What is 2/33 plus 8/21? (Answer: 34/77)

Exact Answer

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Problem: What is 2/33 plus 8/21?
Formula / Expression: 2/33 + 8/21
Final Answer: 34/77
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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 2/33 by 7, and multiply the numerator and denominator of 8/21 by 11 so both fractions share the common base 231.
Working: 2 × 7/33 × 7 = 14/231 and 8 × 11/21 × 11 = 88/231

Step 3: Add the Numerators
Now add the numerators (14 + 88 = 102) and keep the common denominator 231 unchanged.
Working: 14 + 88/231 = 102/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 102 ÷ 3/231 ÷ 3 = 34/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 77 produces a repeating decimal (approximately 0.441558, or 44.1558%).
Working: 34 ÷ 77 = 0.441558 (44.1558%)

Key Values:
- Simplified Fraction: 34/77
- Mixed Number Form: 34/77
- Decimal Value: 0.441558
- Percentage: 44.1558%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-8-21/
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2/33 + 8/21 = 34/77

Simplified Fraction

34/77

Mixed Number

Proper (34/77)

Decimal Value

0.441558

Percentage

44.1558%

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Step-by-Step Solution: 2/33 + 8/21

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 2/33 by 7, and multiply the numerator and denominator of 8/21 by 11 so both fractions share the common base 231.

2 × 7/33 × 7 = 14/231 and 8 × 11/21 × 11 = 88/231

Step 3

Add the Numerators

Now add the numerators (14 + 88 = 102) and keep the common denominator 231 unchanged.

14 + 88/231 = 102/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 231, which is 3. Divide both the numerator and denominator by 3.

102 ÷ 3/231 ÷ 3 = 34/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 77 produces a repeating decimal (approximately 0.441558, or 44.1558%).

34 ÷ 77 = 0.441558 (44.1558%)

Visual Representation

The diagram below illustrates 2/33 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/77`
Mixed Number Form	`34/77`
Decimal Form	`0.441558`
Percentage	`44.1558%`

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Frequently Asked Questions

What is 2/33 plus 8/21 as a fraction?

2/33 + 8/21 in simplest fraction form is 34/77.

What is 2/33 plus 8/21 as a decimal?

2/33 + 8/21 converted to a decimal is 0.441558.

What is 2/33 plus 8/21 as a percentage?

2/33 + 8/21 expressed as a percentage is 44.1558%.

Does 2/33 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.441558...) because the denominator contains prime factors other than 2 and 5.