What is 10/19 plus 12/21? (Answer: 146/133)

Exact Answer

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Problem: What is 10/19 plus 12/21?
Formula / Expression: 10/19 + 12/21
Final Answer: 1 13/133 (146/133)
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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 10/19 by 21, and multiply the numerator and denominator of 12/21 by 19 so both fractions share the common base 399.
Working: 10 × 21/19 × 21 = 210/399 and 12 × 19/21 × 19 = 228/399

Step 3: Add the Numerators
Now add the numerators (210 + 228 = 438) and keep the common denominator 399 unchanged.
Working: 210 + 228/399 = 438/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 438 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 438 ÷ 3/399 ÷ 3 = 146/133

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (146) is greater than the denominator (133), divide 146 by 133: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/133.
Working: 146/133 = 1 13/133

Step 6: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 133 produces a repeating decimal (approximately 1.097744, or 109.7744%).
Working: 146 ÷ 133 = 1.097744 (109.7744%)

Key Values:
- Simplified Fraction: 146/133
- Mixed Number Form: 1 13/133
- Decimal Value: 1.097744
- Percentage: 109.7744%

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Solved with FractionsCalc:
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10/19 + 12/21 = 146/133

Simplified Fraction

146/133

Mixed Number

1 13/133

Decimal Value

1.097744

Percentage

109.7744%

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Step-by-Step Solution: 10/19 + 12/21

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 10/19 by 21, and multiply the numerator and denominator of 12/21 by 19 so both fractions share the common base 399.

10 × 21/19 × 21 = 210/399 and 12 × 19/21 × 19 = 228/399

Step 3

Add the Numerators

Now add the numerators (210 + 228 = 438) and keep the common denominator 399 unchanged.

210 + 228/399 = 438/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 438 and 399, which is 3. Divide both the numerator and denominator by 3.

438 ÷ 3/399 ÷ 3 = 146/133

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (146) is greater than the denominator (133), divide 146 by 133: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/133.

146/133 = 113/133

Step 6

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 133 produces a repeating decimal (approximately 1.097744, or 109.7744%).

146 ÷ 133 = 1.097744 (109.7744%)

Visual Representation

The diagram below illustrates 10/19 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/133`
Mixed Number Form	`1 13/133`
Decimal Form	`1.097744`
Percentage	`109.7744%`

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Frequently Asked Questions

What is 10/19 plus 12/21 as a fraction?

10/19 + 12/21 in simplest fraction form is 146/133 (or 1 13/133 as a mixed number).

What is 10/19 plus 12/21 as a decimal?

10/19 + 12/21 converted to a decimal is 1.097744.

What is 10/19 plus 12/21 as a percentage?

10/19 + 12/21 expressed as a percentage is 109.7744%.

How do you write 10/19 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 146/133 can be written as the mixed number 1 13/133.

Does 10/19 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.097744...) because the denominator contains prime factors other than 2 and 5.