What is 16/31 plus 11/21? (Answer: 677/651)

Exact Answer

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Problem: What is 16/31 plus 11/21?
Formula / Expression: 16/31 + 11/21
Final Answer: 1 26/651 (677/651)
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Step-by-Step Solution:

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.
Working: LCD(31, 21) = 651

Step 2: Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 16/31 by 21, and multiply the numerator and denominator of 11/21 by 31 so both fractions share the common base 651.
Working: 16 × 21/31 × 21 = 336/651 and 11 × 31/21 × 31 = 341/651

Step 3: Add the Numerators
Now add the numerators (336 + 341 = 677) and keep the common denominator 651 unchanged.
Working: 336 + 341/651 = 677/651

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 677 and 651 is 1, confirming that 677/651 cannot be reduced further—it is already in its simplest irreducible form.
Working: 677/651

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (677) is greater than the denominator (651), divide 677 by 651: it goes in 1 whole time(s) with a remainder of 26, giving the mixed number 1 26/651.
Working: 677/651 = 1 26/651

Step 6: Decimal & Percentage Representation
Dividing the numerator 677 by denominator 651 produces a repeating decimal (approximately 1.039939, or 103.9939%).
Working: 677 ÷ 651 = 1.039939 (103.9939%)

Key Values:
- Simplified Fraction: 677/651
- Mixed Number Form: 1 26/651
- Decimal Value: 1.039939
- Percentage: 103.9939%

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Solved with FractionsCalc:
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16/31 + 11/21 = 677/651

Simplified Fraction

677/651

Mixed Number

1 26/651

Decimal Value

1.039939

Percentage

103.9939%

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Step-by-Step Solution: 16/31 + 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 16/31 by 21, and multiply the numerator and denominator of 11/21 by 31 so both fractions share the common base 651.

16 × 21/31 × 21 = 336/651 and 11 × 31/21 × 31 = 341/651

Step 3

Add the Numerators

Now add the numerators (336 + 341 = 677) and keep the common denominator 651 unchanged.

336 + 341/651 = 677/651

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 677 and 651 is 1, confirming that 677/651 cannot be reduced further—it is already in its simplest irreducible form.

677/651

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (677) is greater than the denominator (651), divide 677 by 651: it goes in 1 whole time(s) with a remainder of 26, giving the mixed number 1 26/651.

677/651 = 126/651

Step 6

Decimal & Percentage Representation

Dividing the numerator 677 by denominator 651 produces a repeating decimal (approximately 1.039939, or 103.9939%).

677 ÷ 651 = 1.039939 (103.9939%)

Visual Representation

The diagram below illustrates 16/31 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`677/651`
Mixed Number Form	`1 26/651`
Decimal Form	`1.039939`
Percentage	`103.9939%`

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Frequently Asked Questions

What is 16/31 plus 11/21 as a fraction?

16/31 + 11/21 in simplest fraction form is 677/651 (or 1 26/651 as a mixed number).

What is 16/31 plus 11/21 as a decimal?

16/31 + 11/21 converted to a decimal is 1.039939.

What is 16/31 plus 11/21 as a percentage?

16/31 + 11/21 expressed as a percentage is 103.9939%.

How do you write 16/31 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 677/651 can be written as the mixed number 1 26/651.

Does 16/31 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.039939...) because the denominator contains prime factors other than 2 and 5.