What is 8/21 plus 12/31? (Answer: 500/651)

Exact Answer

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Problem: What is 8/21 plus 12/31?
Formula / Expression: 8/21 + 12/31
Final Answer: 500/651
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Step-by-Step Solution:

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.
Working: LCD(21, 31) = 651

Step 2: Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 8/21 by 31, and multiply the numerator and denominator of 12/31 by 21 so both fractions share the common base 651.
Working: 8 × 31/21 × 31 = 248/651 and 12 × 21/31 × 21 = 252/651

Step 3: Add the Numerators
Now add the numerators (248 + 252 = 500) and keep the common denominator 651 unchanged.
Working: 248 + 252/651 = 500/651

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 500 and 651 is 1, confirming that 500/651 cannot be reduced further—it is already in its simplest irreducible form.
Working: 500/651

Step 5: Decimal & Percentage Representation
Dividing the numerator 500 by denominator 651 produces a repeating decimal (approximately 0.768049, or 76.8049%).
Working: 500 ÷ 651 = 0.768049 (76.8049%)

Key Values:
- Simplified Fraction: 500/651
- Mixed Number Form: 500/651
- Decimal Value: 0.768049
- Percentage: 76.8049%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-21-plus-12-31/
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8/21 + 12/31 = 500/651

Simplified Fraction

500/651

Mixed Number

Proper (500/651)

Decimal Value

0.768049

Percentage

76.8049%

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Step-by-Step Solution: 8/21 + 12/31

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 8/21 by 31, and multiply the numerator and denominator of 12/31 by 21 so both fractions share the common base 651.

8 × 31/21 × 31 = 248/651 and 12 × 21/31 × 21 = 252/651

Step 3

Add the Numerators

Now add the numerators (248 + 252 = 500) and keep the common denominator 651 unchanged.

248 + 252/651 = 500/651

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 500 and 651 is 1, confirming that 500/651 cannot be reduced further—it is already in its simplest irreducible form.

500/651

Step 5

Decimal & Percentage Representation

Dividing the numerator 500 by denominator 651 produces a repeating decimal (approximately 0.768049, or 76.8049%).

500 ÷ 651 = 0.768049 (76.8049%)

Visual Representation

The diagram below illustrates 8/21 plus 12/31 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`500/651`
Mixed Number Form	`500/651`
Decimal Form	`0.768049`
Percentage	`76.8049%`

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Frequently Asked Questions

What is 8/21 plus 12/31 as a fraction?

8/21 + 12/31 in simplest fraction form is 500/651.

What is 8/21 plus 12/31 as a decimal?

8/21 + 12/31 converted to a decimal is 0.768049.

What is 8/21 plus 12/31 as a percentage?

8/21 + 12/31 expressed as a percentage is 76.8049%.

Does 8/21 plus 12/31 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.768049...) because the denominator contains prime factors other than 2 and 5.