What is 12/31 plus 9/21? (Answer: 177/217)

Exact Answer

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Problem: What is 12/31 plus 9/21?
Formula / Expression: 12/31 + 9/21
Final Answer: 177/217
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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 12/31 by 21, and multiply the numerator and denominator of 9/21 by 31 so both fractions share the common base 651.
Working: 12 × 21/31 × 21 = 252/651 and 9 × 31/21 × 31 = 279/651

Step 3: Add the Numerators
Now add the numerators (252 + 279 = 531) and keep the common denominator 651 unchanged.
Working: 252 + 279/651 = 531/651

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 531 and 651, which is 3. Divide both the numerator and denominator by 3.
Working: 531 ÷ 3/651 ÷ 3 = 177/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 177 by denominator 217 produces a repeating decimal (approximately 0.815668, or 81.5668%).
Working: 177 ÷ 217 = 0.815668 (81.5668%)

Key Values:
- Simplified Fraction: 177/217
- Mixed Number Form: 177/217
- Decimal Value: 0.815668
- Percentage: 81.5668%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-31-plus-9-21/
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12/31 + 9/21 = 177/217

Simplified Fraction

177/217

Mixed Number

Proper (177/217)

Decimal Value

0.815668

Percentage

81.5668%

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Step-by-Step Solution: 12/31 + 9/21

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 12/31 by 21, and multiply the numerator and denominator of 9/21 by 31 so both fractions share the common base 651.

12 × 21/31 × 21 = 252/651 and 9 × 31/21 × 31 = 279/651

Step 3

Add the Numerators

Now add the numerators (252 + 279 = 531) and keep the common denominator 651 unchanged.

252 + 279/651 = 531/651

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 531 and 651, which is 3. Divide both the numerator and denominator by 3.

531 ÷ 3/651 ÷ 3 = 177/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 177 by denominator 217 produces a repeating decimal (approximately 0.815668, or 81.5668%).

177 ÷ 217 = 0.815668 (81.5668%)

Visual Representation

The diagram below illustrates 12/31 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`177/217`
Mixed Number Form	`177/217`
Decimal Form	`0.815668`
Percentage	`81.5668%`

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Frequently Asked Questions

What is 12/31 plus 9/21 as a fraction?

12/31 + 9/21 in simplest fraction form is 177/217.

What is 12/31 plus 9/21 as a decimal?

12/31 + 9/21 converted to a decimal is 0.815668.

What is 12/31 plus 9/21 as a percentage?

12/31 + 9/21 expressed as a percentage is 81.5668%.

Does 12/31 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.815668...) because the denominator contains prime factors other than 2 and 5.