What is 2/31 plus 4/9?
2/31 plus 4/9 equals 142/279 (or 0.508961 in decimal form). Learn the step-by-step solution to add 2/31 and 4/9 using Least Common Denominator and simplification.
Exact Answer
2/31 + 4/9 = 142/279
Simplified Fraction
142/279
Mixed Number
Proper (142/279)
Decimal Value
0.508961
Percentage
50.8961%
Step-by-Step Solution: 2/31 + 4/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 31 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 9 = 279.
LCD(31, 9) = 279
Step 2
Convert to Equivalent Fractions with Common Denominator 279
Multiply the numerator and denominator of 2/31 by 9, and multiply the numerator and denominator of 4/9 by 31 so both fractions share the common base 279.
2 × 9/31 × 9 = 18/279 and 4 × 31/9 × 31 = 124/279
Step 3
Add the Numerators
Now add the numerators (18 + 124 = 142) and keep the common denominator 279 unchanged.
18 + 124/279 = 142/279
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 142 and 279 is 1, confirming that 142/279 cannot be reduced further—it is already in its simplest irreducible form.
142/279
Step 5
Decimal & Percentage Representation
Dividing the numerator 142 by denominator 279 produces a repeating decimal (approximately 0.508961, or 50.8961%).
142 ÷ 279 = 0.508961 (50.8961%)
Visual Representation
The diagram below illustrates 2/31 plus 4/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 142/279 |
| Mixed Number Form | 142/279 |
| Decimal Form | 0.508961 |
| Percentage | 50.8961% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 2/31 plus 4/9 as a fraction?
2/31 + 4/9 in simplest fraction form is 142/279.
What is 2/31 plus 4/9 as a decimal?
2/31 + 4/9 converted to a decimal is 0.508961.
What is 2/31 plus 4/9 as a percentage?
2/31 + 4/9 expressed as a percentage is 50.8961%.
Does 2/31 plus 4/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.508961...) because the denominator contains prime factors other than 2 and 5.