What is 15/31 plus 11/21?
15/31 plus 11/21 equals 656/651 (or 1 5/651 as a mixed number) (or 1.00768 in decimal form). Learn the step-by-step solution to add 15/31 and 11/21 using Least Common Denominator and simplification.
Exact Answer
15/31 + 11/21 = 656/651
Simplified Fraction
656/651
Mixed Number
1 5/651
Decimal Value
1.00768
Percentage
100.768%
Step-by-Step Solution: 15/31 + 11/21
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 15/31 by 21, and multiply the numerator and denominator of 11/21 by 31 so both fractions share the common base 651.
15 × 21/31 × 21 = 315/651 and 11 × 31/21 × 31 = 341/651
Step 3
Add the Numerators
Now add the numerators (315 + 341 = 656) and keep the common denominator 651 unchanged.
315 + 341/651 = 656/651
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 656 and 651 is 1, confirming that 656/651 cannot be reduced further—it is already in its simplest irreducible form.
656/651
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (656) is greater than the denominator (651), divide 656 by 651: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/651.
656/651 = 15/651
Step 6
Decimal & Percentage Representation
Dividing the numerator 656 by denominator 651 produces a repeating decimal (approximately 1.00768, or 100.768%).
656 ÷ 651 = 1.00768 (100.768%)
Visual Representation
The diagram below illustrates 15/31 plus 11/21 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 656/651 |
| Mixed Number Form | 1 5/651 |
| Decimal Form | 1.00768 |
| Percentage | 100.768% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 15/31 plus 11/21 as a fraction?
15/31 + 11/21 in simplest fraction form is 656/651 (or 1 5/651 as a mixed number).
What is 15/31 plus 11/21 as a decimal?
15/31 + 11/21 converted to a decimal is 1.00768.
What is 15/31 plus 11/21 as a percentage?
15/31 + 11/21 expressed as a percentage is 100.768%.
How do you write 15/31 plus 11/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 656/651 can be written as the mixed number 1 5/651.
Does 15/31 plus 11/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.00768...) because the denominator contains prime factors other than 2 and 5.