What is 3/57 plus 5/21? (Answer: 116/399)

Exact Answer

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Problem: What is 3/57 plus 5/21?
Formula / Expression: 3/57 + 5/21
Final Answer: 116/399
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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 3/57 by 7, and multiply the numerator and denominator of 5/21 by 19 so both fractions share the common base 399.
Working: 3 × 7/57 × 7 = 21/399 and 5 × 19/21 × 19 = 95/399

Step 3: Add the Numerators
Now add the numerators (21 + 95 = 116) and keep the common denominator 399 unchanged.
Working: 21 + 95/399 = 116/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 116 and 399 is 1, confirming that 116/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 116/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 399 produces a repeating decimal (approximately 0.290727, or 29.0727%).
Working: 116 ÷ 399 = 0.290727 (29.0727%)

Key Values:
- Simplified Fraction: 116/399
- Mixed Number Form: 116/399
- Decimal Value: 0.290727
- Percentage: 29.0727%

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Solved with FractionsCalc:
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3/57 + 5/21 = 116/399

Simplified Fraction

116/399

Mixed Number

Proper (116/399)

Decimal Value

0.290727

Percentage

29.0727%

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Step-by-Step Solution: 3/57 + 5/21

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 3/57 by 7, and multiply the numerator and denominator of 5/21 by 19 so both fractions share the common base 399.

3 × 7/57 × 7 = 21/399 and 5 × 19/21 × 19 = 95/399

Step 3

Add the Numerators

Now add the numerators (21 + 95 = 116) and keep the common denominator 399 unchanged.

21 + 95/399 = 116/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 116 and 399 is 1, confirming that 116/399 cannot be reduced further—it is already in its simplest irreducible form.

116/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 399 produces a repeating decimal (approximately 0.290727, or 29.0727%).

116 ÷ 399 = 0.290727 (29.0727%)

Visual Representation

The diagram below illustrates 3/57 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/399`
Mixed Number Form	`116/399`
Decimal Form	`0.290727`
Percentage	`29.0727%`

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Frequently Asked Questions

What is 3/57 plus 5/21 as a fraction?

3/57 + 5/21 in simplest fraction form is 116/399.

What is 3/57 plus 5/21 as a decimal?

3/57 + 5/21 converted to a decimal is 0.290727.

What is 3/57 plus 5/21 as a percentage?

3/57 + 5/21 expressed as a percentage is 29.0727%.

Does 3/57 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.290727...) because the denominator contains prime factors other than 2 and 5.