What is 3/19 plus 15/21? (Answer: 116/133)

Exact Answer

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Problem: What is 3/19 plus 15/21?
Formula / Expression: 3/19 + 15/21
Final Answer: 116/133
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 3/19 by 21, and multiply the numerator and denominator of 15/21 by 19 so both fractions share the common base 399.
Working: 3 × 21/19 × 21 = 63/399 and 15 × 19/21 × 19 = 285/399

Step 3: Add the Numerators
Now add the numerators (63 + 285 = 348) and keep the common denominator 399 unchanged.
Working: 63 + 285/399 = 348/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 348 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 348 ÷ 3/399 ÷ 3 = 116/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 133 produces a repeating decimal (approximately 0.87218, or 87.218%).
Working: 116 ÷ 133 = 0.87218 (87.218%)

Key Values:
- Simplified Fraction: 116/133
- Mixed Number Form: 116/133
- Decimal Value: 0.87218
- Percentage: 87.218%

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Solved with FractionsCalc:
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3/19 + 15/21 = 116/133

Simplified Fraction

116/133

Mixed Number

Proper (116/133)

Decimal Value

0.87218

Percentage

87.218%

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Step-by-Step Solution: 3/19 + 15/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(19, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 3/19 by 21, and multiply the numerator and denominator of 15/21 by 19 so both fractions share the common base 399.

3 × 21/19 × 21 = 63/399 and 15 × 19/21 × 19 = 285/399

Step 3

Add the Numerators

Now add the numerators (63 + 285 = 348) and keep the common denominator 399 unchanged.

63 + 285/399 = 348/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 348 and 399, which is 3. Divide both the numerator and denominator by 3.

348 ÷ 3/399 ÷ 3 = 116/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 133 produces a repeating decimal (approximately 0.87218, or 87.218%).

116 ÷ 133 = 0.87218 (87.218%)

Visual Representation

The diagram below illustrates 3/19 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/133`
Mixed Number Form	`116/133`
Decimal Form	`0.87218`
Percentage	`87.218%`

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Frequently Asked Questions

What is 3/19 plus 15/21 as a fraction?

3/19 + 15/21 in simplest fraction form is 116/133.

What is 3/19 plus 15/21 as a decimal?

3/19 + 15/21 converted to a decimal is 0.87218.

What is 3/19 plus 15/21 as a percentage?

3/19 + 15/21 expressed as a percentage is 87.218%.

Does 3/19 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.87218...) because the denominator contains prime factors other than 2 and 5.