What is 2/9 plus 7/31?
2/9 plus 7/31 equals 125/279 (or 0.448029 in decimal form). Learn the step-by-step solution to add 2/9 and 7/31 using Least Common Denominator and simplification.
Exact Answer
2/9 + 7/31 = 125/279
Simplified Fraction
125/279
Mixed Number
Proper (125/279)
Decimal Value
0.448029
Percentage
44.8029%
Step-by-Step Solution: 2/9 + 7/31
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 31 = 279.
LCD(9, 31) = 279
Step 2
Convert to Equivalent Fractions with Common Denominator 279
Multiply the numerator and denominator of 2/9 by 31, and multiply the numerator and denominator of 7/31 by 9 so both fractions share the common base 279.
2 × 31/9 × 31 = 62/279 and 7 × 9/31 × 9 = 63/279
Step 3
Add the Numerators
Now add the numerators (62 + 63 = 125) and keep the common denominator 279 unchanged.
62 + 63/279 = 125/279
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 125 and 279 is 1, confirming that 125/279 cannot be reduced further—it is already in its simplest irreducible form.
125/279
Step 5
Decimal & Percentage Representation
Dividing the numerator 125 by denominator 279 produces a repeating decimal (approximately 0.448029, or 44.8029%).
125 ÷ 279 = 0.448029 (44.8029%)
Visual Representation
The diagram below illustrates 2/9 plus 7/31 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 125/279 |
| Mixed Number Form | 125/279 |
| Decimal Form | 0.448029 |
| Percentage | 44.8029% |
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Frequently Asked Questions
What is 2/9 plus 7/31 as a fraction?
2/9 + 7/31 in simplest fraction form is 125/279.
What is 2/9 plus 7/31 as a decimal?
2/9 + 7/31 converted to a decimal is 0.448029.
What is 2/9 plus 7/31 as a percentage?
2/9 + 7/31 expressed as a percentage is 44.8029%.
Does 2/9 plus 7/31 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.448029...) because the denominator contains prime factors other than 2 and 5.