7186%
Step-by-Step Solution: 6/55 + 5/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 55 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 21 = 1155.
LCD(55, 21) = 1155
Step 2
Convert to Equivalent Fractions with Common Denominator 1155
Multiply the numerator and denominator of 6/55 by 21, and multiply the numerator and denominator of 5/21 by 55 so both fractions share the common base 1155.
6 × 21/55 × 21 = 126/1155 and 5 × 55/21 × 55 = 275/1155
Step 3
Add the Numerators
Now add the numerators (126 + 275 = 401) and keep the common denominator 1155 unchanged.
126 + 275/1155 = 401/1155
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 401 and 1155 is 1, confirming that 401/1155 cannot be reduced further—it is already in its simplest irreducible form.
401/1155
Step 5
Decimal & Percentage Representation
Dividing the numerator 401 by denominator 1155 produces a repeating decimal (approximately 0.347186, or 34.7186%).
401 ÷ 1155 = 0.347186 (34.7186%)
Visual Representation
The diagram below illustrates 6/55 plus 5/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 401/1155 |
| Mixed Number Form | 401/1155 |
| Decimal Form | 0.347186 |
| Percentage | 34.7186% |
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Frequently Asked Questions
What is 6/55 plus 5/21 as a fraction?
6/55 + 5/21 in simplest fraction form is 401/1155.
What is 6/55 plus 5/21 as a decimal?
6/55 + 5/21 converted to a decimal is 0.347186.
What is 6/55 plus 5/21 as a percentage?
6/55 + 5/21 expressed as a percentage is 34.7186%.
Does 6/55 plus 5/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.347186...) because the denominator contains prime factors other than 2 and 5.