What is 3/57 plus 6/21? (Answer: 45/133)

Exact Answer

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Problem: What is 3/57 plus 6/21?
Formula / Expression: 3/57 + 6/21
Final Answer: 45/133
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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 6/21 by 19 so both fractions share the common base 399.
Working: 3 × 7/57 × 7 = 21/399 and 6 × 19/21 × 19 = 114/399

Step 3: Add the Numerators
Now add the numerators (21 + 114 = 135) and keep the common denominator 399 unchanged.
Working: 21 + 114/399 = 135/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 135 ÷ 3/399 ÷ 3 = 45/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 133 produces a repeating decimal (approximately 0.338346, or 33.8346%).
Working: 45 ÷ 133 = 0.338346 (33.8346%)

Key Values:
- Simplified Fraction: 45/133
- Mixed Number Form: 45/133
- Decimal Value: 0.338346
- Percentage: 33.8346%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-57-plus-6-21/
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3/57 + 6/21 = 45/133

Simplified Fraction

45/133

Mixed Number

Proper (45/133)

Decimal Value

0.338346

Percentage

33.8346%

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Step-by-Step Solution: 3/57 + 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 3/57 by 7, and multiply the numerator and denominator of 6/21 by 19 so both fractions share the common base 399.

3 × 7/57 × 7 = 21/399 and 6 × 19/21 × 19 = 114/399

Step 3

Add the Numerators

Now add the numerators (21 + 114 = 135) and keep the common denominator 399 unchanged.

21 + 114/399 = 135/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 399, which is 3. Divide both the numerator and denominator by 3.

135 ÷ 3/399 ÷ 3 = 45/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 133 produces a repeating decimal (approximately 0.338346, or 33.8346%).

45 ÷ 133 = 0.338346 (33.8346%)

Visual Representation

The diagram below illustrates 3/57 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/133`
Mixed Number Form	`45/133`
Decimal Form	`0.338346`
Percentage	`33.8346%`

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Frequently Asked Questions

What is 3/57 plus 6/21 as a fraction?

3/57 + 6/21 in simplest fraction form is 45/133.

What is 3/57 plus 6/21 as a decimal?

3/57 + 6/21 converted to a decimal is 0.338346.

What is 3/57 plus 6/21 as a percentage?

3/57 + 6/21 expressed as a percentage is 33.8346%.

Does 3/57 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.338346...) because the denominator contains prime factors other than 2 and 5.