What is 10/31 plus 10/21?
10/31 plus 10/21 equals 520/651 (or 0.798771 in decimal form). Learn the step-by-step solution to add 10/31 and 10/21 using Least Common Denominator and simplification.
Exact Answer
10/31 + 10/21 = 520/651
Simplified Fraction
520/651
Mixed Number
Proper (520/651)
Decimal Value
0.798771
Percentage
79.8771%
Step-by-Step Solution: 10/31 + 10/21
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 10/31 by 21, and multiply the numerator and denominator of 10/21 by 31 so both fractions share the common base 651.
10 × 21/31 × 21 = 210/651 and 10 × 31/21 × 31 = 310/651
Step 3
Add the Numerators
Now add the numerators (210 + 310 = 520) and keep the common denominator 651 unchanged.
210 + 310/651 = 520/651
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 520 and 651 is 1, confirming that 520/651 cannot be reduced further—it is already in its simplest irreducible form.
520/651
Step 5
Decimal & Percentage Representation
Dividing the numerator 520 by denominator 651 produces a repeating decimal (approximately 0.798771, or 79.8771%).
520 ÷ 651 = 0.798771 (79.8771%)
Visual Representation
The diagram below illustrates 10/31 plus 10/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 520/651 |
| Mixed Number Form | 520/651 |
| Decimal Form | 0.798771 |
| Percentage | 79.8771% |
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Frequently Asked Questions
What is 10/31 plus 10/21 as a fraction?
10/31 + 10/21 in simplest fraction form is 520/651.
What is 10/31 plus 10/21 as a decimal?
10/31 + 10/21 converted to a decimal is 0.798771.
What is 10/31 plus 10/21 as a percentage?
10/31 + 10/21 expressed as a percentage is 79.8771%.
Does 10/31 plus 10/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.798771...) because the denominator contains prime factors other than 2 and 5.