What is 12/21 plus 11/19? (Answer: 153/133)

Exact Answer

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Problem: What is 12/21 plus 11/19?
Formula / Expression: 12/21 + 11/19
Final Answer: 1 20/133 (153/133)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 19 = 399.
Working: LCD(21, 19) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 12/21 by 19, and multiply the numerator and denominator of 11/19 by 21 so both fractions share the common base 399.
Working: 12 × 19/21 × 19 = 228/399 and 11 × 21/19 × 21 = 231/399

Step 3: Add the Numerators
Now add the numerators (228 + 231 = 459) and keep the common denominator 399 unchanged.
Working: 228 + 231/399 = 459/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 459 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 459 ÷ 3/399 ÷ 3 = 153/133

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (153) is greater than the denominator (133), divide 153 by 133: it goes in 1 whole time(s) with a remainder of 20, giving the mixed number 1 20/133.
Working: 153/133 = 1 20/133

Step 6: Decimal & Percentage Representation
Dividing the numerator 153 by denominator 133 produces a repeating decimal (approximately 1.150376, or 115.0376%).
Working: 153 ÷ 133 = 1.150376 (115.0376%)

Key Values:
- Simplified Fraction: 153/133
- Mixed Number Form: 1 20/133
- Decimal Value: 1.150376
- Percentage: 115.0376%

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Solved with FractionsCalc:
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12/21 + 11/19 = 153/133

Simplified Fraction

153/133

Mixed Number

1 20/133

Decimal Value

1.150376

Percentage

115.0376%

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Step-by-Step Solution: 12/21 + 11/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 19 = 399.

LCD(21, 19) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 12/21 by 19, and multiply the numerator and denominator of 11/19 by 21 so both fractions share the common base 399.

12 × 19/21 × 19 = 228/399 and 11 × 21/19 × 21 = 231/399

Step 3

Add the Numerators

Now add the numerators (228 + 231 = 459) and keep the common denominator 399 unchanged.

228 + 231/399 = 459/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 459 and 399, which is 3. Divide both the numerator and denominator by 3.

459 ÷ 3/399 ÷ 3 = 153/133

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (153) is greater than the denominator (133), divide 153 by 133: it goes in 1 whole time(s) with a remainder of 20, giving the mixed number 1 20/133.

153/133 = 120/133

Step 6

Decimal & Percentage Representation

Dividing the numerator 153 by denominator 133 produces a repeating decimal (approximately 1.150376, or 115.0376%).

153 ÷ 133 = 1.150376 (115.0376%)

Visual Representation

The diagram below illustrates 12/21 plus 11/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`153/133`
Mixed Number Form	`1 20/133`
Decimal Form	`1.150376`
Percentage	`115.0376%`

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Frequently Asked Questions

What is 12/21 plus 11/19 as a fraction?

12/21 + 11/19 in simplest fraction form is 153/133 (or 1 20/133 as a mixed number).

What is 12/21 plus 11/19 as a decimal?

12/21 + 11/19 converted to a decimal is 1.150376.

What is 12/21 plus 11/19 as a percentage?

12/21 + 11/19 expressed as a percentage is 115.0376%.

How do you write 12/21 plus 11/19 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 153/133 can be written as the mixed number 1 20/133.

Does 12/21 plus 11/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.150376...) because the denominator contains prime factors other than 2 and 5.