What is 6/33 plus 4/21? (Answer: 86/231)

Exact Answer

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Problem: What is 6/33 plus 4/21?
Formula / Expression: 6/33 + 4/21
Final Answer: 86/231
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 6/33 by 7, and multiply the numerator and denominator of 4/21 by 11 so both fractions share the common base 231.
Working: 6 × 7/33 × 7 = 42/231 and 4 × 11/21 × 11 = 44/231

Step 3: Add the Numerators
Now add the numerators (42 + 44 = 86) and keep the common denominator 231 unchanged.
Working: 42 + 44/231 = 86/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 86 and 231 is 1, confirming that 86/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 86/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 231 produces a repeating decimal (approximately 0.372294, or 37.2294%).
Working: 86 ÷ 231 = 0.372294 (37.2294%)

Key Values:
- Simplified Fraction: 86/231
- Mixed Number Form: 86/231
- Decimal Value: 0.372294
- Percentage: 37.2294%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-33-plus-4-21/
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6/33 + 4/21 = 86/231

Simplified Fraction

86/231

Mixed Number

Proper (86/231)

Decimal Value

0.372294

Percentage

37.2294%

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Step-by-Step Solution: 6/33 + 4/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 6/33 by 7, and multiply the numerator and denominator of 4/21 by 11 so both fractions share the common base 231.

6 × 7/33 × 7 = 42/231 and 4 × 11/21 × 11 = 44/231

Step 3

Add the Numerators

Now add the numerators (42 + 44 = 86) and keep the common denominator 231 unchanged.

42 + 44/231 = 86/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 86 and 231 is 1, confirming that 86/231 cannot be reduced further—it is already in its simplest irreducible form.

86/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 231 produces a repeating decimal (approximately 0.372294, or 37.2294%).

86 ÷ 231 = 0.372294 (37.2294%)

Visual Representation

The diagram below illustrates 6/33 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/231`
Mixed Number Form	`86/231`
Decimal Form	`0.372294`
Percentage	`37.2294%`

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Frequently Asked Questions

What is 6/33 plus 4/21 as a fraction?

6/33 + 4/21 in simplest fraction form is 86/231.

What is 6/33 plus 4/21 as a decimal?

6/33 + 4/21 converted to a decimal is 0.372294.

What is 6/33 plus 4/21 as a percentage?

6/33 + 4/21 expressed as a percentage is 37.2294%.

Does 6/33 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.372294...) because the denominator contains prime factors other than 2 and 5.