What is 4/31 plus 4/21?
4/31 plus 4/21 equals 208/651 (or 0.319508 in decimal form). Learn the step-by-step solution to add 4/31 and 4/21 using Least Common Denominator and simplification.
Exact Answer
4/31 + 4/21 = 208/651
Simplified Fraction
208/651
Mixed Number
Proper (208/651)
Decimal Value
0.319508
Percentage
31.9508%
Step-by-Step Solution: 4/31 + 4/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 31 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 21 = 651.
LCD(31, 21) = 651
Step 2
Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 4/31 by 21, and multiply the numerator and denominator of 4/21 by 31 so both fractions share the common base 651.
4 × 21/31 × 21 = 84/651 and 4 × 31/21 × 31 = 124/651
Step 3
Add the Numerators
Now add the numerators (84 + 124 = 208) and keep the common denominator 651 unchanged.
84 + 124/651 = 208/651
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 208 and 651 is 1, confirming that 208/651 cannot be reduced further—it is already in its simplest irreducible form.
208/651
Step 5
Decimal & Percentage Representation
Dividing the numerator 208 by denominator 651 produces a repeating decimal (approximately 0.319508, or 31.9508%).
208 ÷ 651 = 0.319508 (31.9508%)
Visual Representation
The diagram below illustrates 4/31 plus 4/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 208/651 |
| Mixed Number Form | 208/651 |
| Decimal Form | 0.319508 |
| Percentage | 31.9508% |
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Frequently Asked Questions
What is 4/31 plus 4/21 as a fraction?
4/31 + 4/21 in simplest fraction form is 208/651.
What is 4/31 plus 4/21 as a decimal?
4/31 + 4/21 converted to a decimal is 0.319508.
What is 4/31 plus 4/21 as a percentage?
4/31 + 4/21 expressed as a percentage is 31.9508%.
Does 4/31 plus 4/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.319508...) because the denominator contains prime factors other than 2 and 5.