What is 9/57 plus 4/21? (Answer: 139/399)

Exact Answer

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Problem: What is 9/57 plus 4/21?
Formula / Expression: 9/57 + 4/21
Final Answer: 139/399
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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 9/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.
Working: 9 × 7/57 × 7 = 63/399 and 4 × 19/21 × 19 = 76/399

Step 3: Add the Numerators
Now add the numerators (63 + 76 = 139) and keep the common denominator 399 unchanged.
Working: 63 + 76/399 = 139/399

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 399 is 1, confirming that 139/399 cannot be reduced further—it is already in its simplest irreducible form.
Working: 139/399

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 399 produces a repeating decimal (approximately 0.348371, or 34.8371%).
Working: 139 ÷ 399 = 0.348371 (34.8371%)

Key Values:
- Simplified Fraction: 139/399
- Mixed Number Form: 139/399
- Decimal Value: 0.348371
- Percentage: 34.8371%

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Solved with FractionsCalc:
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9/57 + 4/21 = 139/399

Simplified Fraction

139/399

Mixed Number

Proper (139/399)

Decimal Value

0.348371

Percentage

34.8371%

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Step-by-Step Solution: 9/57 + 4/21

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 9/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.

9 × 7/57 × 7 = 63/399 and 4 × 19/21 × 19 = 76/399

Step 3

Add the Numerators

Now add the numerators (63 + 76 = 139) and keep the common denominator 399 unchanged.

63 + 76/399 = 139/399

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 139 and 399 is 1, confirming that 139/399 cannot be reduced further—it is already in its simplest irreducible form.

139/399

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 399 produces a repeating decimal (approximately 0.348371, or 34.8371%).

139 ÷ 399 = 0.348371 (34.8371%)

Visual Representation

The diagram below illustrates 9/57 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/399`
Mixed Number Form	`139/399`
Decimal Form	`0.348371`
Percentage	`34.8371%`

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Frequently Asked Questions

What is 9/57 plus 4/21 as a fraction?

9/57 + 4/21 in simplest fraction form is 139/399.

What is 9/57 plus 4/21 as a decimal?

9/57 + 4/21 converted to a decimal is 0.348371.

What is 9/57 plus 4/21 as a percentage?

9/57 + 4/21 expressed as a percentage is 34.8371%.

Does 9/57 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.348371...) because the denominator contains prime factors other than 2 and 5.