What is 2/9 plus 7/29?
2/9 plus 7/29 equals 121/261 (or 0.463602 in decimal form). Learn the step-by-step solution to add 2/9 and 7/29 using Least Common Denominator and simplification.
Exact Answer
2/9 + 7/29 = 121/261
Simplified Fraction
121/261
Mixed Number
Proper (121/261)
Decimal Value
0.463602
Percentage
46.3602%
Step-by-Step Solution: 2/9 + 7/29
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 29 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 29 = 261.
LCD(9, 29) = 261
Step 2
Convert to Equivalent Fractions with Common Denominator 261
Multiply the numerator and denominator of 2/9 by 29, and multiply the numerator and denominator of 7/29 by 9 so both fractions share the common base 261.
2 × 29/9 × 29 = 58/261 and 7 × 9/29 × 9 = 63/261
Step 3
Add the Numerators
Now add the numerators (58 + 63 = 121) and keep the common denominator 261 unchanged.
58 + 63/261 = 121/261
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 121 and 261 is 1, confirming that 121/261 cannot be reduced further—it is already in its simplest irreducible form.
121/261
Step 5
Decimal & Percentage Representation
Dividing the numerator 121 by denominator 261 produces a repeating decimal (approximately 0.463602, or 46.3602%).
121 ÷ 261 = 0.463602 (46.3602%)
Visual Representation
The diagram below illustrates 2/9 plus 7/29 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 121/261 |
| Mixed Number Form | 121/261 |
| Decimal Form | 0.463602 |
| Percentage | 46.3602% |
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Frequently Asked Questions
What is 2/9 plus 7/29 as a fraction?
2/9 + 7/29 in simplest fraction form is 121/261.
What is 2/9 plus 7/29 as a decimal?
2/9 + 7/29 converted to a decimal is 0.463602.
What is 2/9 plus 7/29 as a percentage?
2/9 + 7/29 expressed as a percentage is 46.3602%.
Does 2/9 plus 7/29 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.463602...) because the denominator contains prime factors other than 2 and 5.