What is 19/38 plus 11/21? (Answer: 43/42)

Exact Answer

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Problem: What is 19/38 plus 11/21?
Formula / Expression: 19/38 + 11/21
Final Answer: 1 1/42 (43/42)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 21 = 798.
Working: LCD(38, 21) = 798

Step 2: Convert to Equivalent Fractions with Common Denominator 798
Multiply the numerator and denominator of 19/38 by 21, and multiply the numerator and denominator of 11/21 by 38 so both fractions share the common base 798.
Working: 19 × 21/38 × 21 = 399/798 and 11 × 38/21 × 38 = 418/798

Step 3: Add the Numerators
Now add the numerators (399 + 418 = 817) and keep the common denominator 798 unchanged.
Working: 399 + 418/798 = 817/798

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 817 and 798, which is 19. Divide both the numerator and denominator by 19.
Working: 817 ÷ 19/798 ÷ 19 = 43/42

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.
Working: 43/42 = 1 1/42

Step 6: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).
Working: 43 ÷ 42 = 1.02381 (102.381%)

Key Values:
- Simplified Fraction: 43/42
- Mixed Number Form: 1 1/42
- Decimal Value: 1.02381
- Percentage: 102.381%

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Solved with FractionsCalc:
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19/38 + 11/21 = 43/42

Simplified Fraction

43/42

Mixed Number

1 1/42

Decimal Value

1.02381

Percentage

102.381%

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Step-by-Step Solution: 19/38 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 21 = 798.

LCD(38, 21) = 798

Step 2

Convert to Equivalent Fractions with Common Denominator 798

Multiply the numerator and denominator of 19/38 by 21, and multiply the numerator and denominator of 11/21 by 38 so both fractions share the common base 798.

19 × 21/38 × 21 = 399/798 and 11 × 38/21 × 38 = 418/798

Step 3

Add the Numerators

Now add the numerators (399 + 418 = 817) and keep the common denominator 798 unchanged.

399 + 418/798 = 817/798

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 817 and 798, which is 19. Divide both the numerator and denominator by 19.

817 ÷ 19/798 ÷ 19 = 43/42

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.

43/42 = 11/42

Step 6

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).

43 ÷ 42 = 1.02381 (102.381%)

Visual Representation

The diagram below illustrates 19/38 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/42`
Mixed Number Form	`1 1/42`
Decimal Form	`1.02381`
Percentage	`102.381%`

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Frequently Asked Questions

What is 19/38 plus 11/21 as a fraction?

19/38 + 11/21 in simplest fraction form is 43/42 (or 1 1/42 as a mixed number).

What is 19/38 plus 11/21 as a decimal?

19/38 + 11/21 converted to a decimal is 1.02381.

What is 19/38 plus 11/21 as a percentage?

19/38 + 11/21 expressed as a percentage is 102.381%.

How do you write 19/38 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 43/42 can be written as the mixed number 1 1/42.

Does 19/38 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.02381...) because the denominator contains prime factors other than 2 and 5.