What is 6/57 plus 3/21? (Answer: 33/133)

Exact Answer

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Problem: What is 6/57 plus 3/21?
Formula / Expression: 6/57 + 3/21
Final Answer: 33/133
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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 6/57 by 7, and multiply the numerator and denominator of 3/21 by 19 so both fractions share the common base 399.
Working: 6 × 7/57 × 7 = 42/399 and 3 × 19/21 × 19 = 57/399

Step 3: Add the Numerators
Now add the numerators (42 + 57 = 99) and keep the common denominator 399 unchanged.
Working: 42 + 57/399 = 99/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 99 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 99 ÷ 3/399 ÷ 3 = 33/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 133 produces a repeating decimal (approximately 0.24812, or 24.812%).
Working: 33 ÷ 133 = 0.24812 (24.812%)

Key Values:
- Simplified Fraction: 33/133
- Mixed Number Form: 33/133
- Decimal Value: 0.24812
- Percentage: 24.812%

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Solved with FractionsCalc:
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6/57 + 3/21 = 33/133

Simplified Fraction

33/133

Mixed Number

Proper (33/133)

Decimal Value

0.24812

Percentage

24.812%

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Step-by-Step Solution: 6/57 + 3/21

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

6 × 7/57 × 7 = 42/399 and 3 × 19/21 × 19 = 57/399

Step 3

Add the Numerators

Now add the numerators (42 + 57 = 99) and keep the common denominator 399 unchanged.

42 + 57/399 = 99/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 99 and 399, which is 3. Divide both the numerator and denominator by 3.

99 ÷ 3/399 ÷ 3 = 33/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 133 produces a repeating decimal (approximately 0.24812, or 24.812%).

33 ÷ 133 = 0.24812 (24.812%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/133`
Mixed Number Form	`33/133`
Decimal Form	`0.24812`
Percentage	`24.812%`

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Frequently Asked Questions

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

6/57 + 3/21 in simplest fraction form is 33/133.

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

6/57 + 3/21 converted to a decimal is 0.24812.

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

6/57 + 3/21 expressed as a percentage is 24.812%.

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

It results in a repeating decimal (approximately 0.24812...) because the denominator contains prime factors other than 2 and 5.