What is 18/57 plus 8/21? (Answer: 278/399)

Exact Answer

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Problem: What is 18/57 plus 8/21?
Formula / Expression: 18/57 + 8/21
Final Answer: 278/399
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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 18/57 by 7, and multiply the numerator and denominator of 8/21 by 19 so both fractions share the common base 399.
Working: 18 × 7/57 × 7 = 126/399 and 8 × 19/21 × 19 = 152/399

Step 3: Add the Numerators
Now add the numerators (126 + 152 = 278) and keep the common denominator 399 unchanged.
Working: 126 + 152/399 = 278/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 278 and 399 is 1, confirming that 278/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 278/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 278 by denominator 399 produces a repeating decimal (approximately 0.696742, or 69.6742%).
Working: 278 ÷ 399 = 0.696742 (69.6742%)

Key Values:
- Simplified Fraction: 278/399
- Mixed Number Form: 278/399
- Decimal Value: 0.696742
- Percentage: 69.6742%

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Solved with FractionsCalc:
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18/57 + 8/21 = 278/399

Simplified Fraction

278/399

Mixed Number

Proper (278/399)

Decimal Value

0.696742

Percentage

69.6742%

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Step-by-Step Solution: 18/57 + 8/21

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 18/57 by 7, and multiply the numerator and denominator of 8/21 by 19 so both fractions share the common base 399.

18 × 7/57 × 7 = 126/399 and 8 × 19/21 × 19 = 152/399

Step 3

Add the Numerators

Now add the numerators (126 + 152 = 278) and keep the common denominator 399 unchanged.

126 + 152/399 = 278/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 278 and 399 is 1, confirming that 278/399 cannot be reduced further—it is already in its simplest irreducible form.

278/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 278 by denominator 399 produces a repeating decimal (approximately 0.696742, or 69.6742%).

278 ÷ 399 = 0.696742 (69.6742%)

Visual Representation

The diagram below illustrates 18/57 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`278/399`
Mixed Number Form	`278/399`
Decimal Form	`0.696742`
Percentage	`69.6742%`

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Frequently Asked Questions

What is 18/57 plus 8/21 as a fraction?

18/57 + 8/21 in simplest fraction form is 278/399.

What is 18/57 plus 8/21 as a decimal?

18/57 + 8/21 converted to a decimal is 0.696742.

What is 18/57 plus 8/21 as a percentage?

18/57 + 8/21 expressed as a percentage is 69.6742%.

Does 18/57 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.696742...) because the denominator contains prime factors other than 2 and 5.