What is 10/41 plus 10/21?
10/41 plus 10/21 equals 620/861 (or 0.720093 in decimal form). Learn the step-by-step solution to add 10/41 and 10/21 using Least Common Denominator and simplification.
Exact Answer
10/41 + 10/21 = 620/861
Simplified Fraction
620/861
Mixed Number
Proper (620/861)
Decimal Value
0.720093
Percentage
72.0093%
Step-by-Step Solution: 10/41 + 10/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 41 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 41 × 21 = 861.
LCD(41, 21) = 861
Step 2
Convert to Equivalent Fractions with Common Denominator 861
Multiply the numerator and denominator of 10/41 by 21, and multiply the numerator and denominator of 10/21 by 41 so both fractions share the common base 861.
10 × 21/41 × 21 = 210/861 and 10 × 41/21 × 41 = 410/861
Step 3
Add the Numerators
Now add the numerators (210 + 410 = 620) and keep the common denominator 861 unchanged.
210 + 410/861 = 620/861
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 620 and 861 is 1, confirming that 620/861 cannot be reduced further—it is already in its simplest irreducible form.
620/861
Step 5
Decimal & Percentage Representation
Dividing the numerator 620 by denominator 861 produces a repeating decimal (approximately 0.720093, or 72.0093%).
620 ÷ 861 = 0.720093 (72.0093%)
Visual Representation
The diagram below illustrates 10/41 plus 10/21 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 620/861 |
| Mixed Number Form | 620/861 |
| Decimal Form | 0.720093 |
| Percentage | 72.0093% |
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Frequently Asked Questions
What is 10/41 plus 10/21 as a fraction?
10/41 + 10/21 in simplest fraction form is 620/861.
What is 10/41 plus 10/21 as a decimal?
10/41 + 10/21 converted to a decimal is 0.720093.
What is 10/41 plus 10/21 as a percentage?
10/41 + 10/21 expressed as a percentage is 72.0093%.
Does 10/41 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.720093...) because the denominator contains prime factors other than 2 and 5.