What is 4/57 plus 6/21? (Answer: 142/399)

Exact Answer

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Problem: What is 4/57 plus 6/21?
Formula / Expression: 4/57 + 6/21
Final Answer: 142/399
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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 4/57 by 7, and multiply the numerator and denominator of 6/21 by 19 so both fractions share the common base 399.
Working: 4 × 7/57 × 7 = 28/399 and 6 × 19/21 × 19 = 114/399

Step 3: Add the Numerators
Now add the numerators (28 + 114 = 142) and keep the common denominator 399 unchanged.
Working: 28 + 114/399 = 142/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 142 and 399 is 1, confirming that 142/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 142/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 142 by denominator 399 produces a repeating decimal (approximately 0.35589, or 35.589%).
Working: 142 ÷ 399 = 0.35589 (35.589%)

Key Values:
- Simplified Fraction: 142/399
- Mixed Number Form: 142/399
- Decimal Value: 0.35589
- Percentage: 35.589%

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Solved with FractionsCalc:
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4/57 + 6/21 = 142/399

Simplified Fraction

142/399

Mixed Number

Proper (142/399)

Decimal Value

0.35589

Percentage

35.589%

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Step-by-Step Solution: 4/57 + 6/21

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 4/57 by 7, and multiply the numerator and denominator of 6/21 by 19 so both fractions share the common base 399.

4 × 7/57 × 7 = 28/399 and 6 × 19/21 × 19 = 114/399

Step 3

Add the Numerators

Now add the numerators (28 + 114 = 142) and keep the common denominator 399 unchanged.

28 + 114/399 = 142/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 142 and 399 is 1, confirming that 142/399 cannot be reduced further—it is already in its simplest irreducible form.

142/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 142 by denominator 399 produces a repeating decimal (approximately 0.35589, or 35.589%).

142 ÷ 399 = 0.35589 (35.589%)

Visual Representation

The diagram below illustrates 4/57 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`142/399`
Mixed Number Form	`142/399`
Decimal Form	`0.35589`
Percentage	`35.589%`

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Frequently Asked Questions

What is 4/57 plus 6/21 as a fraction?

4/57 + 6/21 in simplest fraction form is 142/399.

What is 4/57 plus 6/21 as a decimal?

4/57 + 6/21 converted to a decimal is 0.35589.

What is 4/57 plus 6/21 as a percentage?

4/57 + 6/21 expressed as a percentage is 35.589%.

Does 4/57 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.35589...) because the denominator contains prime factors other than 2 and 5.