What is 19/54 plus 8/21? (Answer: 277/378)

Exact Answer

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Problem: What is 19/54 plus 8/21?
Formula / Expression: 19/54 + 8/21
Final Answer: 277/378
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).
Working: LCD(54, 21) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 19/54 by 7, and multiply the numerator and denominator of 8/21 by 18 so both fractions share the common base 378.
Working: 19 × 7/54 × 7 = 133/378 and 8 × 18/21 × 18 = 144/378

Step 3: Add the Numerators
Now add the numerators (133 + 144 = 277) and keep the common denominator 378 unchanged.
Working: 133 + 144/378 = 277/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 277 and 378 is 1, confirming that 277/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 277/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 277 by denominator 378 produces a repeating decimal (approximately 0.732804, or 73.2804%).
Working: 277 ÷ 378 = 0.732804 (73.2804%)

Key Values:
- Simplified Fraction: 277/378
- Mixed Number Form: 277/378
- Decimal Value: 0.732804
- Percentage: 73.2804%

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Solved with FractionsCalc:
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19/54 + 8/21 = 277/378

Simplified Fraction

277/378

Mixed Number

Proper (277/378)

Decimal Value

0.732804

Percentage

73.2804%

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Step-by-Step Solution: 19/54 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).

LCD(54, 21) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 19/54 by 7, and multiply the numerator and denominator of 8/21 by 18 so both fractions share the common base 378.

19 × 7/54 × 7 = 133/378 and 8 × 18/21 × 18 = 144/378

Step 3

Add the Numerators

Now add the numerators (133 + 144 = 277) and keep the common denominator 378 unchanged.

133 + 144/378 = 277/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 277 and 378 is 1, confirming that 277/378 cannot be reduced further—it is already in its simplest irreducible form.

277/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 277 by denominator 378 produces a repeating decimal (approximately 0.732804, or 73.2804%).

277 ÷ 378 = 0.732804 (73.2804%)

Visual Representation

The diagram below illustrates 19/54 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`277/378`
Mixed Number Form	`277/378`
Decimal Form	`0.732804`
Percentage	`73.2804%`

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Frequently Asked Questions

What is 19/54 plus 8/21 as a fraction?

19/54 + 8/21 in simplest fraction form is 277/378.

What is 19/54 plus 8/21 as a decimal?

19/54 + 8/21 converted to a decimal is 0.732804.

What is 19/54 plus 8/21 as a percentage?

19/54 + 8/21 expressed as a percentage is 73.2804%.

Does 19/54 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.732804...) because the denominator contains prime factors other than 2 and 5.