What is 19/57 plus 9/21? (Answer: 16/21)

Exact Answer

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Problem: What is 19/57 plus 9/21?
Formula / Expression: 19/57 + 9/21
Final Answer: 16/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).
Working: LCD(57, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 19/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.
Working: 19 × 7/57 × 7 = 133/399 and 9 × 19/21 × 19 = 171/399

Step 3: Add the Numerators
Now add the numerators (133 + 171 = 304) and keep the common denominator 399 unchanged.
Working: 133 + 171/399 = 304/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 304 and 399, which is 19. Divide both the numerator and denominator by 19.
Working: 304 ÷ 19/399 ÷ 19 = 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-19-57-plus-9-21/
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19/57 + 9/21 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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Step-by-Step Solution: 19/57 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).

LCD(57, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 19/57 by 7, and multiply the numerator and denominator of 9/21 by 19 so both fractions share the common base 399.

19 × 7/57 × 7 = 133/399 and 9 × 19/21 × 19 = 171/399

Step 3

Add the Numerators

Now add the numerators (133 + 171 = 304) and keep the common denominator 399 unchanged.

133 + 171/399 = 304/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 304 and 399, which is 19. Divide both the numerator and denominator by 19.

304 ÷ 19/399 ÷ 19 = 16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 19/57 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

What is 19/57 plus 9/21 as a fraction?

19/57 + 9/21 in simplest fraction form is 16/21.

What is 19/57 plus 9/21 as a decimal?

19/57 + 9/21 converted to a decimal is 0.761905.

What is 19/57 plus 9/21 as a percentage?

19/57 + 9/21 expressed as a percentage is 76.1905%.

Does 19/57 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.