What is 14/37 plus 9/21? (Answer: 209/259)

Exact Answer

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Problem: What is 14/37 plus 9/21?
Formula / Expression: 14/37 + 9/21
Final Answer: 209/259
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 37 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 21 = 777.
Working: LCD(37, 21) = 777

Step 2: Convert to Equivalent Fractions with Common Denominator 777
Multiply the numerator and denominator of 14/37 by 21, and multiply the numerator and denominator of 9/21 by 37 so both fractions share the common base 777.
Working: 14 × 21/37 × 21 = 294/777 and 9 × 37/21 × 37 = 333/777

Step 3: Add the Numerators
Now add the numerators (294 + 333 = 627) and keep the common denominator 777 unchanged.
Working: 294 + 333/777 = 627/777

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 627 and 777, which is 3. Divide both the numerator and denominator by 3.
Working: 627 ÷ 3/777 ÷ 3 = 209/259

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 259 produces a repeating decimal (approximately 0.80695, or 80.695%).
Working: 209 ÷ 259 = 0.80695 (80.695%)

Key Values:
- Simplified Fraction: 209/259
- Mixed Number Form: 209/259
- Decimal Value: 0.80695
- Percentage: 80.695%

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Solved with FractionsCalc:
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14/37 + 9/21 = 209/259

Simplified Fraction

209/259

Mixed Number

Proper (209/259)

Decimal Value

0.80695

Percentage

80.695%

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Step-by-Step Solution: 14/37 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 37 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 21 = 777.

LCD(37, 21) = 777

Step 2

Convert to Equivalent Fractions with Common Denominator 777

Multiply the numerator and denominator of 14/37 by 21, and multiply the numerator and denominator of 9/21 by 37 so both fractions share the common base 777.

14 × 21/37 × 21 = 294/777 and 9 × 37/21 × 37 = 333/777

Step 3

Add the Numerators

Now add the numerators (294 + 333 = 627) and keep the common denominator 777 unchanged.

294 + 333/777 = 627/777

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 627 and 777, which is 3. Divide both the numerator and denominator by 3.

627 ÷ 3/777 ÷ 3 = 209/259

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 259 produces a repeating decimal (approximately 0.80695, or 80.695%).

209 ÷ 259 = 0.80695 (80.695%)

Visual Representation

The diagram below illustrates 14/37 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/259`
Mixed Number Form	`209/259`
Decimal Form	`0.80695`
Percentage	`80.695%`

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Frequently Asked Questions

What is 14/37 plus 9/21 as a fraction?

14/37 + 9/21 in simplest fraction form is 209/259.

What is 14/37 plus 9/21 as a decimal?

14/37 + 9/21 converted to a decimal is 0.80695.

What is 14/37 plus 9/21 as a percentage?

14/37 + 9/21 expressed as a percentage is 80.695%.

Does 14/37 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.80695...) because the denominator contains prime factors other than 2 and 5.