What is 6/21 plus 10/33? (Answer: 136/231)

Exact Answer

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Problem: What is 6/21 plus 10/33?
Formula / Expression: 6/21 + 10/33
Final Answer: 136/231
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).
Working: LCD(21, 33) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 6/21 by 11, and multiply the numerator and denominator of 10/33 by 7 so both fractions share the common base 231.
Working: 6 × 11/21 × 11 = 66/231 and 10 × 7/33 × 7 = 70/231

Step 3: Add the Numerators
Now add the numerators (66 + 70 = 136) and keep the common denominator 231 unchanged.
Working: 66 + 70/231 = 136/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 136 and 231 is 1, confirming that 136/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 136/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 136 by denominator 231 produces a repeating decimal (approximately 0.588745, or 58.8745%).
Working: 136 ÷ 231 = 0.588745 (58.8745%)

Key Values:
- Simplified Fraction: 136/231
- Mixed Number Form: 136/231
- Decimal Value: 0.588745
- Percentage: 58.8745%

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Solved with FractionsCalc:
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6/21 + 10/33 = 136/231

Simplified Fraction

136/231

Mixed Number

Proper (136/231)

Decimal Value

0.588745

Percentage

58.8745%

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Step-by-Step Solution: 6/21 + 10/33

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).

LCD(21, 33) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 6/21 by 11, and multiply the numerator and denominator of 10/33 by 7 so both fractions share the common base 231.

6 × 11/21 × 11 = 66/231 and 10 × 7/33 × 7 = 70/231

Step 3

Add the Numerators

Now add the numerators (66 + 70 = 136) and keep the common denominator 231 unchanged.

66 + 70/231 = 136/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 136 and 231 is 1, confirming that 136/231 cannot be reduced further—it is already in its simplest irreducible form.

136/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 136 by denominator 231 produces a repeating decimal (approximately 0.588745, or 58.8745%).

136 ÷ 231 = 0.588745 (58.8745%)

Visual Representation

The diagram below illustrates 6/21 plus 10/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`136/231`
Mixed Number Form	`136/231`
Decimal Form	`0.588745`
Percentage	`58.8745%`

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Frequently Asked Questions

What is 6/21 plus 10/33 as a fraction?

6/21 + 10/33 in simplest fraction form is 136/231.

What is 6/21 plus 10/33 as a decimal?

6/21 + 10/33 converted to a decimal is 0.588745.

What is 6/21 plus 10/33 as a percentage?

6/21 + 10/33 expressed as a percentage is 58.8745%.

Does 6/21 plus 10/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.588745...) because the denominator contains prime factors other than 2 and 5.