What is 10/21 plus 15/31?
10/21 plus 15/31 equals 625/651 (or 0.960061 in decimal form). Learn the step-by-step solution to add 10/21 and 15/31 using Least Common Denominator and simplification.
Exact Answer
10/21 + 15/31 = 625/651
Simplified Fraction
625/651
Mixed Number
Proper (625/651)
Decimal Value
0.960061
Percentage
96.0061%
Step-by-Step Solution: 10/21 + 15/31
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 31 = 651.
LCD(21, 31) = 651
Step 2
Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 10/21 by 31, and multiply the numerator and denominator of 15/31 by 21 so both fractions share the common base 651.
10 × 31/21 × 31 = 310/651 and 15 × 21/31 × 21 = 315/651
Step 3
Add the Numerators
Now add the numerators (310 + 315 = 625) and keep the common denominator 651 unchanged.
310 + 315/651 = 625/651
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 625 and 651 is 1, confirming that 625/651 cannot be reduced further—it is already in its simplest irreducible form.
625/651
Step 5
Decimal & Percentage Representation
Dividing the numerator 625 by denominator 651 produces a repeating decimal (approximately 0.960061, or 96.0061%).
625 ÷ 651 = 0.960061 (96.0061%)
Visual Representation
The diagram below illustrates 10/21 plus 15/31 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 625/651 |
| Mixed Number Form | 625/651 |
| Decimal Form | 0.960061 |
| Percentage | 96.0061% |
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Frequently Asked Questions
What is 10/21 plus 15/31 as a fraction?
10/21 + 15/31 in simplest fraction form is 625/651.
What is 10/21 plus 15/31 as a decimal?
10/21 + 15/31 converted to a decimal is 0.960061.
What is 10/21 plus 15/31 as a percentage?
10/21 + 15/31 expressed as a percentage is 96.0061%.
Does 10/21 plus 15/31 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.960061...) because the denominator contains prime factors other than 2 and 5.