What is 18/37 plus 12/21? (Answer: 274/259)

Exact Answer

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Problem: What is 18/37 plus 12/21?
Formula / Expression: 18/37 + 12/21
Final Answer: 1 15/259 (274/259)
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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 18/37 by 21, and multiply the numerator and denominator of 12/21 by 37 so both fractions share the common base 777.
Working: 18 × 21/37 × 21 = 378/777 and 12 × 37/21 × 37 = 444/777

Step 3: Add the Numerators
Now add the numerators (378 + 444 = 822) and keep the common denominator 777 unchanged.
Working: 378 + 444/777 = 822/777

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 822 and 777, which is 3. Divide both the numerator and denominator by 3.
Working: 822 ÷ 3/777 ÷ 3 = 274/259

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (274) is greater than the denominator (259), divide 274 by 259: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/259.
Working: 274/259 = 1 15/259

Step 6: Decimal & Percentage Representation
Dividing the numerator 274 by denominator 259 produces a repeating decimal (approximately 1.057915, or 105.7915%).
Working: 274 ÷ 259 = 1.057915 (105.7915%)

Key Values:
- Simplified Fraction: 274/259
- Mixed Number Form: 1 15/259
- Decimal Value: 1.057915
- Percentage: 105.7915%

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Solved with FractionsCalc:
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18/37 + 12/21 = 274/259

Simplified Fraction

274/259

Mixed Number

1 15/259

Decimal Value

1.057915

Percentage

105.7915%

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Step-by-Step Solution: 18/37 + 12/21

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 18/37 by 21, and multiply the numerator and denominator of 12/21 by 37 so both fractions share the common base 777.

18 × 21/37 × 21 = 378/777 and 12 × 37/21 × 37 = 444/777

Step 3

Add the Numerators

Now add the numerators (378 + 444 = 822) and keep the common denominator 777 unchanged.

378 + 444/777 = 822/777

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 822 and 777, which is 3. Divide both the numerator and denominator by 3.

822 ÷ 3/777 ÷ 3 = 274/259

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (274) is greater than the denominator (259), divide 274 by 259: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/259.

274/259 = 115/259

Step 6

Decimal & Percentage Representation

Dividing the numerator 274 by denominator 259 produces a repeating decimal (approximately 1.057915, or 105.7915%).

274 ÷ 259 = 1.057915 (105.7915%)

Visual Representation

The diagram below illustrates 18/37 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`274/259`
Mixed Number Form	`1 15/259`
Decimal Form	`1.057915`
Percentage	`105.7915%`

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Frequently Asked Questions

What is 18/37 plus 12/21 as a fraction?

18/37 + 12/21 in simplest fraction form is 274/259 (or 1 15/259 as a mixed number).

What is 18/37 plus 12/21 as a decimal?

18/37 + 12/21 converted to a decimal is 1.057915.

What is 18/37 plus 12/21 as a percentage?

18/37 + 12/21 expressed as a percentage is 105.7915%.

How do you write 18/37 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 274/259 can be written as the mixed number 1 15/259.

Does 18/37 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.057915...) because the denominator contains prime factors other than 2 and 5.