What is 14/31 plus 12/21? (Answer: 222/217)

Exact Answer

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Problem: What is 14/31 plus 12/21?
Formula / Expression: 14/31 + 12/21
Final Answer: 1 5/217 (222/217)
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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 14/31 by 21, and multiply the numerator and denominator of 12/21 by 31 so both fractions share the common base 651.
Working: 14 × 21/31 × 21 = 294/651 and 12 × 31/21 × 31 = 372/651

Step 3: Add the Numerators
Now add the numerators (294 + 372 = 666) and keep the common denominator 651 unchanged.
Working: 294 + 372/651 = 666/651

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 666 and 651, which is 3. Divide both the numerator and denominator by 3.
Working: 666 ÷ 3/651 ÷ 3 = 222/217

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (222) is greater than the denominator (217), divide 222 by 217: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/217.
Working: 222/217 = 1 5/217

Step 6: Decimal & Percentage Representation
Dividing the numerator 222 by denominator 217 produces a repeating decimal (approximately 1.023041, or 102.3041%).
Working: 222 ÷ 217 = 1.023041 (102.3041%)

Key Values:
- Simplified Fraction: 222/217
- Mixed Number Form: 1 5/217
- Decimal Value: 1.023041
- Percentage: 102.3041%

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Solved with FractionsCalc:
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14/31 + 12/21 = 222/217

Simplified Fraction

222/217

Mixed Number

1 5/217

Decimal Value

1.023041

Percentage

102.3041%

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Step-by-Step Solution: 14/31 + 12/21

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 14/31 by 21, and multiply the numerator and denominator of 12/21 by 31 so both fractions share the common base 651.

14 × 21/31 × 21 = 294/651 and 12 × 31/21 × 31 = 372/651

Step 3

Add the Numerators

Now add the numerators (294 + 372 = 666) and keep the common denominator 651 unchanged.

294 + 372/651 = 666/651

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 666 and 651, which is 3. Divide both the numerator and denominator by 3.

666 ÷ 3/651 ÷ 3 = 222/217

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (222) is greater than the denominator (217), divide 222 by 217: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/217.

222/217 = 15/217

Step 6

Decimal & Percentage Representation

Dividing the numerator 222 by denominator 217 produces a repeating decimal (approximately 1.023041, or 102.3041%).

222 ÷ 217 = 1.023041 (102.3041%)

Visual Representation

The diagram below illustrates 14/31 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`222/217`
Mixed Number Form	`1 5/217`
Decimal Form	`1.023041`
Percentage	`102.3041%`

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Frequently Asked Questions

What is 14/31 plus 12/21 as a fraction?

14/31 + 12/21 in simplest fraction form is 222/217 (or 1 5/217 as a mixed number).

What is 14/31 plus 12/21 as a decimal?

14/31 + 12/21 converted to a decimal is 1.023041.

What is 14/31 plus 12/21 as a percentage?

14/31 + 12/21 expressed as a percentage is 102.3041%.

How do you write 14/31 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 222/217 can be written as the mixed number 1 5/217.

Does 14/31 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.023041...) because the denominator contains prime factors other than 2 and 5.