What is 10/29 plus 10/21?
10/29 plus 10/21 equals 500/609 (or 0.821018 in decimal form). Learn the step-by-step solution to add 10/29 and 10/21 using Least Common Denominator and simplification.
Exact Answer
10/29 + 10/21 = 500/609
Simplified Fraction
500/609
Mixed Number
Proper (500/609)
Decimal Value
0.821018
Percentage
82.1018%
Step-by-Step Solution: 10/29 + 10/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 29 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 21 = 609.
LCD(29, 21) = 609
Step 2
Convert to Equivalent Fractions with Common Denominator 609
Multiply the numerator and denominator of 10/29 by 21, and multiply the numerator and denominator of 10/21 by 29 so both fractions share the common base 609.
10 × 21/29 × 21 = 210/609 and 10 × 29/21 × 29 = 290/609
Step 3
Add the Numerators
Now add the numerators (210 + 290 = 500) and keep the common denominator 609 unchanged.
210 + 290/609 = 500/609
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 500 and 609 is 1, confirming that 500/609 cannot be reduced further—it is already in its simplest irreducible form.
500/609
Step 5
Decimal & Percentage Representation
Dividing the numerator 500 by denominator 609 produces a repeating decimal (approximately 0.821018, or 82.1018%).
500 ÷ 609 = 0.821018 (82.1018%)
Visual Representation
The diagram below illustrates 10/29 plus 10/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 500/609 |
| Mixed Number Form | 500/609 |
| Decimal Form | 0.821018 |
| Percentage | 82.1018% |
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Frequently Asked Questions
What is 10/29 plus 10/21 as a fraction?
10/29 + 10/21 in simplest fraction form is 500/609.
What is 10/29 plus 10/21 as a decimal?
10/29 + 10/21 converted to a decimal is 0.821018.
What is 10/29 plus 10/21 as a percentage?
10/29 + 10/21 expressed as a percentage is 82.1018%.
Does 10/29 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.821018...) because the denominator contains prime factors other than 2 and 5.