What is 10/23 plus 10/21?
10/23 plus 10/21 equals 440/483 (or 0.910973 in decimal form). Learn the step-by-step solution to add 10/23 and 10/21 using Least Common Denominator and simplification.
Exact Answer
10/23 + 10/21 = 440/483
Simplified Fraction
440/483
Mixed Number
Proper (440/483)
Decimal Value
0.910973
Percentage
91.0973%
Step-by-Step Solution: 10/23 + 10/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.
LCD(23, 21) = 483
Step 2
Convert to Equivalent Fractions with Common Denominator 483
Multiply the numerator and denominator of 10/23 by 21, and multiply the numerator and denominator of 10/21 by 23 so both fractions share the common base 483.
10 × 21/23 × 21 = 210/483 and 10 × 23/21 × 23 = 230/483
Step 3
Add the Numerators
Now add the numerators (210 + 230 = 440) and keep the common denominator 483 unchanged.
210 + 230/483 = 440/483
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 440 and 483 is 1, confirming that 440/483 cannot be reduced further—it is already in its simplest irreducible form.
440/483
Step 5
Decimal & Percentage Representation
Dividing the numerator 440 by denominator 483 produces a repeating decimal (approximately 0.910973, or 91.0973%).
440 ÷ 483 = 0.910973 (91.0973%)
Visual Representation
The diagram below illustrates 10/23 plus 10/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 440/483 |
| Mixed Number Form | 440/483 |
| Decimal Form | 0.910973 |
| Percentage | 91.0973% |
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Frequently Asked Questions
What is 10/23 plus 10/21 as a fraction?
10/23 + 10/21 in simplest fraction form is 440/483.
What is 10/23 plus 10/21 as a decimal?
10/23 + 10/21 converted to a decimal is 0.910973.
What is 10/23 plus 10/21 as a percentage?
10/23 + 10/21 expressed as a percentage is 91.0973%.
Does 10/23 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.910973...) because the denominator contains prime factors other than 2 and 5.