What is 19/55 plus 8/21?
19/55 plus 8/21 equals 839/1155 (or 0.726407 in decimal form). Learn the step-by-step solution to add 19/55 and 8/21 using Least Common Denominator and simplification.
Exact Answer
19/55 + 8/21 = 839/1155
Simplified Fraction
839/1155
Mixed Number
Proper (839/1155)
Decimal Value
0.726407
Percentage
72.6407%
Step-by-Step Solution: 19/55 + 8/21
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 19/55 by 21, and multiply the numerator and denominator of 8/21 by 55 so both fractions share the common base 1155.
19 × 21/55 × 21 = 399/1155 and 8 × 55/21 × 55 = 440/1155
Step 3
Add the Numerators
Now add the numerators (399 + 440 = 839) and keep the common denominator 1155 unchanged.
399 + 440/1155 = 839/1155
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 839 and 1155 is 1, confirming that 839/1155 cannot be reduced further—it is already in its simplest irreducible form.
839/1155
Step 5
Decimal & Percentage Representation
Dividing the numerator 839 by denominator 1155 produces a repeating decimal (approximately 0.726407, or 72.6407%).
839 ÷ 1155 = 0.726407 (72.6407%)
Visual Representation
The diagram below illustrates 19/55 plus 8/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 839/1155 |
| Mixed Number Form | 839/1155 |
| Decimal Form | 0.726407 |
| Percentage | 72.6407% |
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Frequently Asked Questions
What is 19/55 plus 8/21 as a fraction?
19/55 + 8/21 in simplest fraction form is 839/1155.
What is 19/55 plus 8/21 as a decimal?
19/55 + 8/21 converted to a decimal is 0.726407.
What is 19/55 plus 8/21 as a percentage?
19/55 + 8/21 expressed as a percentage is 72.6407%.
Does 19/55 plus 8/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.726407...) because the denominator contains prime factors other than 2 and 5.