What is 4/21 plus 6/29?
4/21 plus 6/29 equals 242/609 (or 0.397373 in decimal form). Learn the step-by-step solution to add 4/21 and 6/29 using Least Common Denominator and simplification.
Exact Answer
4/21 + 6/29 = 242/609
Simplified Fraction
242/609
Mixed Number
Proper (242/609)
Decimal Value
0.397373
Percentage
39.7373%
Step-by-Step Solution: 4/21 + 6/29
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 29 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 29 = 609.
LCD(21, 29) = 609
Step 2
Convert to Equivalent Fractions with Common Denominator 609
Multiply the numerator and denominator of 4/21 by 29, and multiply the numerator and denominator of 6/29 by 21 so both fractions share the common base 609.
4 × 29/21 × 29 = 116/609 and 6 × 21/29 × 21 = 126/609
Step 3
Add the Numerators
Now add the numerators (116 + 126 = 242) and keep the common denominator 609 unchanged.
116 + 126/609 = 242/609
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 242 and 609 is 1, confirming that 242/609 cannot be reduced further—it is already in its simplest irreducible form.
242/609
Step 5
Decimal & Percentage Representation
Dividing the numerator 242 by denominator 609 produces a repeating decimal (approximately 0.397373, or 39.7373%).
242 ÷ 609 = 0.397373 (39.7373%)
Visual Representation
The diagram below illustrates 4/21 plus 6/29 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 242/609 |
| Mixed Number Form | 242/609 |
| Decimal Form | 0.397373 |
| Percentage | 39.7373% |
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Frequently Asked Questions
What is 4/21 plus 6/29 as a fraction?
4/21 + 6/29 in simplest fraction form is 242/609.
What is 4/21 plus 6/29 as a decimal?
4/21 + 6/29 converted to a decimal is 0.397373.
What is 4/21 plus 6/29 as a percentage?
4/21 + 6/29 expressed as a percentage is 39.7373%.
Does 4/21 plus 6/29 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.397373...) because the denominator contains prime factors other than 2 and 5.